Trapping and Manipulation of Laser-Cooled …...Laser cooling and trapping exploits the mechanical...

Trapping and Manipulationof Laser-Cooled Metastable Argon Atoms

at a Surface

Dissertation

zur Erlangung des akademischen Gradesdes Doktors der Naturwissenschaften (Dr. rer. nat.)

an der Universität KonstanzMathematisch-Naturwissenschaftliche Sektion

Fachbereich Physik

vorgelegt von

Dominik Schneble

Tag der mündlichen Prüfung: 20. Februar 2002

Referenten: Prof. Dr. T. PfauPriv.-Doz. Dr. C. BechingerProf. Dr. G. Ganteför

Abstract

This thesis discusses experiments on the all-optical trapping and manipulation of laser-cooled metastable argon atoms at a surface.A magneto-optical surface trap (MOST) has been realized and studied. This novelhybrid trap combines a magneto-optical trap at a metallic surface with an opticalevanescent-wave atom mirror. It allows laser-cooling and trapping of atoms in con-tact with an evanescent light field that separates the atomic cloud from the surface bya fraction of an optical wavelength.Based on this work, the continuous loading of a planar matter waveguide has beendemonstrated. Loading into the waveguide, which was formed by the optical potentialof a red-detuned standing light wave above the surface, was achieved via evanescent-field optical pumping from the MOST in sub-�m distance from the surface.In subsequent experiments, several light-induced atom-optical elements have beendemonstrated in the planar waveguide geometry, including a continuous atom source,a switchable channel guide, an atom detector and an optical surface lattice. The source,the channel and the detector have been combined to form the first, albeit simple, atom-optical integrated circuit.

Contents

1 Introduction 11.1 General Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 This Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Basic Issues 92.1 Theoretical and Experimental Concepts . . . . . . . . . . . . . . . . . . . 9

2.1.1 Light Forces in the Dressed-Atom Picture . . . . . . . . . . . . . . 92.1.2 Laser Cooling and Trapping . . . . . . . . . . . . . . . . . . . . . 152.1.3 Reflection of Atoms from an Evanescent Wave . . . . . . . . . . . 232.1.4 Generating Evanescent Waves with Surface Plasmons . . . . . . . 26

2.2 Experimental Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.2.1 Argon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.2.2 Beam Machine and Laser System . . . . . . . . . . . . . . . . . . 322.2.3 The Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3 Surface-Assisted Detection of Ar� 393.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.2 Experimental Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.3 Characterization of the Detector . . . . . . . . . . . . . . . . . . . . . . . 43

3.3.1 Focusing, Length Calibration and Spatial Resolution . . . . . . . 433.3.2 Detection Efficiencies for the 1s5 and 1s3 States . . . . . . . . . . 453.3.3 Sensitivity to Magnetic Fields . . . . . . . . . . . . . . . . . . . . 48

3.4 Application: 3D Time-of-Flight Measurements . . . . . . . . . . . . . . . 493.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4 Magneto-Optical Surface Trap 534.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.2 Configuration of the MOST . . . . . . . . . . . . . . . . . . . . . . . . . 544.3 Simple Model for Properties of the MOST . . . . . . . . . . . . . . . . . 554.4 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.4.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . 61

i

ii CONTENTS

4.4.2 Properties of the Atom Cloud far from the Surface . . . . . . . . . 624.4.3 Behavior of the Trap for Varying Magnetic-Field Zero Position . . 664.4.4 Evanescent-Wave Bichromatic Atom Mirror . . . . . . . . . . . . 684.4.5 Combined MOT–Atom Mirror . . . . . . . . . . . . . . . . . . . . 73

4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5 Continuous Loading and Manipulation of Atoms in a Surface Waveguide 775.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775.2 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.2.2 The Waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . 805.2.3 Continuous Loading . . . . . . . . . . . . . . . . . . . . . . . . . 825.2.4 Surface-Sensitive Detection. . . . . . . . . . . . . . . . . . . . . . 84

5.3 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.3.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . 855.3.2 Continuous Loading . . . . . . . . . . . . . . . . . . . . . . . . . 855.3.3 Integrated Atom Source and Switchable Channel Guide . . . . . 925.3.4 Integrated Atom Detector and Simple Integrated Circuit . . . . . 945.3.5 Optical Surface Lattice . . . . . . . . . . . . . . . . . . . . . . . . 95

5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

A Dressed Atom in a Bichromatic Light Field 101

Bibliography 103

Zusammenfassung 119

Danksagung 121

List of Figures

1.1 Trapping and manipulation of metastable argon at a surface . . . . . . . 5

2.1 Dressed atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2 Model of the 1D MOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.3 3D 6-beam MOT configuration . . . . . . . . . . . . . . . . . . . . . . . 182.4 Sisyphus cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.5 Evanescent-wave optical atom mirror . . . . . . . . . . . . . . . . . . . . 242.6 Total potential of an evanescent-wave optical atom mirror . . . . . . . . 262.7 Surface-plasmon evanescent-wave mirror . . . . . . . . . . . . . . . . . 272.8 Level scheme of argon . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.9 Clebsch-Gordan coefficients . . . . . . . . . . . . . . . . . . . . . . . . . 322.10 Schematic of the beam machine. . . . . . . . . . . . . . . . . . . . . . . 332.11 View into the beam machine lab. . . . . . . . . . . . . . . . . . . . . . . 342.12 The laser system for experiments with metastable argon. . . . . . . . . . 352.13 The surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.14 Characterization of the surface-plasmon resonance . . . . . . . . . . . . 372.15 Characterization of the straylight distribution above the surface . . . . . 38

3.1 The surface atom detector . . . . . . . . . . . . . . . . . . . . . . . . . . 403.2 Surface deexcitation mechanisms . . . . . . . . . . . . . . . . . . . . . . 413.3 Creating a test object for the atom detector . . . . . . . . . . . . . . . . 443.4 Detection efficiency profile . . . . . . . . . . . . . . . . . . . . . . . . . . 463.5 Measurement of the electron yield . . . . . . . . . . . . . . . . . . . . . 473.6 Switching the detector with a magnetic field . . . . . . . . . . . . . . . . 483.7 Experimental 3D TOF spectrum for a cloud of laser-cooled atoms . . . . 51

4.1 General concept for the MOST . . . . . . . . . . . . . . . . . . . . . . . . 554.2 3D configuration of the MOST . . . . . . . . . . . . . . . . . . . . . . . . 564.3 Model for a MOT near a surface . . . . . . . . . . . . . . . . . . . . . . . 574.4 Light field distribution at the mirror surface . . . . . . . . . . . . . . . . 594.5 Experimental setup for the MOST . . . . . . . . . . . . . . . . . . . . . . 624.6 Fluorescence image of a trapped cloud . . . . . . . . . . . . . . . . . . . 634.7 Temperatures of the trapped cloud . . . . . . . . . . . . . . . . . . . . . 65

iii

iv LIST OF FIGURES

4.8 Method for shifting the position of the magnetic field zero . . . . . . . . 664.9 Shifting the cloud toward the surface . . . . . . . . . . . . . . . . . . . . 674.10 Properties of the trapped cloud for different heights . . . . . . . . . . . . 694.11 Characterization of the bichromatic atom mirror . . . . . . . . . . . . . . 724.12 Lifetime of the MOST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.1 Experimental schematic and transitions for the waveguide experiments . 795.2 The waveguide potential . . . . . . . . . . . . . . . . . . . . . . . . . . . 815.3 Scheme and model for continuous loading . . . . . . . . . . . . . . . . . 835.4 Surface-sensitive detection . . . . . . . . . . . . . . . . . . . . . . . . . . 855.5 Experimental configuration for the waveguide . . . . . . . . . . . . . . . 865.6 Experimental setup for the waveguide . . . . . . . . . . . . . . . . . . . 875.7 TOF signal of the CW loaded waveguide . . . . . . . . . . . . . . . . . . 885.8 Sequence for measuring the loading curve . . . . . . . . . . . . . . . . . 895.9 Loading curve of the waveguide . . . . . . . . . . . . . . . . . . . . . . . 895.10 Parameter dependence of the loading process . . . . . . . . . . . . . . . 915.11 Integrated atom source and channel guide . . . . . . . . . . . . . . . . . 925.12 Propagation of atoms in the channel guide . . . . . . . . . . . . . . . . . 935.13 Integrated atom detector and atom-optical integrated circuit . . . . . . . 955.14 A quasi-1D optical surface lattice . . . . . . . . . . . . . . . . . . . . . . 965.15 Localization of atoms in the surface lattice . . . . . . . . . . . . . . . . . 97

Chapter 1

Introduction

1.1 General Context

The development of laser cooling and trapping [1, 2, 3] and atom optics [4] over thelast two decades has stimulated and contributed to a wide range of fundamental andapplied research including optical lattices as model systems for solid-state physics, ul-tracold collisions, nano lithography, atom interferometry, precision sensing and metrol-ogy, and quantum information processing [5, 6, 7, 8, 9, 10, 11, 12]. In particular, it hasalso paved the way to the achievement of Bose-Einstein condensation in dilute, weaklyinteracting atomic gases [13,14,15].

Laser cooling and trapping exploits the mechanical effects of light on atoms whichcan be described in terms of spontaneous and dipole forces [16, 17, 18]. The spon-taneous force arises when an atom scatters photons from a laser beam. While theabsorption of photons is directed, the momenta of spontaneously emitted photons av-erage to zero and so the atom experiences, averaged over many cycles, a nonzeromomentum transfer from the beam. Since the emission is irreversible the resulting netforce (also called radiation pressure) is dissipative. The dipole force, on the contrary,arises from the coherent interaction of an inhomogeneous laser field with the inducedatomic dipole moment. It is conservative as no spontaneous emission is involved, andcan be written as the gradient of an optical potential. These forces can be used to coolthe motion of atoms and confine and manipulate them in traps. Radiation pressure onfree atoms was observed as early as 1933 [19] yet remained without experimental rel-evance until after the advent of lasers in the 1960s. The idea of laser cooling, based onthe high spectral intensity of lasers, was introduced in 1975 [20,21], and in the 1980sthe first demonstration of a slowed thermal atomic beam [22] led to the developmentof optical molasses [23] and of the magneto-optical trap (MOT) [24]. The MOT hasbeen intensely studied and improved in the last decade [25] and today is a standardinitial step for experiments that involve trapping and cooling of neutral atoms. Theusual design consists of three mutually orthogonal pairs of counterpropagating laserbeams that intersect at the zero of a quadrupole magnetic field. In MOTs and molassesthe equilibrium temperature can reach down to the �K range [26, 27, 28] correspond-

1

2 CHAPTER 1. INTRODUCTION

ing to a few photon recoils, and special laser cooling schemes have been demonstratedthat allow to cool even below the one-photon recoil limit [29, 30]. Based on the op-tical dipole force, which was first observed for an atomic beam [31] in 1978, opticaltraps and microscopic optical lattices have been realized and studied [32, 5, 33, 34].In optical lattices, the atomic de Broglie wavelength [35] typically is of the size of theconfinement, such that these lattices can also be considered atom-optical cavities witha mode structure. Laser cooling and trapping got public attention in 1997 when thephysics Nobel prize was awarded to S. Chu, C. Cohen-Tannoudji and W. Phillips fortheir contributions to the field.

In atom optics [4], methods and elements for reflection, focusing, diffraction andinterference of atoms have been demonstrated much in analogy to “photon optics”,based on optical and magnetic potentials as well as material structures. In analogyto “photon optics”, one can distinguish de Broglie wave atom optics (e.g. in an atominterferometer [36,37]), from the special case of geometrical atom optics in which themotion of atoms follows classical trajectories. An important atom-optical element forour experiments is the atom mirror. One type is based on the reflection of atoms at a re-pulsive optical dipole potential [38]. Such a mirror was first demonstrated in 1987 [39]in an experiment with a blue-detuned evanescent light wave at a surface from whicha grazing-incidence thermal beam was reflected. In later experiments, laser-cooledatoms were employed [40, 41, 42, 43, 44] and recently the coherent reflection of anatomic Bose-Einstein condensate from an optical atom mirror was reported [45]. Thesecond type of atom mirror is based on the repulsive interaction of an atom with amagnetic field via its magnetic moment. Over recent years, magnetic atom mirrorswith exponentially decaying magnetic fields above a surface have been realized, usingsinusoidally magnetized tapes [46, 47], arrays of alternating permanent magnets [48]and lithographically patterned current-carrying wires [49]. A third type of atom mir-ror exploits the quantum reflection of slow atoms from the attractive van der Waalspotential at a solid surface [50] (atom-surface interactions also play an important rolein evanesent-wave optical atom mirrors [44]).

Ultracold atoms have proven powerful tools for the study of quantum degenerategases. In a dilute, ultracold atomic gas of density n, quantum degeneracy sets in whenthe thermal de Broglie wavelength � (which scales as 1=

pT , where T is the tempera-

ture of the gas) becomes comparable to the average interatomic distance, n�3 >�1, such

that the atomic wavepackets overlap. For bosonic atoms this leads to Bose-Einstein con-densation (BEC) [51,52], resulting in the macroscopic population of a single quantumstate. BEC in a dilute, weakly interacting trapped atomic gas was first achieved in1995 for rubidium, sodium and lithium [13, 14, 15] and very recently for metastablehelium [53, 54] by combining laser cooling and trapping techniques with magnetictrapping [55] and evaporative cooling [56]. In evaporative cooling, the hottest atomsin a conservative atom trap are allowed to escape while the remaining atoms rether-malize at a lower equilibrium temperature via elastic collisions. In 1998, BEC wasachieved in atomic hydrogen by evaporative cooling from a cryogenically loaded mag-netic trap [57]. Over the last years, a wealth of fundamental phenomena in trapped

1.1. GENERAL CONTEXT 3

atomic BEC have been studied such as coherence, excitations, spinor condensates,Feshbach resonances, superfluidity and solitons [58, 59, 60, 61, 62, 63, 64]. BECs havebeen transferred from magnetic traps into purely optical traps [65, 66, 45], and veryrecently the first all-optical BEC was achieved by evaporative cooling from an opti-cal dipole trap [67]. The way to the study of low-dimensional quantum degenerategases [68, 69, 70, 71, 72, 73] has been opened in with a cryogenically cooled, degener-ate 2D atomic hydrogen gas at a surface [74] and with the very recent realization of2D and 1D BECs in highly anisotropic optical and magnetic traps [75]. For a trappedfermionic atomic gas, quantum degeneracy was first observed in 1999 [76].

One of the major implications of BEC for atom optics is the advent of atom lasersas sources of coherent atomic matter waves. Their impact on the field can be expectedto be comparable to that of the laser on optics. In the laboratory, coherent matter-wave pulses and beams have already been created by coupling atoms out of a trappedBEC [77, 78, 79, 80, 66], and bosonic stimulation [81] and matter-wave amplificationin BECs [82, 83] have been investigated as crucial elements of an atom laser. As oneof the first applications, four-wave mixing of coherent matter waves has been demon-strated [84], opening the way to nonlinear atom optics. The major issue that is stillopen experimentally is a method to replenish a BEC from a reservoir in order to real-ize a continuous-wave atom laser [85, 86]. A number of CW pumping schemes basedon collisional dissipation [87, 88, 89, 90, 91] and laser cooling [92, 93, 94, 95, 96, 97]have been proposed (a third possibility based on molecule dissociation was proposed inRef. [98]). In the laser-cooling schemes for reaching BEC, an atom is optically pumpedfrom a reservoir into the bound levels of a trap under the spontaneous emission of afinal photon. Ideally this photon leaves the system, dissipating the excess energy. How-ever, it can also get reabsorbed by other atoms in the pumped level, which excites thoseatoms to higher energy and thereby thwarts the effect of the pump. Photon reabsorp-tion thus limits the achievable phase-space density n�3 [99]. In particular, it has beenshown that in macroscopic 3D traps (having linear extensions that are large comparedto the optical wavelength), n�3 cannot reach the critical value for BEC if the recoilenergy ~!R imparted on the atom by the absorbed photon is larger than the trap levelspacing ~! [94]. Several scenarios for getting around this problem have been workedout, including planar traps [100], tightly confining 3D traps with ! � !R [101], andthe so-called festina lente regime for which ! is much larger than the pumping rate� [102]. the reabsorption. A recent proposal employs a pumping-laser induced Autler-Townes level splitting in the region of the thermal component of a BEC cloud to turnthe emitted photons out of resonance with the atoms in the BEC [96]. Another recentscheme is based on a lambda level configuration with large branching ratio, for whichthe reabsorption on the weak transition is suppressed [97]. This scheme is currentlybeing investigated for chromium, for which the first continuous loading of a magnetictrap from an overlapped MOT has recently been demonstrated [103]. Experimentally,the highest phase-space density in laser-cooling schemes has so far been achieved bycooling strontium on an optically forbidden transition, only one order of magnitudebelow quantum degeneracy [104].


Over recent years, several proposals have been made for the realization of pla-nar atom traps, based on tightly confining optical and magnetic potentials at sur-faces [105,106,107,108]. In these systems, which can also be considered planar atom-optical waveguides, the atomic motion is quasi-free parallel to the surface, while normalto it only a few bound states (ideally: one) are populated. Besides their relevance forreaching BEC with laser cooling, planar atom traps are of interest for the study ofatomic gases in low-D and close to surfaces [109]. One of the schemes [107, 100] forsuch a trap has so far been demonstrated experimentally [110]. In this experiment,which was performed by us in 1998, laser-cooled metastable argon atoms releasedfrom a MOT were transferred into a single (anti-)node of a standing light wave abovea mirror surface. The optical trapping potential had five bound states and was sepa-rated from the surface by less than 1 �m. Atoms were loaded into the waveguide bycombining evanescent-wave reflection with a single dissipative optical pumping stepin a second, overlapped evanescent field [111]. A related scheme is currently beingpursued for rubidium [112]. In another experiment, a laser-cooled cesium gas witha barometric thickness of 20 �m has been prepared in a weakly confining gravito-optical potential above a planar surface [113]. Here the loading scheme is based onmotion-induced pumping between unequally shifted hyperfine states in the potentialof an evanescent-wave atom mirror (evanescent Sisyphus cooling) [114, 106], and ef-forts are under way to achieve BEC in this system [115]. In restricted geometries, ex-perimental methods have furthermore been demonstrated to guide ultracold atoms inhollow-core optical fibers and laser beams [116,117,118,119,45], and close to current-carrying wires [120, 121, 122, 123], using axially symmetric optical and magnetic po-tentials, respectively. The wire concept has been extended to the use of microfabri-cated wires on substrates, for which over the last two years several weakly confininglinear [124, 125, 126] and (switchable) Y-branch atom guides [127, 128] in a distancein the range 10 to 100 �m from the substrate surface have been demonstrated. Micro-fabricated wires have also been used for the realization of magnetic traps [129] anda conveyor belt [130]. In these experiments, “mirror MOTs” [131, 111, 129] close tothe reflecting surface were used for the loading of atoms into the confining potential.Recently, the first guiding of a BEC in a hollow laser beam was demonstrated [45],and the first creation of BECs in magnetic potentials above wire microstructures wasreported [132,133].

The manipulation of atoms in tightly confining structured potentials close to sub-strate surfaces, both magnetic and optical, opens the way to integrated atom optics.This nascent field may be defined as the realization and combination of miniaturizedatom-optical elements to form atom-optical integrated circuits in substrate-based geome-tries. This is in analogy to integrated optics, where optical integrated circuits havebeen built that combine a number of miniaturized, interconnected optical componentson a common substrate [134]. An example for a future atom-optical integrated circuitmight be a high-sensitivity integrated atom interferometer consisting of a (coherent)atom source, a large enclosed area between two waveguide beamsplitters, and a de-tector. By bringing ”established” atom optics down to a small scale, integrated atom

1.2. THIS THESIS 5

optics should allow for improved, cheap and easily reproducible setups. Many aspectsaccessible with integrated atom optics are currently being discussed, such as quantuminformation processing [135,136], atom-surface interactions [137], cold collisions andnonlinear atom optics [138].

1.2 This Thesis

In this thesis I present and discuss experiments performed with metastable argon onthe all-optical trapping and manipulation of laser-cooled atoms at a metallic surface.In these experiments the first continuous loading of a planar atom-optical waveguidewas demonstrated, which as discussed above is of conceptual interest for schemes[92, 100, 112] to reach quantum degeneracy with laser cooling. The loading of thewaveguide was achieved via evanescent-field optical pumping from a novel magneto-optical surface trap that was used as a reservoir of pre-cooled atoms. This work wasextended to the manipulation of atoms in the waveguide, which allows for a novelimplementation of integrated atom optics. Several light-induced atom-optical elementsin the planar waveguide geometry in sub-�m distance from the surface were demon-strated and were combined to form the first, albeit simple, atom-optical integratedcircuit.

Ar* (1s3)

OPEWM

820 nm

MOST

De

tec

tio

n

e-

WG

1s5 1s3

WGD

1.5 mm

Figure 1.1: Principle of trapping and manipulation of metastable argon in a planar waveguideat a surface. A planar waveguide for 1s3 metastable argon atoms is formed by a single layerof the periodic optical potential of a standing light wave (WG). Atoms are loaded into thewaveguide with evanescent-wave optical pumping (OP) from the magneto-optical surface trap(MOST) for 15 atoms, which combines a modified MOT at the surface with an evanescent-waveatom mirror (EWM). The optically pumped 1s3 atoms propagate along the waveguide and aresubsequently detected (WGD) via secondary electrons released upon impact on the surface.

The magneto-optical surface trap (MOST) is a combination of a modified MOT withan optical atom mirror above a gold-coated prism surface. The trapped atoms are incontact with an evanescent field that separates the atomic cloud from the surface bya fraction of an optical wavelength. The evanescent field is generated by the resonant


excitation of surface plasmons in the gold film. In the experiment, up to (1:3�0:4)�105

atoms could be trapped with a lifetime of up to (390 � 30) ms. The properties of theMOT were investigated for decreasing distances of its center from the surface and adrastic decrease of the lifetime due to losses to the surface was observed. The atommirror was investigated in the presence of the MOT light and a a strong influence of thebichromatic light field on its performance was found. Combining the atom mirror witha MOT whose center was located on the surface, it was shown that the evanescent fieldof the atom mirror can increase the lifetime of the trapped atom cloud by at least oneorder of magnitude by suppressing losses to the surface. The properties of the MOSTare explained in a simple model.

The planar waveguide for ultracold metastable argon atoms is formed by the peri-odic optical potential of a red-detuned standing light wave above the surface. In thissystem the atomic motion is quasi free parallel to the surface while normal to it onlya few bound states exist. A continuous, surface-sensitive loading mechanism for thelowermost waveguide layers was demonstrated and characterized experimentally. Themechanism is based on the MOST as a reservoir of laser-cooled atoms at the surface,from which atoms are optically pumped into the waveguide in the short range of asecond evanescent light field. A loading rate on the order of 103/s was achieved, whichcorresponds to a flux of 105/(s cm2). The evanescent loading mechanism led to a rel-ative population of around 30% for the lowest confining waveguide layer centered at820 nm above the surface, orders of magnitude closer to the surface than achieved inthe work on atoms trapped in magnetic potentials at surfaces.

Based on the continuous loading scheme for the planar waveguide, a local atomsource in the planar waveguide geometry was implemented. A switchable channelguide connected to the source was realized and the propagation of atoms in this guidewas directly observed. An atom detector in the channel guide was realized via a localdeformation of the confining waveguide potential with another evanescent light field.The source, the guide and the detector were combined into an integrated circuit for asimple atomic beam experiment in the lowest waveguide layer. Also, the localizationof atoms in a quasi-1D surface lattice (realized by retroreflecting the waveguide laserbeam) was demonstrated.

The atom detection in the experiments was largely based on the imaging of sec-ondary electrons released from the surface upon impact of single atoms. The sur-face atom detector was characterized with atom-optical methods, and the detectionefficiencies for the metastable 1s5 and 1s3 states of argon used in the experimentswere determined. A method for 3D time-of-flight spectroscopy of ultracold atoms wasdemonstrated that exploits the spatial and temporal resolution of the detector.

1.3 Outlook

The manipulation of atoms in a structured optical potential close to a substrate surfaceopens the way to integrated atom optics. The waveguide as the fundamental elementprovides a planar geometry above a substrate surface into which atom-optical compo-

1.4. OUTLINE 7

nents can be subsequently incorporated, and transverse guiding can be achieved bylaterally structuring the waveguide potential (the shutterable channel guide and thequasi-1D lattice are simple examples). This scheme is extremely flexible since the con-fining optical potential of the waveguide can be modulated easily both in space andtime – in future applications, one might envision using addressable liquid crystal pixelarrays as transmission masks in the waveguide beam that are combined with a high-resolution imaging system to ”write” arbitrary light fields onto the surface. In this way,miniaturized and time-dependent atom-optical setups could be realized, paving theway to novel integrated elements and complex integrated circuits. In addition, the ex-treme closeness to the surface makes our system interesting for probing atom-surfaceinteractions in such applications.

Continuous loading of planar atom waveguides has been discussed in connectionwith schemes to reach quantum degeneracy in open systems [92, 100, 112]. With ourwork, we have shown for the first time that such a continuous scheme can indeed berealized. In the present proof-of-principle realization the loading flux into the waveg-uide is comparable to that achieved with our previously realized pulsed scheme [110],being three orders of magnitude short of what would be required for a scenario fordegeneracy in bosonic ground-state argon [100,111]. Our data suggest, however, thatsignificant improvements in the flux might still be possible in an optimized experimen-tal setup in which the loading rate of the MOST and the pumping rate of the evanescentpumping field are increased. Our work therefore might also encourage further studiesin this direction.

Finally, our scheme for bringing a magneto-optical trap near a mirror surface is ofuniversal interest when laser-cooled atoms are desired in the vicinity of surfaces. Infact, adaptions of this kind of MOT have already been employed recently as startingpoints for loading atoms into magnetic potentials [129, 126] and reaching BEC nearsurfaces [133]. The additional combination of these surface MOTs with an atom mirrorshould allow to minimize initial losses to the surface and thereby allow for a significantincrease in the starting phase-space density.

1.4 Outline

This thesis contains five chapters and one appendix. In this first introductory chapter, ageneral overview of the current status of the field and the scope of this particular workhas been given.

The second chapter contains an introduction to important aspects of atom-light in-teractions and to more general concepts related to the experiment, with a focus on themagneto-optical trap and the evanescent-wave optical atom mirror (as constituents ofthe magneto-optical surface trap). The chapter also summarizes important propertiesof argon and shortly describes the beam machine and laser system and its modifica-tions as compared to that used in previous experiments. Finally the properties of thecoated prism surface for the generation of evanescent fields with surface plasmons arediscussed.


The third chapter deals with our work on the surface atom detector as a crucialpart of the experimental apparatus. A short overview of the detection principle and thepresent improved setup is given, and our experiments to characterize the performanceof the detection scheme with laser-cooled atoms and an evanescent wave mirror arediscussed.

The fourth chapter and the appendix are devoted to the magneto-optical surfacetrap. The trap configuration and a simple model picture for the behavior of the MOSTare discussed, and the experimental study of the MOST and its constituents is pre-sented.

The fifth chapter focuses on the continuous loading of the planar waveguide and themanipulation of atoms in the waveguide potential. Basic issues for the waveguide anda simple model for the loading process are discussed, and the experiments and resultson continuous loading and the realization of light-induced atom-optical elements arepresented.

Chapter 2

Basic Issues

2.1 Theoretical and Experimental Concepts

2.1.1 Light Forces in the Dressed-Atom Picture

In laser cooling and trapping the external degrees of freedom of a free atom are ma-nipulated and controlled by exploiting the coupling of the atom to a quasi-resonantlaser field. The following subsections shortly review the concept of optical forces in theso-called dressed atom picture, following the description in Refs. [17,16,139].

Dressed states for the two-level atom. Consider a free two-level atom A at restinteracting with a monochromatic laser mode L. The total Hamiltonian of the systemis given by

HAL = HA +HL + VAL: (2.1)

The first two terms describe the state of the atom HA and the laser field HL, and thethird term VAL describes the atom-field coupling. The coupling of the atom to thevacuum field is neglected for the moment; instead it will be introduced below via thespontaneous decay rate �, which is the linewidth of the excited state of the atom.

The non-interacting part of the Hamiltonian H0 � HA +HL is given by

HA = ~!0 jeihej � 1

2~!0 ; HL = ~!L (aya+

1

2); (2.2)

where !0 is the transition frequency between the internal states jgi and jei of the atom,and ay (a) is the creation (annihilation) operator for a photon in the laser mode withfrequency !L. The eigenstates of H0 are given by the bare states ji;Ni, where i = e; gand N = hayai is the photon number. For a small detuning of the laser field withrespect to the atomic transition frequency

ÆL � !L � !0 � !0; (2.3)

9

10 CHAPTER 2. BASIC ISSUES

the states jg;N + 1i and je;Ni are quasi-degenerate with a small energy difference of~ÆL and can be grouped into manifolds E(N) = fjg;N + 1i; je;Nig.

In the semiclassical dipole approximation, the interaction Hamiltonian VAL is givenby VAL = �d � E(R), where d and E are the operators for the electric dipole and fieldat the classical position R of the atom:

d = dge�jeihgj + jgihej� (2.4)

E = u (a+ ay) with u �p~!L=(2"0V ) �L (2.5)

Here, dge � hgjdjei is the atomic dipole matrix element, �L is the unit vector repre-senting the polarization of the laser field, and V is a normalization volume. In therotating-wave approximation [16] only the quasi-resonant terms in VAL for the cou-pling within E(N) are considered such that

VAL = �dge � u�jgihejay + jeihgja�: (2.6)

For a sufficiently intense coherent laser field the field can also be described classi-cally by its expectation value E = E0 cos!Lt, where E0 = 2 u

phNi. In that case the

interaction, expressed in the bare state basis of E(N), is simply given by

VN = he;N jVALjg;N + 1i = ~ !R=2; (2.7)

where !R is the (on-resonance) Rabi frequency

!R � �deg �E0=~ = �pI=(2IS) : (2.8)

The last equation relates !R to experimentally accessible quantities using theWeisskopf-Wigner theorem [140] that connects the dipole matrix element to thelinewidth � of the excited state of the atom. The field intensity I is given byI = "0cjE0j2=2, and

IS � 2�2~c�=(3�30) with �0 = 2�c=!0 (2.9)

is the so-called saturation intensity.Using the contributions HA, HL and VAL thus determined, the total Hamiltonian

HAL can now be diagonalized in the basis of the bare states of E(N). This leads tostationary eigenstates of the atom+field system

j1(N)i = sin � jg;N + 1i+ cos � je;Nij2(N)i = cos � jg;N + 1i � sin � je;Ni; (2.10)

the so-called dressed states, with corresponding energy eigenvalues

EN;1 = (N + 1)~!L + ~=2; (2.11)

EN;2 = (N + 1)~!L � ~=2: (2.12)

2.1. THEORETICAL AND EXPERIMENTAL CONCEPTS 11

The mixing angle � is defined by the condition

tan 2� = �!R=ÆL (�=4 � � � 3�=4); (2.13)

and the quantity

�qÆ2L + !2R (2.14)

is the off-resonance Rabi frequency.

Spontaneous emission and transitions between dressed states. In the discussionof the dressed atom the coupling of the atom to the vacuum has not been included sofar. This section describes how this coupling influences the population of the dressedstates; subsequent sections then address the issue in the context of light forces.

In a spontaneous emission process the state je;Ni decays into jg;Ni, thereby lead-ing to a transition from the manifold E(N) to E(N�1). The next emission then leads toE(N�2), etc. in a radiative cascade. As long as the Rabi frequency is large comparedto the decay rate �, the decay will not perturb the dressed-state coupling which buildsup on the time scale �1.

The populations of the dressed states and the coherences between them can bederived from the master equation [16]

d

dt� = � i

~[HAL; �] � �

"1

2(L+L�� + �L+L�)�L��L+

#; (2.15)

where � is the density operator of the dressed atom and HAL is defined as in the lastsection, and the term containing L+ � jeihgj1, L� � jgihej1 describes the couplingto the vacuum. This operator equation leads to equations of motion for the reducedmatrix elements

�ij =XN

hi(N)j�jj(N)i; (2.16)

obtained by summing up over the ladder of dressed states. Since � �, the couplingbetween the populations �11, �22 and the coherences �12, �21 can be neglected [16](secular limit), and the populations are then described by

_�11 = ��11 �12 + �22 �21

_�22 = ��22 �21 + �11 �12; (2.17)

where the transition rates �ij (see figure 2.1) are given by [16]

�11 = �22 = �cos2 � sin2 �;

�21 = �sin4 �

�12 = �cos4 �: (2.18)


The transition frequencies are !0, !0 � , give rise to the Mollow triplet [141] inthe emission spectrum. The steady-state populations are determined by the stationarysolution ( _�ii = 0)

�st11 =sin4 �

(sin4 � + cos4 �)and �st22 =

cos4 �

(sin4 � + cos4 �)(2.19)

which build up with the rate �pop = �21 + �12 that is on the order of the decay rate.The coherences vanish, �st12 = �st21 = 0, with a comparable rate �coh = �22 + �=2.

{

{

E(N)

E(N � 1)

~!L

je;Ni

jg;N + 1i

je;N � 1i

jg;Ni

~ÆL

~ÆL

�12 �11�22�21

j1(N)i

j2(N)i

j1(N � 1)i

j2(N � 1)i

~(R)

~(R)

�

Figure 2.1: Two manifolds E(N) and E(N � 1) of the dressed atom. With increasing coupling!R to the field, which in this example increases exponentially from left to right starting fromzero, the uncoupled bare states (at left) couple to dressed states (at right) with energetic sepa-ration ~. The example is for blue detuning ÆL > 0 (for red detuning the energetic order of thebare states within a manifold is reversed). Transitions arise as a result of spontaneous decay,leading to a radiative cascade over the manifolds.

Optical dipole force and dipole potential. If the laser field possesses a spatial varia-tion of the field intensity, the energies of the dressed states become spatially dependent,giving rise to the conservative optical dipole forces

Fj = �rENj = (�1)j ~

2r (2.20)


as a gradient of the optical potentials (also called light shifts) ENi acting on the dressedstates jj = 1(N)i and jj = 2(N)i, respectively.

The transitions between the states discussed in the previous section now lead torandom jumps between F1 and F2 which in the steady state can be expressed by themean force

hFdipi = �st11F1 + �st22F2 = �~

2r

��st11 � �st22

�: (2.21)

which is the gradient of the potential [16]

Udip =~ÆL2

ln

�1 +

!2R=2

Æ2L + (�2=4)

�: (2.22)

As a function of detuning, the force has the shape of a Lorentz dispersion curve: ForÆL > 0 (blue detuning) the state j1(N)i contains the larger admixture of jg;N +1i andis therefore more stable against spontaneous decay than j2(N)i such that �11 > �22.In that case the contribution of F1 dominates and the atom is therefore repelled fromhigh intensity regions. On resonance, ÆL = 0, the force vanishes and for ÆL < 0 it takesthe opposite sign such that the atom is attracted to high-intensity regions.

An important special case is the case of large detunings Æ2L � !2R for which thetransition rates tend to zero, such as for optical dipole traps and evanescent-wave atommirrors. The light shift is then given by

Udip ! �~

2(� jÆLj) � � ~

4

!2RjÆLj ; (2.23)

where the � sign is for the j2(N)i state and the + sign is for the j1(N)i state.

Scattering force. For the case of a homogeneous light field L with wave vector kL,the optical dipole force on the dressed atom discussed so far vanishes. However thereare still transitions between je;Ni and jg;Ni as a result of absorption and spontaneousemission that are themselves connected to momenta ~kL. While the momentum trans-fer from spontaneous emission averages to zero, the absorption is unidirectional andis therefore connected to a net momentum transfer to the atom. Averaged over manyabsorption and emission cycles this gives rise to the so-called scattering force which isdissipative and can be used for laser cooling.

The scattering force can be described easily using the so-called optical Bloch equa-tions which are obtained by expressing the master equation 2.15 in the basis ofthe bare states je;Ni and jg;Ni and summing up over the radiative cascade, i.e.eliminating the laser field from the model [16]. By defining the reduced elements�̂ij =

PN hi;N j�jj;Ni, i.e. by eliminating the laser field, and introducing the quanti-

ties u = (�̂ge + �̂eg)=2, v = (�̂ge � �̂eg)=(2i) and w = (�̂ee � �̂gg)=2, eq. 2.15 takes theform 0

@ _u_v_w

1A =

0@ ��=2 ÆL 0

�ÆL ��=2 �!R0 !R ��

1A �

0@ u

vw

1A�

0@ 0

0�=2

1A : (2.24)


This describes, in the reduced bare-state basis, a damped Rabi oscillation of the coher-ences u; v and the population difference 2w, in analogy to the Bloch equations knownfrom nuclear magnetic resonance.

The population of the excited state, from which spontaneous transitions occur, isgiven by �ee = w + 1=2 (since �gg + �ee = 1). In the steady state, it takes the value

�stee =1

2

s

s+ 1with s =

!2R=2

Æ2L + �2=4; (2.25)

where s is called the saturation parameter (for small saturations, �stee � s). Since sponta-neous decay from jei occurs at the rate �, the steady-state rate for absorption-emissioncycles is then given by

�sc = �stee � (2.26)

which finally leads to the scattering force (also called radiation pressure)

hFsci = �sc ~kL =s~�

2(s+ 1)kL =

!2R=2

Æ2L + �2=4 + !2R=2

~�

2kL: (2.27)

The scattering force, which takes a maximum value of (~�=2) kL for s!1, is a non-conservative force that cannot be derived from a potential. As a function of detuning,it has the shape of a Lorentzian centered about the atomic resonance frequency.

It follows already from the discussion of the optical dipole force that transitionsbetween the states, i.e. the scattering force, can be made arbitrarily small comparedto the dipole force by increasing the laser detuning such that jÆLj � !R. In that case,Fsc=Fdip / 1=ÆL.

Force fluctuations. The spontaneous transitions not only influence the dipole forceand give rise to the scattering force, but they also lead to fluctuations of these lightforces which are connected to random momentum kicks. In this section, a simple 1Dsituation is assumed. The force fluctuations ÆF (t) = F (t) � hF i are characterizedby [139]

hÆF (t)i = 0 (2.28)

hÆF (t)ÆF (t0)i = 2D g(t� t0); (2.29)

The quantity D in the autocorrelation function of eq. 2.29 is called the momentumdiffusion coefficient. The function g has unit area and a width that is given by thecorrelation time �c. Because of the random nature of photon emission, this time issimply given by the photon scattering time, �c � ��1sc .

Consider the case of the scattering force, then integration of the autocorrelationfunction yields 2D � hFsc(0)2i ��1sc , such that, by using eq. 2.27,

Dsc � (~kL)2�sc: (2.30)


For the case of the dipole force, eq. 2.21, the diffusion coefficient can be estimatedsimilarly as above for �st11 � �st22, i.e. for the case of saturation hFdipi � 0 at which�sc � �=2:

Ddip � 2(~r)2 ��1 (2.31)

The fluctuations are connected to heating and limit the temperatures achievable inlaser cooling. This is discussed further in section 2.1.2.

Multilevel atoms. The two-level atom picture can be extended to atoms with mag-netic Zeeman substructure by taking the angular dependence of the induced dipolemoment and the polarization state of the light field (with respect to the quantizationaxis) into account. For an atom with states jg;mgi and je;mei, the dipole moment isgiven by hg;mgjdje;mei. For light with the correct angular momentum to drive thetransition, i.e. with ~(me �mg), the connection to the two-level atom picture is thenmade by the substitution !R ! !R Cmg;me in eq. 2.8, where Cmg ;me is the Clebsch-Gordan coefficient of the transition.

For multilevel atoms with a branching in the excited state the linewidth � is givenas � =

PiAi, where the Ai are the Einstein A coefficients for the different transitions

jgii $ jei. For the case that the laser mode L interacts with a single transition jgki $jei (detuning ÆL;k), the system can be described in the two-level dressed atom pictureby substituting �! Ak in eqs. 2.8 and 2.9, which yields a corresponding on-resonanceRabi frequency !R;k and (effective) saturation intensity Is;k.

These direct analogies to the two-level atom generally break down when spon-taneous decay is involved, being connected to a continual loss of population from theeffective two-level atom via decay to the other ground states. For the effective two-levelatom fjgji; jeig, the optical pumping rates to the states jgii are given by �sc;i = Ai �ee.For the case of weak coupling !R;k � � with slow pumping, it can be shown that thepopulation �ee takes a quasi-stationary value given by �ee � !2R;k=(�

2 + 4Æ2L;k) [107].

2.1.2 Laser Cooling and Trapping

For a moving atom, the Doppler frequency shift can be exploited to dissipate the kineticenergy of the atom by means of the scattering force. Consider an atom moving againsta red detuned laser beam (ÆL < 0). In the atom’s rest frame the frequency of the beamis shifted closer to resonance due to the Doppler shift ÆD = �v � kL: In the ideal case,the light field is shifted into resonance, 0 = Æ0L = ÆL + ÆD. In the rest frame of theatom, the photons are then isotropically scattered with the maximum scattering rate�=2. Due to the Doppler effect, photons that are not re-emitted in the direction ofthe laser beam are shifted towards higher energies. The energy balance is maintainedby a reduction of the kinetic energy of the atom. Since the photon scattering is alsoconnected to an increase in entropy the effect is irreversible. This principle of lasercooling was suggested in 1975 by Hänsch and Schawlow [20] and independently byWineland and Dehmelt [21].


Slowing of an atomic beam. For a thermal atomic beam the Doppler shift can exceedthe natural linewidth � by orders of magnitude. To use the scattering force efficiently,the atoms therefore have to be kept on resonance as they slow down to small velocities.The two most common techniques for the preparation of slow atomic beams consistof sweeping the frequency of the counterpropagating laser beam accordingly (chirp-slowing, 1985 [142]) or by varying the transition frequency along the trajectory via aZeeman shift of magnetic sublevels in a static magnetic field, while keeping the lightfrequency constant (Zeeman-slowing, 1982 [22] ). This creates a continuous beam ofslow atoms. The Zeeman shift of a transition between states jgi and jei in a magneticfield B is given by

ÆZ = (geme � ggmg)�B B=~ =: �0B=~; (2.32)

where gg;e are the Landé factors, mg;e the magnetic quantum numbers, and �B is theBohr magneton.

Optical molasses configuration. Atoms can be trapped in momentum space in theso-called optical molasses configuration, which was first realized by Chu et al. [23] in1985. This configuration can best be illustrated in a 1D model. Consider a slow atomat velocity v in a laser field configuration consisting of counterpropagating laser beamsL1; L2 with uniform intensities and red detunings ÆL < 0. For an atom at rest, thetwo mean scattering forces balance each other and no net force is exerted. Supposenow that the atom moves in the direction of propagation of L1 and therefore againstL2. This produces a small Doppler shift jkvj � jÆLj that brings L2 closer to resonance,and at the same time shifts L1 further away from resonance. As a consequence thescattering forces of the two beams become unbalanced, and the total scattering forceopposes the motion of the atom. In eq. 2.27 for the scattering force the detuning hasto be replaced by ÆL ! ÆL�vkL such that hFsci = hFsci(ÆL�vkL). For small saturations� 1, the effects of the beams can be treated independently, such that

hFsc;toti(v) = hFsci(ÆL + vkL) � hFsci(ÆL � vkL) � � v (2.33)

with [143]

= �4~k2LI

IS

2ÆL=�

[1 + 4(ÆL=�)2]2> 0: (2.34)

hFsci is a velocity dependent friction force that damps the atomic motion with a rate =M which typically is on the order of 105 s�1(M is the mass of the atom). The 1Dmodel can easily be extended to 3D by setting up three orthogonal beam pairs. Forlarge saturation, the effects of the forces from the beams can no longer simply beadded; however the model remains qualitatively valid.

Magneto-optical trap configuration. A configuration that provides spatial confine-ment as well as cooling in momentum space is the so-called magneto-optical trap


(MOT), first realized by Raab et al. in 1987 [24]. The MOT is illustrated in figs. 2.2and 2.3. The underlying mechanisms are most easily explained in the 1D model shownin fig. 2.2 for a Jg = 0 $ Je = 1 transition (this can be extended to any J $ J + 1transition). The magnetic field B has a zero crossing at z = 0 and increases linearly toeither side, with a constant gradient b = jdB=dzj. Then as a function of position theZeeman sublevels of the excited state of the atom split up energetically, with m = 1having the highest energy when choosing the local direction of B (cf. fig. 2.2) as thequantization direction. Suppose the atom is situated in a pair of counterpropagating,red-detuned laser beams (as in the discussion of the 1D molasses) that now are right-handed circularly polarized. The “inbound” beams propagating towards z = 0 are then�� beams, driving only the jJ = 0;m = 0i $ j1;�1i transition because of angular mo-mentum selection. After passing z = 0 and becoming “outbound” beams, they revertto �+, now driving j0; 0i $ j1; 1i. Because of the Zeeman shift, the m = �1 level isalways closest to resonance. As a result the scattering force from the �� beam exceedsthe one from the �+ beam and the atom is pushed towards the center. In addition to

{

z

z

B BB

rhc

rhc

��

��+

�+~!0 ~!L

Energy+1

�10

m = +1

m = �1m = 0

m = 0

J = �1

J = 0

Figure 2.2: One-dimensional MOT model for a J = 0 $ J = 1 transition. The large arrowsrepresent a pair of right-handed circular (rhc), red detuned laser beams (~!L) whose polar-ization changes from �� to �+ with respect to B which is chosen as the quantization axis.

the above limits for saturation and atomic velocity, the Zeeman shifts �ÆZ (eq. 2.32)with the limit jÆZ j � � must also be included. Now the mean scattering force in theMOT is given by1

hFsc;toti(z; v) = hFsci(ÆL + vkL � ÆZ(z)) � hFsci(ÆL � vkL + ÆZ(z)) (2.35)

� � v � � z; (2.36)

with [144]

� =�0

kL

��dBdz�� (2.37)

1For Jg = 0$ Je = 1 all Clebsch-Gordan coefficients are equal to 1.


which is the force of a damped harmonic oscillator (�0 is defined in eq. 2.32). Thedamping constant is the same as for the molasses in eq. 2.34. The spring constant� is connected to an oscillation frequency

p�=M which typically is of order 102 s�1.

Since this is much smaller than the damping rate =M the motion of atoms in thepotential is strongly overdamped. The spatial capture range zc within which atoms canbe trapped is defined by the condition jÆZ(z)j < jÆLj and is typically in the mm range.The depth of the trap, i.e. the capture range in velocity space, can be estimated byconsidering that atoms with the maximum allowable velocity vc must be slowed downin a distance � zc while experiencing the maximum scattering force ~kL�=2 of thecounterpropagating beam. Typical values for vc are a few m/s, corresponding to trapdepths around 1 K.

The 1D configuration of a MOT can be extended to 3D. The configuration of themost commonly used 6-beam MOT is shown in figure 2.3. A quadrupole field withconstant field gradients near the center is generated by a pair of coils with equal butopposite currents, and three orthogonal laser beam pairs provide for 3D cooling andconfinement. Due to the rotational symmetry of the coils (and Maxwell’s equationr �B = 0), the field gradients are dBx=dx = dBy=dy = �(1=2) dBz=dz:

B

rhc

rhc

rhc

rhc

lhc

lhc I

I

x

y

z

Figure 2.3: 3D 6-beam MOT configuration. All beams traveling towards the trap center are ��

beams (the direction of B is chosen as a quantization axis). The situation in the radial planecorresponds to the 1D model; for the axial direction, the beams are left-handed circular (lhc)because of the opposite direction of B

Momentum diffusion and Doppler temperature. The fluctuations of the scatteringforce discussed in section 2.1.1 are connected to a heating process that counteractsthe produced by the net friction force. Considering a 1D molasses, eq. 2.33, the forceacting on a single two-level atom including fluctuations is then given by

Fsc;tot(t) = � v(t) + ÆFsc;tot(t) (2.38)


Using the definition of the force fluctuations, eq. 2.29, this equation can be transformedinto the following equation for the velocity v of the atom,

d

dtv = �( =M) v + (

pDsc;tot=M) G(t); (2.39)

where M is the mass of the atom, and G(t) is defined by hG(t)i = 0 and hG(t)G(t0)i =2g(t � t0). The momentum diffusion coefficient

pDsc;tot has already been discussed

above. This stochastic differential equation is the so-called Langevin equation knownfrom diffusion theory [145]. A solution can be given in terms of the probability distri-bution function p = p(v; t) for the atom to have velocity v at time t. For the case of aMarkov process g(t� t0) � Æ(t� t0), i.e. for vanishing correlation time �c, this functionis defined by the Fokker-Planck equation [145]

@

@tp =

2Xn=1

�� @

@v

�nD(n)p; (2.40)

with D(1)(v) = �( =M) v and D(2) = Dsc;tot=M2. For laser cooling the Æ-correlation

is a reasonably good approximation when �c = ��1sc is much smaller than the dampingtime �d =M= , as is generally the case. For the stationary case @p=@t � 0, the Fokker-Planck equation yields

pv(v) =1

�vp2�

e�v2=(2�2v) with �v =

qDsc;tot=( M) ; (2.41)

which has the form of a 1D Maxwell-Boltzmann distribution for thermal equilibriumwith temperature T for which

�v =pkBT=M (2.42)

This formalism for the description of the molasses is the same as for Brownian motion[145]. However the molasses is an open system far from thermal equilibrium (thelaser photons and vacuum fluctuations cannot be considered as a thermal reservoir).The “temperature” T is therefore simply defined as a measure for the width of pv.

By equating �v in eqs. 2.41 and 2.42 and plugging in the values for Dsc;tot and according to eqs. 2.30 and 2.34 one obtains

kBT =Dsc;tot

=

~�

8

1 + (2Æ=�)2

jÆj=�Æ=��=2�! ~�

2� kBTD (2.43)

The minimum temperature TD is called the Doppler temperature [143], and the corre-sponding velocity width �v � vD the Doppler velocity.

Density distribution in a MOT. As described above, the force in the simple MOTmodel describes a strongly overdamped harmonic oscillation that would lead to a alocalization of atoms at the trap center in the absence of fluctuations. When the forcefluctuation term is included in eq. 2.35, it can be shown, again in analogy to Brownian


motion that the density distribution p = p(z; t) for atoms in the overdamped limit canbe described by a Fokker-Planck equation of the form of eq. 2.40 with the stationarysolution of a Gaussian [145] 2 (the force fluctuation term is the same as that for themolasses because to first order, the total scattering rate is constant everywhere in thetrap):

pz(z) =1

�zp2�

e�z2=(2�2z ); where �z =

pkBT=� (2.44)

The temperature T is the same as that of the molasses. In a 3D MOT p = p(x; y; z; t) isanisotropic because of the anisotropy of the magnetic field gradient.

The single-atom discussion can be extended to a cloud of atoms trapped in theMOT. If the atoms can be treated independently (which is the case for low densities),the density in a MOT increases linearly with the atom number N . This is called the“temperature limited regime” as the volume of the trapped cloud is only determinedby the trap temperature. The cloud then has a Gaussian shape3 with center density

n0 =N

�x�y�z(p2�)3

: (2.45)

However, for densities n0 > 1010 cm�3, collective optical effects (photon reabsorp-tion and beam attenuation [150]) start to become important. In this “multiple scatter-ing regime” [25] the independent-atom approach breaks down and the density staysconstant while the volume grows linearly with the atom number4.

MOT loading and decay. The evolution of the local density n(r; t) in the MOT isdescribed by [152]

@

@tn = l � �n� �n2 (2.46)

Here, l accounts for the loading of atoms into the trap, e.g. from a slow atomic beam,and the second and third terms with constants � and � describe one-body and two-body losses, respectively. The one-body losses in a MOT arise from collisions with hotbackground-gas atoms that are in thermal equilibrium with the walls of the vacuumchamber (at pressures � 10�8 mbar, the rate � � 1 s�1).

2It is important to note that even though it looks as if eq. 2.44 could also be obtained from eq. 2.41 bysimply applying the equipartition theorem, this is not justified as the system is not in thermal equilibrium;in fact the velocity distribution pv(v) and therefore the mean kinetic energy are the same everywhere inthe trap.

3For imperfect beam alignments, shapes deviating from the Gaussian can be observed, such as cloudswith interference fringes [146] (see also the discussion of the MOST) or clumps and rotating rings [147,148,149].

4A third (yet transient) regime, is the “two component regime” that can be reached by compressing aMOT in the multiple scattering regime by rapidly increasing the magnetic field gradient [151]. The cloudthen spills out into the high magnetic field region without polarization gradient cooling.


In the temperature limited regime, eq. 2.46 can be integrated spatially and thensolved for the center density n0(t) (which is directly connected to the atom numberN(t) via eq. 2.45). The beginning of the loading process for an initially empty trap ischaracterized by

d

dtn0 = L=V (t! 0); (2.47)

where L is the total loading rate and V � (p2�)3�x�y�z. With increasing density, the

trap losses become larger, and finally the density reaches a steady state

n0;st =p

[�=(2�0)]2 + L=(V �0) � �=(2�0); (2.48)

with �0 = �=(2p2). For large L with L=(�0V ) � [�=(2�0)]2, this density scales withp

L. The trap decay, characterized by L � 0, is given by

n0(t) =n0(0)

e�t (1 + n0(0)�0=�) � n0(0)�0=�: (2.49)

The decay becomes exponential n0(t) / e��t for long times or for n0(0)�0=�� 1.

Polarization gradient cooling. The Doppler temperature is the cooling limit for thetwo-level atom. For atoms whose ground state consists of two or more Zeeman sub-states, additional cooling mechanisms due to polarization gradients in the laser fieldcan come into play that lead to lower temperatures. Such mechanisms were firstobserved in 1988 by Lett et al. [26] and described in 1989 by Dalibard and Cohen-Tannoudji in an intuitive model [18].

In the so-called “lin?lin” configuration, the 1D molasses beams have orthogonallinear polarizations (cf. fig. 2.4). The superposition is then a stationary gradient ofalternating linear and circular polarizations. The simplest model system to illustratethis mechanism is an atom with a J = 1=2 $ 3=2 transition. At a position with ��

polarization the population for the atom at rest is optically pumped to the j12 ;�12 i

substate. At the same time this state experiences a larger negative light shift than j12 ; 12 idue to the difference in the Clebsch-Gordan coefficients and is therefore the lowestenergetically.

For low saturation s (cf. eq. 2.25), the rate for optical pumping is of order �p � s �and therefore can be arbitrarily small. If the atom is allowed to move out of the ��

region before getting pumped, the internal energy of the atom increases at the cost ofits kinetic energy, and the light shift of the other sublevel finally exceeds the shift ofthe occupied one. If optical pumping then occurs at such a point, the emitted photonis bluer than the absorbed one, and therefore energy is dissipated. In the next cycle,the atom then runs up the potential hill again, this time in the other substate, getspumped, and so on. Because of the analogy to the Greek myth this scheme is alsocalled Sisyphus cooling. The ultimate limit of this cooling scheme is given by the recoilvelocity vR = ~kL=M arising from the emission of the last photon5.

5The recoil limit can be overcome with the methods of velocity-selective coherent population trapping(VSCPT) [29] and Raman cooling [30].


............

............

............

z0 �=8 �=4 3�=8 �=2 5�=8 3�=4

lin linlinlin �� +

j 12; 12i

j12;12i

j 12; �1

2i

j12;�

1

2

i

j12;�

1

2

i

j 32; 12ij 3

2; �1

2i j 3

2; 32ij 3

2; �3

2i

11 1

3

1

3

2

3

2

3

Ener

gy

Figure 2.4: Illustration of the Sisyphus cooling scheme for a J = 1=2 $ 3=2 transition (thenumbers in the level scheme give the squares of the Clebsch-Gordan coefficients).

For the limit of large detuning ÆL � � and low intensity !R � �, it can be shown[18] that the damping coefficient is � �~k2L(ÆL=�) and that the diffusion coefficientis dominated by the dipole force fluctuations, Ddip � (~kL)

2!2R=� such that

kBT = Ddip= �~!2RCjÆLj (2.50)

where C = 8 from a more exact calculation [18].A second 1D configuration is the “�+��” molasses formed by two circularly polar-

ized (both right-handed or left-handed) counterpropagating laser beams. In that case,the polarization gradient consists of a spatially rotating linear polarization, and thereare no light shifts, such that Sisyphus cooling does not occur. However as the atommoves along the beam direction, it sees a temporally rotating polarization vector. ForJg � 1 this induces an alignment of the substates that changes the radiation-pressurebalance such as to slow down the motion of the atom [18]. Here the friction coeffi-cient is given by � �~k2L(�=ÆL) which is much weaker than for Sisyphus cooling, butthis is in turn compensated by a weaker diffusion coefficient that is exclusively due tofluctuations in the photon emission and absorption rates. From this, an equilibrium ofthe form of eq. 2.50 results, with C � 10.

For 3D �+�� molasses and 3D MOTs with uncontrolled relative phases the lightfield from the interference of the 6 laser beams contains mainly �+ and �� regionsand the stronger Sisyphus mechanism dominates [144]. Close to the recoil limit the


atoms start getting localized in the light shift potential wells. When the light shiftpotentials are reduced below a critical value the channeling of atoms in the potentialleads to a breakdown of friction, which is connected to an abrupt increase of tem-perature [153, 154]. The achievable minimum kinetic energies turn out to be oneorder of magnitude above the recoil limit, in agreement with experimental observa-tions [155,156,157]. Polarization gradient cooling is very sensitive to the ground-statesublevel Zeeman shifts [143] which must not exceed the light shifts. Nevertheless, in3D MOTs temperatures close to those for a molasses can be reached [158,27].

Optical dipole traps. Laser-cooled atoms can be stored in optical dipole traps (ODTs)formed by local extrema of a laser field [5,34]. Depending on the sign of the detuningof the laser light from the atomic resonance, atoms can be confined in maxima (reddetuning) or minima (blue detuning) of the field intensity. Such traps allow for co-herent storage of atoms since for a given potential the spontaneous scattering rate cansuppressed by increasing both the detuning and the intensity of the laser. ODTs aretypically up to a few 100 �K deep and allow for storage of up to several minutes [159].In macroscopic (weakly confining) ODTs, the potential varies on a length scale that islarge compared to the atomic de Broglie wavelength, and the atomic motion in thosetraps is classical. The simplest (macroscopic) ODT can be realized in the focus of asingle red-detuned Gaussian laser beam, as was first shown in 1986 [32]. Tight con-finement is provided in optical lattices [5] which are produced through the interferencebetween laser beams. The interference gives rise to a periodic sinusoidal intensity mod-ulation typically on the length scale of an optical wavelength. The confinement in theresulting periodic array of microscopic potential wells generally is comparable to the deBroglie wavelength of the trapped atoms, and the atomic motion is strongly quantized,giving rise to a band structure.

In our experiments, we have trapped atoms in the optical potential of a red-detunedstanding light wave formed by the reflection of a Gaussian laser beam. This trap ischaracterized by tight confinement in one dimension and weak confinement in theother two, and thereby forms a planar waveguide for atoms. A more detailed discussioncan be found in chapter 5.

2.1.3 Reflection of Atoms from an Evanescent Wave

Evanescent waves. The simplest evanescent-wave atom mirror [38, 39] is realizedby total internal reflection of a blue-detuned laser beam at an interface of a bare glassprism (dielectric number "1). The evanescent wave gives rise to a repulsive opticalpotential at which incident atoms can be reflected.

Let the laser beam be incident in the 0x0z plane with wave vector k � kL at anangle �i beyond the critical angle �c = arcsin

p"1 (cf. fig. 2.5). By applying Snell’s law,

the propagation of the field on the vacuum side of the interface, E(r; t) = E0 exp[ik �


xy

zI(z)" = 1

" = "1 > 1

�i

atom

Figure 2.5: Evanescent-wave mirror realized by total internal reflection in a glass prism

r� i!t], is characterized by wave vector components

kx =2�

�

p"1 sin �i ; ky = 0 ; kz = i

2�

�

p"1 sin

2 �i � 1; (2.51)

where � is the vacuum wavelength. This is an evanescent wave characterized by anexponential decay into the vacuum and a running component parallel to the surface.The decay length of jEj2 in the z direction is given by

� =1

2 jkzj =�

4�

1p"1 sin

2 �i � 1: (2.52)

For a Gaussian beam with power P , a 1=e2-radius (waist) w � � and lateral intensityprofile

I(d) = I0 exph� 2d2

w2

iwith I0 =

2P

�w2; (2.53)

that is reflected at the interface symmetrically about r = 0, the intensity of the evanes-cent wave above the surface is given by

Iev(r) = Iev;0(x; y) e�z=� with Iev;0(x; y) = FI0 exp

h� 2x2

(w= cos �i)2� 2y2

w2

i: (2.54)

The profile parallel to the surface is a Gaussian spot with waists w perpendicular andw= cos �i > w parallel to the plane of incidence of the beam. The factor F (“inten-sity enhancement factor”) connects the surface intensity of the evanescent wave in thecenter of the Gaussian spot to the peak intensity of the incident laser beam. The ana-lytical expression (which can be obtained from Fresnel’s formulae [160]) describes anenhancement of the field intensity that depends on �i as well as on the polarization ofthe wave. Typical maximum values reached with BK7 glass at the critical angle are wellbelow 10. Large intensity enhancement factors for the realization of evanescent-wave


atom mirrors can be achieved by resonant amplification. The highest factors F � 103

have been demonstrated with dielectric layer systems on the prism [161]. Anotherpossibility is the use of thin metallic films coated on the surface. Such films are usedfor the resonant excitation of surface plasmons (see below).

Optical potential of the evanescent wave. The dipole potential for the atom mirrorcan be obtained directly from the discussion of the dipole force. In the far blue-detunedlimit, ÆL � !R, and for a two-level atom initially in the ground state which evolves intothe dressed state j1i, the dipole potential is given by

UEWM;dip = +~�2

8ÆL

Iev;0(x; y)

ISe�z=� : (2.55)

For the state j2i it has the opposite sign, i.e. it corresponds to an attractive force6.

Atom-surface interaction. Near a surface, the modification of the vacuum field dis-tribution changes the radiative properties of a nearby atom. The general solution forthis quantum-electrodynamical problem in the case of a conducting surface is givenin [162], and the special case of a two-level atom (transition wavelength �) is ad-dressed in [163], including a discussion of important limits. For small atom-surfacedistances, z � �=(4�), the interaction is determined by the electrostatic interactionof the fluctuating atomic dipole with its instantaneous mirror image, giving rise to theattractive van der Waals interaction

UvdW = � 1

4��0

1

16z3[hgjd2�jgi+ 2hgjd2z jgi] (2.56)

for the ground state, where d� and dz are the components of the dipole moment paralleland perpendicular to the surface. It can be shown that an equal shift results for theexcited state. For large distances, z � �=(4�), the interaction is given by a position-dependent Stark shift produced by the modified vacuum field mode density near thesurface. This gives rise to the attractive Casimir-Polder interaction7

UCP = � 1

4��0

3~c

8�z4�0 ; (2.57)

for the ground state, where �0 = �2jhejdjgij2=(3~!) is the static polarizability of theatom. The shift of the excited state in that case is dominated by an oscillatory contribu-tion (around zero) that also depends on the dipole orientation and vanishes for z !1,similar to the energy of a classical dipole antenna in its own reflected radiation field.

6For an ground-state atom incident with velocity vinc, the repulsive potential holds for the reflection aslong as the atom evolves adiabatically in the state j1i. This requires (1) the scattering time ��1

21to be long

compared to the time spent in the evanescent field, and (2) the absence of motion-induced, nonadiabatictransitions between the dressed states (vinc=� � Æ which is typically fulfilled for laser-cooled atoms).

7Casimir and Polder [164] originally interpreted this interaction as a retarded van der Waals interac-tion.


For intermediate distances the van der Waals ground-state shift agrees with the generalsolution [162,163] to within a factor of 2 for z < 0:12�, while the Casimir-Polder shiftis the better approximation beyond that point.

The case of multilevel atoms can be treated by including the contributions fromthe different optical transitions with frequencies !eg [162]. The variance of thedipole is then hgjd2jgi =

Pe jhgjdjeij2 = 3��0~c

3P

e �eg=!3eg, where the last equal-

ity is the Weisskopf-Wigner theorem [140]. The static polarizability is then given by�0 = �2Pe jhejdjgij2=(3~!eg).

Total potential. The total potential of the evanescent-wave atom mirror is deter-mined both by the optical potential and the attractive atom-surface interaction as dis-cussed in the next paragraph. Close to the surface it can be written as

UEWM = UEWM;dip + UvdW (2.58)

to a good approximation8. As illustrated in figure 2.7, the short-ranged atom-surfaceinteraction leads to a reduction of the maximum potential value UEWM;dip(0) (for theoptical potential only) to Umax at a position zmax, which must be determined numeri-cally. This value defines the maximum kinetic energy an incident atom can have classi-cally in order to be reflected.

-2

10

2

4

6

8

0.2 0.4 0.6 0.8 1

UEWM;dip

UvdW

Umax

zmax

distance from surface [�]

pote

ntia

l[~�]

Figure 2.6: Illustration of the total reflection potential of the evanescent-wave mirror formetastable argon used in our experiments for the parameters of the 1s5 $ 2p9 (812 nm)transition (the sublevel structure is neglected) as the sum of the optical potential and the vander Waals interaction in the electrostatic approximation. The evanescent field is characterizedby � = 333 nm and F = 114, and the (local) intensity in the excitation laser beam is 100mW/cm2.

2.1.4 Generating Evanescent Waves with Surface Plasmons

Surface plasmons [165] are coherent charge fluctuations propagating along the surfaceof a metal film, i.e. of the metal(" = "2)-dielectric(" = "3 = 1) interface. They are

8The simple algebraic summation requires the potentials to be independent which is the case if therelative level shift between the ground and excited state due to the atom-surface interaction is smallcompared to the detuning of the evanescent wave. For metastable argon and detunings ÆL � 2�� 1 GHz,this condition breaks down for distances below 50 nm [43] (where the total force is already attractive).


accompanied by evanescent fields on both sides j of the interface. For surface plasmonspropagating along 0x in the z = 0 plane, it can be shown [165] that the fields have theform E(r; t) = (Ex;j; 0; Ez;j) exp[ikj � r� i!t] with

kx;j =2�

�

r"2"3"2 + "3

� kx ; ky = 0; kz;j = (�1)j�1 2�

�

s"2j

"2 + "3: (2.59)

The metal’s dielectric number "2 = <"2+i ="2 for a given optical frequency ! in generalhas a large negative real part9 �<"2 � "3. As a consequence, both components kz;jperpendicular to the surface have a large imaginary part which leads to evanescentdecay both into the vacuum and into the metal. The vacuum intensity decay length asdefined above is given by � = 1=(2=kz;3), which by using "3 = 1 simplifies to

� =�

4�=p"2 + 1: (2.60)

Because of damping in the metal, ="2 > 0, the intensity of the surface plasmons alsodecays in the propagation direction with a 1/e damping length (2=kx)�1 which is con-nected to the resistive heating inside the metal.

E

"1

"2

"3

�sp

Figure 2.7: Evanescent-wave mirror realized by the resonant excitation of surface plasmonsvia attenuated total internal reflection (ATR) of a p polarized laser beam, also known as theKretschmann configuration [167].

The setup for the resonant optical excitation of surface plasmons on the surface ofa metallic film on a glass prism is shown in figure 2.7. In this so-called Kretschmannconfiguration [167], a p polarized beam of frequency ! is incident at an angle �larger than the critical angle in the glass ("1) and generates an evanescent field withkx(�) = 2�=�

p"1 sin � that penetrates into the film ("2), thereby coupling to the surface

plasmons. For a resonant excitation at a given !, the wave vector kx can be matched tothe required value of the surface plasmon by adjusting the angle of incidence (as kz;3 isimaginary, kx must exceed 2�=�

p"3 which explains why a dielectric "1 > "3 is needed

for this kind of optical excitation). For the surface-plasmon resonance angle � = �spand perfect matching of the film thickness, all power is absorbed and dissipated in thefilm10, in the form of heat and straylight [165].

9In the Drude model for the free electron gas, "2(!) = 1�(!P =!)2 [166], where the plasma frequency!P lies in the UV for metals.

10The surface-plasmon evanescent wave that penetrates back into the film transforms into a traveling


Surface plasmons - intensity enhancement. The field intensity enhancement fac-tor F (�i) for the Kretschmann configuration can be calculated by propagating awave through the interface system and applying Fresnel’s formulae at each inter-face [160,168]:

For the regions i between the interfaces (i = 1: glass, i = 2: metal, i = 3: vac-uum/air) one can decompose the p-polarized electric field E into components E+;�

i

propagating in upward (+) and downward (�) directions (assume that the film has hor-izontal orientation). The field amplitudes immediately below and immediately abovethe metal film then are related by�

E+1

E�1

�= T �

�E+3

E�3

�; (2.61)

where the matrix T = T (�i) describes the transmission of the fields through the inter-face system. T can be written as

T = T(1;2) � �(d2) � T(2;3); (2.62)

where the matrices T(i;i+1) describe the field behavior at the interfaces and �(d2) de-scribes the field transmission through the metallic film (thickness d2),

T(i;i+1) =1

2p�i

��i + �i �i � �i�i � �i �i + �i

�; �(d2) =

�eik2d2 00 e�ik2d2

�:

In these expressions, the �i = "i="i+1 relate the dielectric numbers on either side ofthe single interfaces, and so do the �i = kz;i=kz;i+1 for the wave vector componentsperpendicular to the surface. These are given by ki;? = 2�

�

p"i � "1 sin

2 �i. Now, sincethere is no interface above the surface, E�

3 � 0. Setting E+3 � 1, one obtains

F �� E+

3p"1 E

+1

��2

=1

"1

�� 1

T11

��2

and R ��E�

1

E+1

��2

=

��T13T11

��2

: (2.63)

Surface plasmons - straylight. Due to surface corrugations z = s(R), hsi = 0, thenon-radiative surface plasmons can decay into straylight by scattering at surface im-purities. Often (as in our experiments) this is an unwanted effect that needs to beminimized. In the following we concentrate on the case of a small rms surface rough-ness � =

phs2i as compared to the optical wavelength � = !=(2�c). This case has

been discussed by Henkel et al. [169] for the case of a dielectric evanescent-wavemirror, however this also applies to the case of surface plasmons11. The scatteredfield amplitude E(1)

2 is linearly related to the Fourier spectrum of the surface profile,S(Q) =

Rd2R s(R)e�iQ�R , by [169]

E(1)2 (K0) = (2�)�1S(K0 �K) f(K0)E2; (2.64)

wave at the interface with the glass. This wave interferes destructively with the totally reflected wave fromthe excitation laser beam. For the optimum film thickness, the interference is completely destructive.

11A more general description for surface plasmons can be found in Ref. [165].

2.2. EXPERIMENTAL APPARATUS 29

where f(K0) = 2�(ip

(e0!=c)2 � jK0j+(2�0)�1) is an electromagnetic scattering factor,E2 denotes the evanescent field amplitude at the surface and K0 �K is the in-planewave-vector transfer between the the incident waveK � (kx; 0) and the scattered waveK0 = (k0x; k

0y). For cases where the final wave vector jK0j � k2, we then have �kx < 0

(see the previous section) which means that the surface plasmon has lost its evanescentcharacter and has decayed into a straylight photon.

For a description of the straylight intensity profile above the surface, one has to takethe finite spot size of the excitation laser beam into account. It can be shown that thestraylight intensity, averaged over the surface roughness spectrum, is the incoherentsum over Gaussian laser beams (t w � � ) propagating into the vacuum above theprism,

Isc(r) =ZjK0j�k2

d2K0

(2�)2(2�)�2 S(K0 �K) jf(K0)j2 E2

2 G(K0; r); (2.65)

where G(K; r) = exp[�2(R � zK=kz)2=w2] is the profile of a Gaussian beam centered

around (x; y) = 0 that is scattered in the direction of K. Under the assumption ofisotropic scattering, S(K0 �K) jf(K0)j2 � const, integration yields [137]

Isc(0; 0; z) = I2

��eff2�

�2 1� z2ez

2=w2

w2E1(z2=w2)

!(2.66)

for points on the axis above the spot center, where I2 = jE2j2 = FI0cos� is the spotcenter intensity at the surface, �eff = [(k22=4�)Sjf j2]1=2 is an effective rms roughness,and E1(x) =

R1x dt e�t=t is an exponential integral [170].

The straylight intensity therefore is proportional to the square of the surface rough-ness. It approaches a constant value at the surface and decays on a scale given by thelaser spot radius w.

2.2 Experimental Apparatus

2.2.1 Argon

Our experiments were carried out with 4018Ar (natural isotopic abundance: 99.6%), a

bosonic atom without nuclear spin and electronic hyperfine structure. The electronicground state has the closed-shell configuration 1s22s22p63s23p6, and the lowest elec-tronic excitation possible requires more than 11 eV for an electron to be transferredfrom 3p to higher shells nel. Due to its large distance from the core, the excited elec-tron couples with the core only weakly. The coupling is described in the jl (or Racah)approximation [171]: the angular momentum L and spin S of the core couple to amomentum j which couples with the angular momentum of the excited electron l toa momentum K which, finally, couples with the excited electron’s spin s to the totalangular momentum J. A complete description of the singly excited state is then givenby the Racah notation 2s+1Ljnel[K]J . A simplified spectroscopic description is given


by the Paschen notation Nlr(J), where N labels the shell configuration, and r countsthe states in the configuration with decreasing energy.

The level scheme of argon with the lowest-lying excitations (to the 4s and 4p shells)using Paschen notation is shown in figure 2.8. The scheme is divided into a left and

2p1

1s2

1s13p

6

3 4p s5

3 4p p5

23

3

4

4

5

5

0

0

1

1

1

1

3212

0

2

12

6789

1 0

J=

J=

{

{

j = 1/2 j = 3/2{ {

J=0

812 nm

715 nm795 nm

105 nm

Figure 2.8: 4018Ar energy levels in the 3p6 (ground state), 3p54s and 3p54p configurations [171]

with transitions relevant for our experiments (Paschen notation).

right side according to the core momenta j = 1=2 and 3=2, corresponding to the singletand triplet sides for LS coupling, such as e.g. in helium. There are four states 1s2:::;5 inthe 4s configuration (the momentum number J is omitted for simplicity) and ten states2p1;:::;10 in the 4p configuration. As an exception to the rule, the term 1s1 is attributedto the ground state. The transitions between these two configurations are in the nearinfrared. Intercombination transitions between the two sides that change the state j ofthe core are weak. In the 4s configuration the states 1s3 and 1s5 are metastable. Thelifetime of 1s5 has been measured to be 38+8�5 s [172]. For the state 1s3 a value of 45 shas been predicted [173].

In our experiments, the closed 1s5 $ 2p9 transition at 812 nm was used for lasercooling and atom reflection in the MOST. The weak intercombination line from 1s5 to2p4 at 715 nm was used for optical pumping to the state 1s3, with a pumping efficiencyof 56% (with 42% probability, the state 2p4 decays to the state 1s2, which subsequentlydecays to the ground state under emission of a 105 nm UV photon with a lifetime of 2ns. The decay of 2p4 back to 1s5 contributes with 2% probability). The open 1s3 $ 2p4transition at 795 nm was used for far-off resonance optical trapping and manipulationof 1s3 atoms in the waveguide. Properties of these transitions are listed in table 2.1.


1s5(J = 2)$ 2p9(J = 3) �0 = 811.757 nm [174](MOST) A = 33:1� 106 s�1(�8%) [174]

= � (closed transition)IS = 1:29 mW/cm2

TD = 127 �KvD = 17 cm/sTR = 361 nKvR = 1.2 cm/sh1s5jd

2j1s5i = 2:0� 10�57 (Cm)2 [174]�0 = 4��0 � (44:7� 0:9)� 10�30 m [175]

1s5(J = 2)$ 2p4(J = 1) �0 = 714.903 nm [174](optical pumping) A = 0:625� 106 s�1(�8%) [174]

IS = 0:036 mW/cm2

1s2(J = 1)$ 2p4(J = 1) �0 = 852.381 nm [174]A = 13:9� 106 s�1(�8%) [174]

1s4(J = 1)$ 2p4(J = 1) �0 = 747.322 nm [174]A = 0:022� 106 s�1(�8%) [174]

1s3(J = 0)$ 2p4(J = 1) �0 = 795.036 nm [174](waveguide) A = 18:6� 106 s�1(�8%) [174]

IS = 0:77 mW/cm2

�0 = 4��0 � (49:5� 1:0)� 10�30 m [175]

Table 2.1: Properties of optical transitions in 4018Ar for experiments in laser cooling: �0 =

vacuum wavelength; A = Einstein A coefficient; � = linewidth, IS =(effective) saturationintensity; TD = Doppler temperature; vD = Doppler velocity; TR = recoil temperature; vR =recoil velocity; �0 = static polarizability.

In trapped atomic ensembles, the metastability of the 1s3 and 1s5 states gives riseto strong collisional losses that limit achievable densities to around 109 cm�3. Thelosses are dominated by Penning processes Ar� + Ar� ! Ar + Ar+ + e� and associativeionizations Ar� + Ar� ! Ar+2 + e�. With an argon MOT, one generally is well in thetemperature-limited regime. For our standard MOT parameters12, the value for thetwo-body loss constant � for collisions between atoms trapped on the 1s5 $ 2p0 tran-sition is � � 1� 10�8 cm3s�1. The values for � in the case of collisions between atomsthat are optically trapped on the 1s3 $ 2p4 transition appear to be of the same order ofmagnitude [110]. The same holds for ”two-species” collisions between atoms trappedon the 1s5 $ 2p9 and 1s3 $ 2p9 transitions (cf. chapter 5).

12The collisional loss rate generally depends on the laser beamparameters because of the influence oflight-induced molecular interaction potentials [6]. We determined � = (1:4�0:2)�10�8 cm3s�1 [177] inmeasurements on a 6-beam MOT with detuning ÆL = �8 MHz, single-beam intensity = 22 mW cm�2 andmagnetic field gradient b = 5 G cm�1. This value agrees with results obtained in previous measurements[178].


1

-2J = 2

J = 3

(812 nm)

-2

-1

-1

0

0

1

1

2

2 3-3

1

J = 0

J = 1

(795 nm)

-1

0

0 1

1 1 1

-2J = 2

J = 1

(715 nm)

-1

-1

0

0

1

1

2

11

mJ =

mJ =

mJ =

mJ =

mJ =

mJ =

1

2

1

2

1

2

1

2

1

6

1

6

2

3

2

3

2

3

2

5

2

5

1

3

1

3

8

15

8

15

3

5

1

15

1

15

1

5

1

5

Figure 2.9: Kastler diagram for the J = 0 $ J = 1, J = 2 $ J = 1 and J = 2 $J = 3 transitions used in the experiments, containing the the squares of the Clebsch-Gordancoefficients [176].

2.2.2 Beam Machine and Laser System

Beam machine. The experiments were performed in the atomic beam machineshown in figure 2.10. A beam of metastable 1s5 argon atoms is generated in a DCdischarge source [179] cooled with liquid nitrogen. The beam is collimated in a 2Doptical molasses at 812 nm with multiple beam recycling [180] and is decelerated witha counterpropagating laser beam at 812 nm in a �+�� Zeeman slower [181]. Thepressure difference between the source chamber (2 � 10�5 mbar) and the main UHVchamber (5� 10�9 mbar) is maintained by differential pumping.

The atom source emits 2 � 1014 1s5 atoms/(s sr) corresponding to an excitationefficiency of 10�4. The velocity distribution of the cooled source is characterized byhvi = 300 m/s and hvi=�v = 2:5. The Zeeman slower transforms this distribution intoa slow 1s5 beam in which 70% of the atoms have a velocity below 30 m/s. The 2D trans-verse laser cooling stage is realized in a separate chamber behind the source [182,183]and typically yields a 20-fold enhancement of the beam intensity, resulting in loadingrates in the main chamber of around 107 atoms/s for a standard [184] argon MOT. Theatom beam can be shuttered electro-mechanically behind the collimation stage. Thelarge main chamber (inner diameter 45 cm, height 28 cm) houses the experimentalsetup, several pressure gauges and a mass spectrometer. The atomic beam machine isdescribed in detail in [178] where also a characterization of the Zeeman-slowed atomicbeam can be found.


atomic beamsource

beamcollimation

Zeeman slower

atom detectormain chamber

prism

turbomolecular pumpsLN2 baffle

oil diffusion pumps

0 0.5 m 1 m

Figure 2.10: Schematic of the beam machine.

Laser system. The laser system used in our experiments is depicted in figure 2.12.Laser beams were needed for a variety of purposes including transverse atomic beamcollimation (ABC), atomic beam slowing (ABS), magneto-optical trapping (MOT), re-flection from the surface (EWM), internal transfer from 1s5 to 1s3 via optical pumping(OP), trapping in the waveguide (WG) and local detection (WGD). The laser setup islocated on a laser table in a separate temperature-stabilized room, and single-modefibers are used to guide the light to the beam machine.

For the 812 nm transition we modified the setup used in previous experiments[184,182,185] by turning the ABC laser into a master laser for injection-locking [186]the three slave lasers ABS, MOT and EWM which are frequency detuned by means ofacousto-optic modulators (AOMs)13. The ABC laser (output power: 13 mW, detun-ing +9 MHz) is a commercial external-grating cavity diode laser (TUI DL-100 with aSharp LTO16MFO diode) that is stabilized to the 1s5 $1p9 transition via Doppler-freesaturation spectroscopy (cf. [187]) in a RF argon discharge cell. The injection-lockedslave lasers are single-mode high-power laser diodes (SDL 5422-H1) operated at apower of about 100 mW each [184, 188]. The seeding of the ABS and MOT diodes isdone with part of the ABC light at a detuning of -161 MHz. The beam emitted fromthe MOT diode, before entering the fiber, is shifted close to resonance with an AOMwhose frequency and power can be controlled externally via PC [184]. We have set upan additional feedback-loop stabilization for the MOT beam power. This is achieved byreferencing the MOT beam to a photodiode behind the fiber and regulates to better that1% within 10�s. The ABS beam enters the fiber without an additional frequency shift.A part of this beam, after being shifted to +687 MHz in a quadruple pass through anAOM (single-pass efficiency > 90%), is used as an injection beam for the EWM diode.

The OP laser for the 715 nm transition is a cryogenic external grating cavity diode

13Previously a separate master laser had been used, however its frequency stability was too poor for thestringent requirements in the experiments with the MOST.


sourcechamber

beamcollimation

Zeeman slower

Main chamber

Optics setup

oil diffusion pumps

turbomolecular pumpsL N

baffle2

1 m

Figure 2.11: View into the beam machine lab.

laser [184,185] that is stabilized to the transition by means of optical double-resonancespectroscopy (cf. [187]), for which a part of the frequency-modulated spectroscopybeam from the ABC laser is used. The diode setup is located in a liquid nitrogen cryostatwhich is used to lower the emission wavelength of the laser diode (Sharp LTO30MDO)from 750 nm at room temperature down to 715 nm. This laser is operated at 1.5mW. Due to the boiling of liquid nitrogen in the cryostat the laser has a mechanicalfrequency jitter of about 20 MHz [184].

The WG and WGD beams for the 795 nm transition are generated with a single-mode Ti:Sapphire ring laser (Coherent 899-21) that is pumped by an argon ion laser(Coherent Innova 400). The Ti:Sapphire laser is locked to an external cavity and hasan experimentally measured drift around 20 MHz per minute. The WG and WGDbeams behind the fiber are limited to about 300 mW each by stimulated Brillouinscattering [189] in the monomode fiber. This can be exploited for a passive stabilizationof the beam power. The WGD beam is fed into the same fiber as the EWM beam with anorthogonal linear polarization, and behind the fiber the beams are separated again witha polarizing beam splitter cube. The available beam powers for the ABC, ABS, MOT andOP beams after the fiber outputs are 3 mW, 12 mW, 8 mW and 100 �W, respectively. TheMOT laser beam power is switched by controlling the corresponding AOM power, andthe other laser beams are switched with commercial electro-mechanical shutters behindthe fiber within 100�s after a delay of about 2 ms. The experimental reproducibility is


. . -. . -

Lam

bda

met

er

WG

-1+

1

+1

-1

+1

EW

M

AB

S

WG

D

MO

T

OP

AB

C

ArI

lase

rT

i:S

apphir

eri

ng

lase

r

81

2n

m(M

OS

T:

MO

Tb

eam

s)

81

2n

m(M

OS

T:

evan

esce

nt-

wav

em

irro

r)

71

5n

m(o

pti

cal

pu

mp

ing

)7

96

nm

(wav

egu

ide)

79

6n

m(W

Gd

efo

rmat

ion

/det

ecti

on

)

81

2n

m(a

tom

icb

eam

coll

imat

ion

)

81

2n

m(a

tom

icb

eam

slo

win

g)

MO

T

EW

M

OP

WG

WG

D

AB

C

AB

S

. . -

mir

ror

lase

rd

iod

e

mai

nb

eam

seed

bea

m/

spec

tro

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py

bea

md

iag

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Cd

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RF

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erco

up

ler

AO

Mfr

eq.

(MH

z)d

iffr

acti

on

ord

er

op

t.d

iod

e/

Fo

tod

iod

e

Fab

ry-P

ero

t

curr

ent

div

ider

Far

aday

iso

lato

r

spec

tro

sco

py

cell

bea

msp

litt

er

flip

mir

ror

mir

ror

lift

sph

eric

alle

ns

cyl.

len

s

po

l.b

eam

spli

tter

cub

e

anam

orp

hic

pri

smp

air

hal

fw

ave

pla

te

qu

arte

rw

ave

pla

te

cav

ity

dio

de

lase

r

spec

tru

man

aly

zer

71

+m

od.

60...1

00

80

+1

71

212

85

Figure 2.12: The laser system for experiments with metastable argon.


in the range of a few �s.

Data acquisition. The experiments using the beam machine are typically performedby sequentially stepping the shutters for the atomic beam, the laser beams, the mag-netic field and the power and detuning values of the MOT beams, as well as settingtriggers for data acquisition devices. Depending on the signal-to-noise ratio, individualsequence runs were typically repeated from 10 to up to 10000 times. For this purposeour sequence PC runs the control software ISAMES [184] that allows the user to de-fine sequences with minimum step durations of 35 �s. To make the sequence controlmore flexible, we use additional self-built digital delays in the output lines, e.g. for thecompensation of individual differences between the shutter delays. The control PC isconnected via trigger lines to two auxiliary PCs that control the CCD camera and theatom detector. The CCD camera (Sony CV-M10BX with a Inspecta-2S frame grabbercard from Microtron GmbH) has a 1/2“ chip with a spatial resolution of 736� 581 pix-els and a dynamical resolution of 8 bit. The camera is asynchronously triggerable, andthe control software [177] can be used to sum up images or to immediately save themto hard disk. The atom detector consists of an electron optics that allows to imageatomic arrivals on the surface onto a multichannel plate detector. The setup and theproperties of the atom detector are described in the next chapter.

2.2.3 The Surface

An important part of the experimental apparatus is a gold-coated prism surface locatedin the main chamber. It was used as a mirror for the MOT beams of the magneto-opticalsurface trap (cf. chapter 4), as a negatively biased conversion electrode for the atomdetector (as described below), and for the generation of the surface-plasmon enhancedevanescent fields for the MOST’s evanescent-wave atom mirror (EWM) and for opticalpumping (OP) and local detection (WGD) in the waveguide experiments (cf. chapter5).

2.0cm

Figure 2.13: The gold-coated prism surface. The prism is mounted to the surface atom detector(cf. chapter 3) with alumina rods.

Preparation. The mirror surface was prepared by thermal evaporation of a gold filmonto the 2 cm � 2:8 cm hypotenuse face of a clean, right-angle isosceles BK7 glass


prism (Melles Griot 01PRB019). Gold as a coating material combines favorable opticalproperties in the IR with high thermal and chemical stability14, and smooth surfacescan be grown. To improve the adhesion of the gold film on the prism, we coveredthe prism face with a few monolayers of chromium before depositing the gold film.The depositions were performed at room temperature and a background pressure of3�10�6 mbar prior to deposition in a commercial vapor deposition machine (Univex-450). The deposition rate for the gold film was held at about 2 nm/s and and a filmwith a thickness of around 45 nm (as measured with an oscillating crystal probe) wasproduced to optimize the surface-plasmon resonance at 812 nm for the evanescent-wave atom mirror.

R(t)

P-pol.

41 41.5 42 42.5 43 43.5 440

1

2

3

4

5

6

7(a) (b)

photo diode

galvanometer

�i(U)

U

U

refle

cted

inte

nsit

y

R

[a.u

.]

angle of incidence �i[Æ]

Figure 2.14: Characterization of the surface plasmon resonance. (a) – Setup to measure thereflected intensity as a function of the angle of incidence. (b) – Experimental ATR curve for812 nm, together with the curve fit from the transfer matrix model.

Optical properties. The dielectric numbers of the gold film and the properties ofthe evanescent fields above the surface were determined by recording surface plasmonresonance curves. For this purpose we built a setup with which the reflected intensityR could be recorded as a function of the angle of incidence �i of a collimated beam(cf. figure 2.14 (a) ). The measurement for an incident 812 nm beam in the BK7 glassprism is shown in figure 2.14 (b), together with a fit of eq. 2.63 to the data. The resultsfor the dielectric numbers of the gold film and the parameters of the evanescent fieldsat 812 nm (EWM), 796 nm (WGD) and 715 nm (OP) are listed in table 2.2.

The straylight intensity distribution above the gold film resulting from the radiativedecay of the surface plasmons was measured, for the excitation with a 812 nm laserbeam of waist w = 0:67 mm, by scanning a photodiode over the surface at differentheights. Experimental results are shown in figure 2.2.3 together with theory curves

14In previous experiments we had also tried silver coatings which, despite their superior optical proper-ties, were subject to rapid thermal degradation at high laser powers and yielded much rougher surfaces.For those coatings, the ratio of evanescent-field to straylight intensities was more than an order of magni-tude worse than for the present case.


�0 [nm] "2 �SP [o] � [nm] F

812 -29.6 + i 0.99 42.4 333 114796 -27.9 + i 0.90 42.6 316 111715 -25.5 + i 2.96 42.7 277 32

Table 2.2: Dielectric numbers of the gold film and resonance angle �SP, field intensity decaylength �, field intensity enhancement factor F of the evanescent fields obtained from the fit ofthe model eq. 2.63 to the measured ATR curves. The fits consistently yield a film thickness of41� 1 nm.

Iz

Isc

0(0

,)

/[%

]

0 1 2 3 4 5 6

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

w = 0.67 mm

PD

()

[norm

.]I

x,z

sc

Lateral position [mm]xHeight [mm]z

0 105-10 -5

1

0

0

10

1

z= 1.0 mm

z= 4.0 mm

z= 7.0 mm

Figure 2.15: Characterization of the straylight distribution above the surface resulting fromsurface-plasmon decay. A photodiode was scanned over the surface in the lateral and normaldirections. (a) – Straylight intensity above the spot center (relative to the intensity of theincident beam) vs. distance from the surface. The data points correspond to a measurementwith a photodiode with an area of 2�2 mm2 and a directional characteristics �(�) � cos(�). Thedotted line is a fit of eq. 2.65 averaged numerically over the these quantities; the solid line givesthe corresponding on-axis intensity Isc(0; z) ( eq. 2.66). (b) – Normalized results of lateralscans (along the surface plasmon propagation direction) at different heights z, together withnormalized theory curves Isc(x; z). The measurement shows that the scattering is isotropic.

of the model, eq. 2.66. The lateral scans at different heights show that the straylightdistribution is indeed isotropic, which justifies the assumption made in the theory. Froma fit of the theory to the data, we deduce a maximum straylight intensity Isc(0) =(7 � 1) � 10�3I0, corresponding to an effective surface roughness of �eff = (6:0 �0:3) nm. For a comparison we characterized the surface with a scanning atomic forcemicroscope. From these measurements we deduce a rms roughness of about 1 nmon the sampling area of 16 � 16 �m2, from which one would expect a much smallerstraylight intensity. It therefore is likely that the main part of the scattering is dueto the presence of gold clusters and/or dust on the surface that were not statisticallyaccessible in the measurement.

The reflectivity of the gold film for laser beams at 812 nm and 795 nm was deter-mined, by direct measurement, to be about 96%.

Chapter 3

Surface-Assisted Detection of Ar�

We have studied an experimental scheme for the detection of argon atoms in themetastable 1s5 and 1s3 states at a gold-coated surface. Based on this scheme wehave demonstrated a method for 3D time-of-flight spectroscopy of laser-cooledmetastable atoms.

3.1 Introduction

For our experiments with metastable argon close to a prism surface, an efficient detec-tion scheme can be realized by letting the atoms collide with the gold-coated surface.Upon impact, the metastable states decay to the electronic ground state, and singleelectrons are ejected out of the metal which carry information about the time andlateral position of the single-atom impact events. These electrons are imaged ontoa detection element with temporal and spatial resolution using an electrostatic lenssystem. Our detector was originally designed by M. Hartl [185] after that described inRef. [190] and has already been used in earlier experiments [110,111]. For the presentwork, which placed greater demands on the detector, it was modified to improve its per-formance, and subsequently characterized and calibrated using atom-optical methods.These measurements are described in the following subsections, after a brief summaryof the principles and technical realization of the detector. As a physical “byproduct” wehave also determined the hitherto unknown electron yield for the 1s3 state of argon ata gold surface (cf. Ref. [191]).

3.2 Experimental Scheme

Overview. The surface atom detector is shown in fig. 3.1. The electron optics of thedetector consist of a column of hollow electrodes set to different voltages. The surface,a 40 nm thick gold film deposited onto a glass prism, is held at negative voltage and actsas a conversion electrode from which the ejected electrons are accelerated upward tothe grounded entrance electrode. The open aperture of the electrode forms a divergent

39

40 CHAPTER 3. SURFACE-ASSISTED DETECTION OF AR�

+ 3 kV

e-

tube lens

tube lens

hole lens

conversionelectrode

PosA

HBM

Trig

PreA

RAEMCPs

Ar*

detectionunit

L1

L2

L3

L4

U1

U2

d

D

(a) (b)

l

l

Figure 3.1: The surface atom detector. (a) – The electron optics. The cylindrical electrodes aremade of polished stainless steel and are mounted to alumina rods. The unit also includes coilsand mirrors used for the realization of the magneto-optical surface trap and the waveguide. (b)– The components of the detector. The gold-coated prism surface acts as a conversion electrode(U1 = �4:56 kV) for incident metastable argon atoms. The electrons are accelerated towardsthe hole lens in the grounded entrance electrode (d = 3 mm, L1 = 15:6 mm), and two tubelenses (U2 = �2:76 kV, l = 0:8 mm, D = 10 mm, L2 = 15:8 mm, L3 = 20:8 mm) are then usedto image the electron emission pattern onto a detection unit (L4 = 315 mm). This unit consistsof a stack of two multichannel plates (MCPs) with a resistive area element (RAE). After pre-amplification (PreA) the signal of the RAE is digitized in a position analyzer (PosA) and storedin a histogramming buffer memory (HBM). The data acquisition and readout of the HBM iscontrolled with a PC.

3.2. EXPERIMENTAL SCHEME 41

(a) (b) (c)

metal metal metal

M* M* M*adsorbate

E+EF

�

e-

E*

�

e- e-

Figure 3.2: Deexcitation mechanisms for metastable atoms M* at a metallic surface: (a) Reso-nance ionization followed by Auger neutralization, (b) Auger deexcitation, (c) Penning ioniza-tion of adsorbates.

hole lens [192] behind which two convergent tube lenses [192] are used to image theelectrons onto a multichannel plate (MCP). In our earlier experiments, one of the mainshortcomings of the electron optics was severe image distortion due to inhomogeneitiesin the acceleration field (cf. Ref. [111]). In the present work, this effect was reducedsubstantially by using a prism with a linear surface extension much larger than the 3mm aperture of the hole lens and by reducing the distance between the prism and thehole lens.

The detection unit consists of a stack of two multichannel plates(MCPs) in a chevronconfiguration and a resistive area element (RAE). Each incident electron produces a lo-calized charge avalanche which is deposited onto the RAE. This generates currents atthe four contacted corners of the RAE, encoding the position of the electron. The pro-cessing of the signal is done with a commercial system (2502A Position Analyzer and3300/2500 Series Imaging Detector System, Quantar Technology, Inc. (Santa Cruz,California)). The imaging detector system consists of a pre-amplifier (PreA), a posi-tion analyzer (PosA) where the analog signal is digitized, and a histogramming buffermemory (HBM) for data storage. The HBM is controlled and read out by PC, and theHBM data are subsequently processed with a self-written MATHEMATICA package thatcontains the results of the experimental calibration.

Atom-to-electron conversion. The most fundamental aspect of the detection schemeis the conversion of metastable atoms into electrons at the surface. In general, two maindeexcitation mechanisms for metastable atoms at an atomically clean metallic surfacecan be distinguished [193,191]. For large work functions � the atom (internal energyE�) can undergo resonant ionization, followed by Auger neutralization if the recombi-nation energy E+ � 2�, as shown in figure 3.2 a. Without an empty resonant state inthe metal, e.g. when � is too small, the excited electron can still be ejected by Augerdeexcitation, cf. figure 3.2 b. For adsorbate-covered surfaces, Auger deexcitation withadsorbed molecules (i.e. Penning ionization of the adsorbate) can become dominant,cf. figure 3.2 c.

A crucial parameter is the electron yield % of an atom at the surface, where % is


defined as the average number of electrons emitted per metastable atom. A survey ofdifferent metastables and metals is given in Ref. [191]. From our experiments with agold film (� = 5:1 eV), a stable and constant value % = %0 > 0:14 for both metastable1s5 (E� = 11:5 eV) and 1s3 (E� = 11:2 eV) states can be deduced, as will be explainedfurther below.. On the time scale accessible with the detection unit the electron emis-sion process can be considered instantaneous (typical time scales are 10�13s [194]).The maximum kinetic energy of the electrons is given by " = (E� � �) � 7 eV.

Imaging with the electron optics. The components of the electron optics are dis-cussed in detail in Refs. [190,185]; therefore only some very relevant aspects are sum-marized here.

Electrons ejected at a point P on the surface at varying angles follow classical,parabolic trajectories in the homogeneous acceleration field. In the plane of the holelens in the entrance electrode, the bundle of trajectories lies within a circle of diameterÆ = 4L1

p"=(eU1) � 2:4 mm (using the parameters of fig. 3.1). Due to the finite

aperture d = 3 mm of the hole lens, trajectory bundles originating from points P atmore than 0:6 mm distance from the optical axis get truncated, giving rise to a positiondependence of the local detection efficiency. A second consequence of the spreading isa blurring of points in the image plane of �x � L1"=(eU1) � 24 �m [195]. However,this blurring is a negligible contribution compared to the resolution of 100 �m imposedby the detection unit.

The hole lens in the entrance electrode acts as a thin divergent lens with focallength f � �4L1 [192]. Together with the parabolic spreading of the trajectories itacts to displace the origin P downward to a virtual origin P 0 at a distance L1=3 belowthe surface. The tube lenses between the adjacent electrodes can be described by ABCDray transfer matrices T = T( ) with focal lengths and principal plane positions thatdepend on the ratio of the potentials of the adjacent electrodes between which thetube lenses are realized (cf. Ref. [190]). Using standard light-ray ABCD matrices [196]H for the hole lens and Pi for free propagation (distances 4/3 L1, L2, L3, L4), theelectron optics is described by

M = P4 T( �1r ) P3 T( r) P2 H P1; (3.1)

where r = U1=(U1 � U2). The matrix M relates input rays with axis distance ri andslope r0i to output rays ro,r0o according to t(ro; r

0o) = M t(ri; r

0i). Focusing is reached

for a given voltage U1 by adjusting U2 such that M12 = 0. The linear magnificationis then given by M = M11. For U1 = �4:56 kV a numerical calculation using theexpressions of Ref. [190] for the matrix T yields a focusing voltage of U2 = �2:85 kVand a magnification of M = 3:4. This is comparable to our experimentally determinedvalues as described below.

Detection and data acquisition. Both the PosA and HBM units impose limitationswhich are important for the performance of the detector. In the setup, we used HOT1

1HOT = “high-output technology”

3.3. CHARACTERIZATION OF THE DETECTOR 43

MCPs (Burle Electro Optics, Inc.) with an active diameter of 25 mm. These MCPsare characterized by a small recharging time [197] and allow for count rates around106 s�1 on the area of a single electronic bin of the RAE. However, the maximumallowable overall count rate for error-free analog-to-digital conversion is one order ofmagnitude lower due to the contribution of statistical coincidences2. At a rate of 1 �105 s�1 for incident electrons, the counting error is less than 5%; yet at 1:5�106 s�1 theoverall count rate is already suppressed by a factor of 2. In our experiments involvingthe magneto-optical surface trap, care had to be taken to keep the count rate lowenough to avoid such errors.

The spatial resolution of the MCP/RAE unit is specified to 250 �m, which corre-sponds to a resolution of � 100 �m on the surface. The 20-bit HBM unit is configuredas to store the incoming data in a temporal sequence of 64 images with 128 pixels x128 pixels spatial resolution each. The time interval between the single images is freelydefinable, and the start of the entire sequence can be triggered. Splitting a single runinto two 32-image sub-sequences for a main run and a reference run is possible, aswell as a summation over multiple experimental runs. The HBM’s temporal resolutionis limited to a minimum exposure of 20 �s per recorded image.

3.3 Characterization of the Detector

For the characterization of the detector, we performed in-situ experiments with atomsfrom a magneto-optical trap realized above the surface, combined with an evanescent-wave atom mirror (A discussion of these components can be found in chapters 2 and4).

3.3.1 Focusing, Length Calibration and Spatial Resolution

In order to determine the focusing voltage and to characterize the spatial imagingproperties of the electron optics, a test object (i.e. a well-defined electron emissionpattern) needed to be created. This experimentally challenging problem was solvedby using an evanescent-wave surface-plasmon atom mirror at 812 nm with spatiallymodulated reflectivity that was illuminated with 1s5 atoms released from a MOT. At thepositions of high intensity, atoms did not collide with the surface and no electrons wereejected. In this way, the electron emission pattern could be obtained as the “negative”of the optical intensity distribution of the atom mirror.

The structured mirror was realized by diffracting the EWM beam at an absorptiongrating and then imaging the diffraction pattern onto the gold film using a cylindricallens, as shown in figure 3.3. Absorption gratings were realized with the help of alaser printer on transparent foils, with periods p = 0:6 mm : : : 3:0 mm and slit widthsa = p=2. The corresponding imaged diffraction patterns then had fringe separations of1.0 mm: : : 200 �m. As a result of the finite diameter of the EWM beam, only a small

2Single charge pulses must be separated by at least 300 ns, otherwise one pulse or even both pulses(for separations below 100 ns) are discarded [198].


cyl. 750 mm

absorptiongrating

MOT

w ~ 1 cm

E

�1.5 �0.75 0 0.75 1.5

x � mm �

�1.5

�0.75

0

0.75

1.5

y�

mm

�

�Cts. � % �

0.

25.

50.

75.

100.(a) (b)

EWM

Figure 3.3: (a) – Experimental setup for creating a test object for the atom detector. A blue-detuned laser beam (waist 1 cm) is diffracted from an absorption grating and used to forman evanescent-wave atom mirror (EWM) with spatially modulated intensity. The diffractionpattern is imaged onto the prism with a cylindrical lens (f = 750 mm) at the surface-plasmonresonance angle. When the surface is “illuminated” with atoms released from a MOT, the in-tensity fringes lead to a local reflection of atoms and thus to a suppression of the electronemission. (b) – Measured distribution for a 1.5 mm-period grating, resulting in a stripe sepa-ration of 400 �m (the length scale of the image has been calibrated accordingly). The countsin the displayed field of view represent the relative change in the distribution compared to thecase for which the mirror beam is blocked.


number of slits were illuminated, and typically only the 0th and 1st order fringes hadenough intensity to reflect atoms (which was sufficient for our purpose, however). Asa criterion for focusing, the visibility of the stripe patterns was measured for differentvoltages U1 and U2. The best values were obtained for U1 = �4:56 kV and U2 =�2:76 kV. The ratio of these values deviates by only 3% from the calculation3. Anexample for a measured pattern is shown in fig. 3.3 (b).

From the test-object measurements, the length scale of the detector was determinedto be (14 � 1) pixels/mm. Since in the image plane 128 pixels correspond to the 25mm active diameter of the MCP, this yields a magnification of the electron optics ofM = 2:7 � 0:2. If one calculates the magnification for the chosen set of voltages, oneobtains a similar value of M = 3:0.

The smallest diffraction pattern that could be realized experimentally had a 200 �mperiod, a value only slightly above the effective, full reflective width of the evanescentintensity fringes4. This pattern could still be resolved in the center of the field of view;however its visibility reduced by 50% when shifted to the outer regions, indicatinginhomogeneous focusing. Another distortion is apparent in the slight curvature of thestripes, in contrast to the optical intensity distribution. Such effects, which were alsoobserved in Ref. [190], are probably due to residual inhomogeneities in the electricacceleration field or insufficiently compensated magnetic fields.

3.3.2 Detection Efficiencies for the 1s5 and 1s3 States

Spatial profile. As discussed above, the local detection efficiency of the detector isexpected to vary with the distance from the optical axis due to the truncation of theelectron trajectory bundles. In addition, there can be a contribution from the MCPitself, e.g. due to contamination by dust particles. We determined the detection effi-ciency profile of the focused detector by comparing a known physical arrival distribu-tion with the corresponding recorded electron emission pattern. For this purpose, aMOT located on the symmetry axis of the electron optics with a temperatures of about200 �K parallel to the surface was prepared, and the ballistically expanded Gaussianarrival distribution was recorded 30 ms after release at which time the Gaussian � was5.5 mm. The efficiency profile was deduced from 104 experimental runs by comparingthe calculated and measured arrival distributions and is shown in fig. 3.4. The profiledeviates from cylindrical symmetry, probably as a result of residual inhomogeneities inthe electric acceleration field or insufficiently compensated magnetic fields inside themain chamber. Also, variations in the electron yield of the MCP cannot be excluded(a similar profile behavior was observed in Ref. [190]). This profile was used as a

3In order to minimize the spreading of the trajectories between the surface and the hole lens, onewould like to choose jU1j as large as possible, which also requires larger values for jU2j. However, forvalues of jU2j above 2:8 kV, spark discharges would occasionally occur between the tube lens electrodes.

4The reflective width depends on the atomic velocity distribution arriving at the surface which is timedependent for a released MOT cloud. In the experiment, we averaged over the entire time-of-flightspectrum.


0 10 20 30 40 50 600

10

20

30

40

50

60

x [pixel]

y[p

ixel

]

Figure 3.4: Contour plot of the experimentally determined detection efficiency profile of theatom detector (the contours are equally spaced, the black region corresponds to zero counts).The visible diameter of the recorded distribution (� 40 pixels) corresponds roughly to thediameter of the hole lens aperture. The “field of view” of the detector is defined operationallyas the circle centered about pixel (32,32) with radius 23 pixels.

dynamical normalization for all subsequent experiments5.

Detection efficiency for 1s5. The absolute detection efficiency for 1s5 atoms (E� =11:5 eV) was determined from the arrival distribution of a MOT with known position,temperature and atom number. The atom number was determined from fluorescencemeasurements and carries a 30% uncertainty from the effective Clebsch-Gordan cou-pling coefficient. By comparison of the calculated and measured arrival distributions(cf. the section on the TOF method further below), the efficiency of the atom detectorwas found to be (5:5 � 1:6)% averaged over the field of view with a local maximumof (14:4 � 4)%. At the same time this maximum is the lower bound for the physicalelectron yield %(1s5).

The case of metastable argon (1s5) at a gold-coated substrate has previously beenstudied in Refs. [199, 200] in a 10�7 mbar environment. The measured values werefound to be in a wide range between 0:7% to 4:4% (at 300 K) and 26% (at 360 K),which the authors ascribe to the presence of adsorbates, in particular water, that wereremoved by heating. Given the low pressure of less than 10�9 mbar in our experimentand considering the relatively high and stable value for %measured, it can be concludedthat the role of adsorbates in the deexcitation process in our case was small.

5An additional electronic artifact was compensated first. The fast analog-to-digital converters (separatefor the x and y directions) in the position analyzer exhibit nonlinearities that result in a variation of thewith of neighboring electronic bins of up to 50% and give rise to a pronounced small-period modulationpattern. This pattern was independently assessed by defocusing the detector completely, such that aphysically smooth and slowly varying distribution was obtained over the whole active area of the MCP.The modulation was extracted from the data by applying high-frequency linear filters to the measureddata until it just disappeared. By comparing the smoothed distribution with the data, local compensationfactors c(xi; yj) = c(xi)� c(yj) for the data bins (i; j) were then calculated and subsequently used for anormalization of all measurements.


�s5

�s3

500 µs

OP

MOT

EWM

CCD

Figure 3.5: Scheme for the measurement of the electron yield for 1s3 atoms. An optical pump-ing pulse is applied to atoms trapped in a MOT above the surface, releasing a defined fractionof 1s3 atoms. Residual 1s5 atoms are shielded from the surface with an evanescent-wave atommirror.

Detection efficiency for 1s3. The detection efficiency for 1s3 atoms is important forexperiments that involve the storage of atoms in the optical potential of the atomwaveguide. Compared to the case of 1s5 atoms, the efficiency can be expected tobe directly connected to the electron yield % for the electron emission process. Theinternal energy of E� = 11:2 eV for 1s3 is only slightly lower than for 1s5(11:5 eV) suchthat differences in the imaging of the ejected electrons can be neglected.

In the literature the yield %(1s3) for argon has so far only been measured for astainless steel surface, for which it was found to coincide with %(1s5) to within anexperimental uncertainty of 6% [201]. On the other hand, in a comparison of 1s5 to2p9(13:1 eV) at a chemically clean gold surface, differences in the electron yield of upto a factor of 4 were observed [200], which indicates the possibility of a strong energydependence, depending on the nature and state of the surface. Therefore it seemeduseful to test the case of 1s3 atoms at the gold film experimentally.

To determine %(1s3), the following scheme was used. First a MOT (containing 1s5atoms) was prepared above the surface. A short optical pumping pulse at 715 nmwas then applied, transferring a defined fraction of the 1s5 atoms to the 1s3 state. Forthese atoms the electron emission was then measured, and the detection efficiencywas obtained by a comparison of the counts with the number of pumped atoms. Thepractical realization of this scheme is shown in fig. 3.5. The MOT was turned offimmediately after applying the 500 �s long pumping pulse (this was necessary sincethe atom detector does not work when the magnetic field of the trap is on). Themixture of ballistically expanding 1s3 and 1s5 atoms was then “filtered” for 1s3 atomsat the surface by using the 812 nm evanescent-wave atom mirror to repel the 1s5 atoms(the residual 1s5 transmission was (0:7� 0:2)%.

To get the electron yield, we first determined the relative decrease in the cloudfluorescence caused by the 715 nm pumping pulse of duration 500 �s. The decreasewas determined to be �1s5 = (253 � 3) � 10�3 in the experiment. The error bar is


time [ms]

B-switch

ABco

unts

0 1 2 3 4

Figure 3.6: Suppression of the detector overall count rate in the presence of the magneticquadrupole field of the MOT. The surface was illuminated by the atomic beam at grazing inci-dence while the B field was switched electronically. When the field is on, the count rate dropsto 1� 10�3. The rise and fall times of about 300 �s agree with measurements using a test coil.

given by fluctuations in the MOT light intensity. Using the branching ratio for opticalpumping to 1s3, q = 0:561 � 0:05 (which is obtained from the transition rates givenin [174]), the fraction of 1s3 atoms in the cloud is then deduced to be �1s3 = �1s5q =0:142 � 0:01. Next, we compared the arrival spectra for the case with and withoutthe pumping pulse (in the latter case the atom mirror was not turned on). Whilethe first measurement is sensitive to the fraction of pumped 1s3 atoms, the secondmeasurement yields the arrival distribution of 1s5 atoms from the MOT. By comparingthe total number of counts, the 1s3 signal was found to be 0:144 � 0:01 of the 1s5signal. Here the uncertainty is determined by a slight difference in the shape of thearrival distributions (both temporally and spatially) due to the finite duration of thepumping pulse and the photon momentum kicks in the optical pumping process. Bycomparing atom detector and CCD measurements, one therefore finds that

%(1s5)=%(1s3) = 0:98 � 0:1: (3.2)

Therefore the detection efficiency of the atom detector for 1s3 atoms is indeed the sameas for 1s5 atoms.

3.3.3 Sensitivity to Magnetic Fields

When the quadrupole field of the MOT is turned on (field gradient 5 G/cm), the countrate is suppressed almost completely (to a fraction of 1 � 10�3), as illustrated in fig.3.6. On the one hand, this forbids measurements on a MOT in the stationary state.On the other hand it can be employed for gating the detector during data acquisition,thereby only exposing part of the triggered sequence of HBM pages to the electron flux.This proved to be a very useful feature for the measurement of the loading and decaycurves of the atom waveguide.

3.4. APPLICATION: 3D TIME-OF-FLIGHT MEASUREMENTS 49

3.4 Application: 3D Time-of-Flight Measurements

A standard technique for measuring the temperatures of trapped atoms is the time-of-flight (TOF) method [26]. A probe laser beam passing at some distance below atrapped atom cloud is usually employed to monitor the arrival signal for atoms afterthe trap is turned off. After release, the atom cloud expands ballistically according toits velocity distribution, and from the probe fluorescence signal the temperature canbe deduced. For metastable rare gas atoms, a MCP below the trap is usually employedinstead of a probe laser beam. By using the surface atom detector it is now possibleto implement TOF measurements with spatially resolved resolution. This allows todirectly assess the 3D velocity distribution in the trap. On a practical side, it providesan excellent method to test the detector calibration.

Ballistic expansion and TOF signal. For an atomic cloud trapped in a MOT thespatial and velocity distributions along any axis 0x through the center of the trap aregiven by

px(x) =1

�0p2�

e�x2=(2�2

0); pv(v) =

1

�vp2�

e�v2=(2�2v); (3.3)

where �v =pkBT=M defines the temperature T of the cloud along 0x. At a given time

t after release, atoms originating from a position x0 with initial velocity v have movedto the position x = x0 + vt + 1

2 �gt2, where �g denotes the on-axis gravity component.

Taking the initial distribution of velocities into account, the spatial distribution for theatoms released from x0 is given by

px0(x; t) = pv(v)dv

dx=

1

(�vt)p2�

e�(x�x0�1

2�gt2)2=(2(�vt)2) (3.4)

The spatial distribution function after the time t for the entire cloud is obtained fromthe contribution from all positions x0 in the initial spatial distribution, i.e. by theconvolution

px(x; t) =

Z 1

�1dx0 px(x0)px0(x; t) =

1

�x(t)p2�

e�(x�1

2�gt2)2=(2�2x(t)); (3.5)

where

�x(t) =q�20 + (�vt)2: (3.6)

During the ballistic expansion the Gaussian shape of the cloud is maintained, howeverthe variance �x increases with time, depending on the temperature T .

To get an expression for the TOF signal produced at the prism surface, Cartesiancoordinates f0xig = f0x; 0y; 0zg, are introduced with 0z pointing downward to thesurface along the optical axis of the detector. First of all, the ballistically expanded


spatial distribution at time t is given as the product pr(r; t) =Q

i pxi(xi; t), where pxand py are defined as in eq. 3.4 6. To calculate the distribution pz perpendicular tothe surface, the upper integration limit must be chosen as zc instead of 1, where zcis the height of the Gaussian density maximum above the surface, as there cannot beany atoms below the surface. This is irrelevant as long as zc � �z(0), yet it becomesimportant for low clouds zc � �z(0) for which the Gaussian profile is “truncated” bythe surface. The TOF signal, up to a constant amplitude factor, is then simply given bythe evolution of the spatial distribution at the plane of the surface,

TOF(x; y; t) = pr(r; t)jz=zc=

1

(2�)3=2�x(t)�y(t)�z(t)exp

h� x2

2�2x(t)� y2

2�2y(t)� (zc � 1

2gt2)2

2�2z(t)

i

�1

2

�1 + erf

h(g�z(0)2 + 2zc�2v)tp

2 �v�z(0)�z(t)

i�; (3.7)

where the quantity �v;z is the variance of the velocity distribution along 0z, g =9:81 m=s2, and �x, �y and �z are defined along the coordinate axes analogously asin eq. 3.6. From this spectrum, the temperatures Tx; Ty and Tz of the cloud can bededuced.

Experiment. For the experiment, a MOT with zc = (665�30) �m and �z(0) = (170�2) �m (as determined from a Gaussian fit to the cloud fluorescence measured with theCCD camera) was prepared above the surface. The data acquisition of the detector wastriggered upon release of the cloud when the MOT light and the magnetic quadrupolefield were turned off.

For the analysis of the experimental data TOFe(xi; yj; tk), the marginal distributionsTOFx(xi; tk) =

Pyi

TOFe; TOFy(y; t) =P

xiTOFe and TOFz(t) = maxxi;yj (TOFe) are

considered. To determine the temperatures Tx;y, the distributions TOFx;y are first fittedwith 1D Gaussians (in accordance with eq. 3.7), yielding variances �x;y(t). A fit ofeq. 3.6 to these variances then yields Tx;y. To determine the temperature Tz, thedistribution TOFz is fitted with TOF(0,0,t) as given in eq. 3.7, with Tz as a free fitparameter. The measured sequence of detector images is shown in fig. 3.7 (a). Thededuced distributions TOFx, TOFy and TOFz are shown in fig. 3.7 (b), (c) and (d),respectively. The weighted least-square fits yield temperatures Tx = (49� 1) �K, Ty =(41 � 1) �K parallel to and Tz = 36+6�4 �K perpendicular to the surface. The fit curvesare shown as solid lines7.

For a consistency check, temperatures were determined alternatively from strobo-scopic fluorescence measurements of the variance �(t) using the CCD camera (as de-scribed in ch. 4), along the axis 0z and along an axis at 45Æ between 0x and 0y along the

6An alternative derivation of this formula is given in Ref. [202] on the basis of a Green’s function.7Due to the finite detector resolution �D(� 100 �m), the measured variances �M exceed the physical

values �P according to �M =p�2P + �2D. However, this does not affect the temperatures when fitting eq.

3.6.

3.4. APPLICATION: 3D TIME-OF-FLIGHT MEASUREMENTS 51

0 1 2 3 4 5 60

0 1 2 3 4 5 6

0.45

0.5

0.55

0.6

0.65

0.7

loca

lpea

kval

ue

3.53.02.52.01.51.0t=0.5 ms 4.0 4.5 5.0 5.5 6.0 ms

counts0

x

y

0 1 2 3 4 5 6

0.4

0.5

0.6

0.7

-1.5 1.5x [mm]

TO

Fx

-1.5 1.5y [mm]

TO

Fy

(a)

(b) (c) (d)

�x

[mm

]

�y

[mm

]

t [ms]t [ms] t [ms]

Figure 3.7: Ballistic TOF data of an atom cloud released from a MOT at a height zc = (665�30) �m above the surface, obtained from a summation over 800 measurement runs. (a) –Excerpt of the sequence of 64 detector images, showing every fifth image. (b) and (c) – Fittedvariances �x and �y of the Gaussian marginal distributions along the x and y directions. Theinsets show typical TOFx;y distributions obtained by summing over centered windows of 40pixels � 14 pixels, with the long side along x and y, resp. The solid curves are weighted modelfits that yield temperatures Tx = (49� 1) �K and Ty = (41� 1) �K. (d) – Local peak values ofthe TOF data obtained from a summation over the four brightest pixels. The fit of the model,shown as a solid curve, yields a temperature Tz = 36+6

�4 �K perpendicular to the surface.


viewing direction. This leads to values Tz;Cam = (28�2) �K, and Tw;Cam = (38�5) �K,which are comparable results.

3.5 Conclusion

We have studied a detection scheme for metastable atoms at a surface with atom-optical methods. This scheme is based on the imaging of secondary electrons releasedfrom the surface upon impact of single atoms. We have separately determined the de-tection efficiencies for the metastable 1s5 and 1s3 states of argon. This has allowed usto access the hitherto unknown electron yield for the 1s3 state at gold surfaces, whichwas found to coincide with that for the 1s5 state at a value � 14%. We have demon-strated a method for time-of-flight spectroscopy of ultracold atoms in three dimensions.

The properties of the detector can be summarized as follows. The detector has acircular field of view of 3 mm diameter, a spatial resolution of about 100 �m and anelectronically limited temporal resolution of 20 �s. The single-atom detection efficiencynear the center of the field of view is 14%. The maximum allowable overall atom fluxwithout significant counting errors is � 1� 106atoms/s.

Chapter 4

Magneto-Optical Surface Trap

We have realized and studied a novel magneto-optical surface trap (MOST) formetastable argon atoms. This hybrid trap combines a magneto-optical trap with anoptical evanescent-wave atom mirror. It allows us to laser-cool and trap atoms incontact with the evanescent field that separates the atomic cloud from the surfaceby only a fraction of an optical wavelength. In the experiment, we were able totrap (1:3� 0:4) � 105 atoms in the MOST with a lifetime of (390� 30) ms, whichwas limited by collisions with the surface.

4.1 Introduction

In laser cooling and trapping [203], one of the most common configurations is themagneto-optical trap (MOT), first demonstrated in 1987 by Raab et al. [24]. The MOThas been intensely studied and improved in the last decade [25] and today is a standardinitial step for experiments that involve trapping and cooling of neutral atoms. Theusual design consists of three mutually orthogonal pairs of counterpropagating laserbeams that intersect at the zero of a quadrupole magnetic field (cf. chapter 2). Variantshave been described that match special design needs of experiments [204, 205, 206,207] and more recently, MOT geometries have been realized to prepare atom cloudsclose to surfaces [129, 126], following work by Lee et al. [131] and ourselves [111].The loss of atoms from a MOT close to a surface was examined in Ref. [208].

The reflection of atoms from a blue-detuned optical evanescent wave, suggested in1982 by Cook and Hill [38], was first demonstrated in 1987 by Balykin et al. [39] withatoms from a grazing-incidence thermal beam, to be followed by experiments with coldatoms from a MOT [40, 41, 44]. In these experiments, the evanescent field that buildsup when a laser is totally internally reflected at a glass-vacuum interface was used.In other experiments, surface plasmons [42, 43] (cf. chapter 2) and dielectric layersystems [161] were employed to resonantly enhance the evanescent field.

A combination of the two techniques, i. e. a MOT in contact with an evanescentfield that separates the atomic cloud from the surface by only a fraction of an opticalwavelength, is useful for the realization of a reservoir of cold atoms close to a surface.

53

54 CHAPTER 4. MAGNETO-OPTICAL SURFACE TRAP

It allows for the implementation of a continuous loading scheme for the planar sur-face matter waveguide demonstrated by us in an earlier work [110]. In the followingdescription this configuration is called a magneto-optical surface trap (MOST). Prelim-inary results on the MOST, which is realized with metastable argon on the 1s5 $ 2p9transition at 812 nm, can be found in Refs. [188,111].

This chapter is organized as follows. The next section introduces the basic conceptsand the configuration of the MOST, and the third section discusses a simple model forits physical properties. The fourth section is devoted to the experiments, in which theproperties of the trap and its components are studied.

4.2 Configuration of the MOST

The magneto-optical surface trap (MOST) discussed in the following is a hybridtrap that combines a magneto-optical trap (MOT) with an evanescent-wave surface-plasmon atom mirror (these components are discussed in chapter 2). In order to bringa magneto-optically trapped cloud close to a mirror surface, one first needs to find asuitable beam configuration. For geometrical reasons it is clear that the standard 6-beam MOT configuration (cf. fig. 2.3) is not suited for such a purpose since inevitablyone or more beams would get chopped by the mirror surface 1. The basic idea forgetting around this problem is to use the surface itself to generate MOT beams byreflection.

2D representation. The principle can best be illustrated by starting in 2D with thestandard 6-beam configuration as depicted in fig. 4.1 (a) in a radial-axial plane of thequadrupole field. In agreement with fig. 2.3 the axial beams are left-handed circularly(lhc) polarized and the radial beams are right-handed circularly (rhc) polarized. Thecounterpropagating beams are usually generated by retroreflection at a mirror, com-bined with a double pass through a quarter-wave plate in order to reverse the ensuinghelicity flip. Yet for our purpose this flip can be actively used to realize the MOT atthe mirror surface, as shown in fig. 4.1 (b). The beams are incident at 45Æ such thatthe mirror reflects the axial beams into the radial direction, and vice versa2. One caneasily see that the light field above the surface is the same as for the standard MOTwith respect to its polarization, and atoms therefore can be trapped right down to thesurface. The combination with the atom mirror is then simply realized by adding thelaser beam for the excitation of the surface plasmons (EWM), fig. 4.1 (c).

3D configuration. An extension to 3D is not immediately evident, however. For ex-ample, if a 2D cut in a radial-radial plane were considered instead of the above radial-axial plane, the beams would all be right-handed circular, and therefore the mirror

1A 6-beam MOT close to a transparent glass slide was demonstrated by the authors of Ref. [208] whoshifted a glass-cell MOT into the vicinity of one of the walls.

2The one-beam MOT in a hollow mirror [131] makes use of the same principle.

4.3. SIMPLE MODEL FOR PROPERTIES OF THE MOST 55

{

{

( )c

coil

lhclhcrhc rhc

EWM

�=4

�=4

B

(a) (b)

Figure 4.1: Principle for the realization of the MOST in a 2D representation. (a) - standardMOT, (b) - MOT near the mirror surface, (b+c) - magneto-optical surface trap (MOST)

reflection scheme would not work. Still, it is possible to find a 3D beam configurationthat is entirely based on mirror reflection and also satisfactorily fulfills the require-ments for the operation of a MOT. This configuration is illustrated in figure 4.2: Fourof altogether eight MOT beams propagate essentially in radial directions, being rhcpolarized as required (those to the right-hand side in the figure). They are connectedvia reflection to the other four beams which are lhc polarized and propagate in semi-axial directions. The axial components of these beams fulfil the requirement for thegeneration of a restoring MOT force; the radial components cannot be expected to pro-vide confinement from simple 1D MOT theory but still contribute to molasses friction.The magnetic coil configuration allows to shift the magnetic field zero normal to thesurface. This configuration provides for both to trapping and the investigation of theproperties of the trapped cloud at different heights.

4.3 Simple Model for Properties of the MOST

In this section, a simple model of the MOST is developed, focusing on two aspects.First, the influence of losses to the surface at the trapping behavior is discussed, andexpressions are given for the density distribution and the one-body loss rate of thetrapped cloud, which depend on the position of the magnetic field zero. A secondimportant point concerns the physics at the evanescent-wave mirror in the presenceof MOT light. Both laser fields couple to the same transition, and during the reflec-tion process the atoms interact with a bichromatic light field. A simplified picture isdeveloped for how this changes the behavior of the atom mirror and influences thelifetime of the MOST. On the basis of this model, the main experimental results will beexplained.

Density distribution and temperature: model ansatz As discussed in chapter 2, theatom cloud in a well-aligned MOT in the temperature-limited regime has a Gaussiandensity profile. Under the assumption of a homogeneous light field in the overlapregion of the MOT beams, the cloud can be shifted freely along 0z by adjusting the


Figure 4.2: Configuration of the MOST in 3D. Eight MOT beams at 45Æ to the surface providefor confinement and cooling above the prism surface, and the EWM beam is used to generatea surface-plasmon enhanced evanescent field for the reflection of atoms. The axis of the coilpair for generating the magnetic quadrupole field (“MOT coils”) is tilted by 45Æ with respectto the surface and lies symmetrically between the MOT beam pairs. An additional coil pair(”offset field coils”) is used to generate a homogeneous magnetic field to control the height ofthe magnetic field zero above the surface (and therefore the center of the trapped atom cloud).The trap is loaded from a slow atomic beam. The laser beam used for atomic beam slowing(not shown in the figure) passes the surface at grazing incidence.

height z0 of the magnetic field zero. The trapping potential perpendicular to the surfaceis then described by UMOT = 1

2�[r � (0; 0; z0)]2 with an absorbing boundary at z = 0.

When the cloud is near the surface (z = 0), i.e. when z0 is comparable to the 1=pe

radius �z of the cloud, this boundary condition requires, in a rigorous treatment, tofind the new density distribution n(r; t) on the basis of a Fokker-Planck or Langevinequation, e.g. with a numerical molecular dynamics method [145]. This will not beattempted here; instead a phenomenological, quasi-stationary 1D ansatz is made that isin good qualitative agreement with our fluorescence measurements of the cloud densityprofile (cf. the experimental section below):

Parallel to the surface, the density distribution remains unaffected as the harmonicoscillator potential and diffusive motion separate spatially. After integrating parallel tothe surface, the remaining 1D density profile nz can be written as nz(z; t) = n1(z)n0(t),taking the form of a truncated Gaussian profile n1(z) centered about z0 with decaying“amplitude” n0(t),

nz(z; t : z0) = n0(t)he�(z�z0)

2=(2�2z) u(z)i

(4.1)


The function u(z) describes the local density variation at the surface (on a length scale

z0z0

nznz

UMOTUMOT

�z�z

(a) (b)

Figure 4.3: Model for a MOT near a surface: (a) For large distances z0 � �z , the confiningpotential UMOT leads to a Gaussian density n(z; t). (b) For small distances the surface acts as anabsorbing boundary that truncates the Gaussian density profile; surface losses combined withthe diffusive motion in the volume above the surface lead to the global decay of the density.

that is small compared to �z); in the following it is approximated by a unit step func-tion. The width �z =

pkBT=� is not expected to change with z0 since the temperature

T is homogeneous over the volume of the trap according to the simple 1D MOT model.

Dependence of the one-body loss rate on z0. For a cloud trapped in the 8-beamMOT configuration well above the surface (z0 � �z), the probability for trapped atomsto reach the surface is small, and therefore the same one-body loss rate as for a standardMOT can be expected. However when z0 becomes comparable to �z, collisions oftrapped atoms with the surface (which is at room temperature) start to play a role.These lead to a one-body loss of atoms from the cloud with high probability, similarto collisions with thermal background gas3. The dynamics of the trapped cloud nearthe surface can still be described locally by the expansion _n(r) = l � �n(r) � �n2(r),just as in the standard MOT, but one must now be careful with the definition of �. Inthe presence of surface losses, � necessarily becomes position-dependent, remainingconstant in the cloud volume while taking a large value at the surface. On the otherhand, as a result of the diffusive random walk of the trapped atoms, the surface lossesend up affecting the entire cloud. In the following we therefore introduce an overallloss rate �(z0) that describes the decay of the total atom number N in the trap. Thisrate will increase smoothly with decreasing z0 as the available volume for diffusionabove the surface becomes smaller and smaller.

3One would expect losses from adsorption and/or heating to thermal energies. However, formetastable argon, a major additional mechanism is the decay to the electronic ground state. In pre-vious experiments with metastable argon, we determined (from measurements of the reflectivity of thebare mirror surface) the overall survival probability for an Ar� atom colliding with the gold-coated surfaceto be below 0.1 % [182].


The decay rate �(z0) for the evolution of n0(t) can be written as the sum of thebackground-gas collisional value �0 and the loss rate due to the presence of the surface,�s(z0),

�(z0) = �0 + �s(z0): (4.2)

To find an expression for �s one can exploit that, since the distribution nz above thesurface remains Gaussian, according to the ansatz, the diffusive motion in that partof the potential must be the same as it would be in a large-distance case, i. e. it isnot influenced by the presence of the surface. Therefore, by direct correspondence, thecollision probability at any point in time equals the relative statistical weight of theextrapolated fraction of the density distribution behind the surface (shown as a dashedline in fig. 4.3) which is given by the integral over nz=n0 from �1 to 0. This directlyleads to the loss rate

�s(z0) = RZ 0

�1dz

e�(z�z0)2=(2�2z )p

2��z

=R2

�1� erf

�z0

�zp2

��: (4.3)

The proportionality constant R can be interpreted as a uniform trial rate for an atomin the trap to collide with the surface.

Reduction of the one-body loss rate with the atom-mirror potential. The velocitydistribution of atoms at the surface is given by the 1D Maxwell-Boltzmann distribution,eq. 2.41, for which at any point in time half of the atoms are incident on the surface.When the evanescent-wave mirror is turned on, the repulsive optical potential reflectsthose incident atoms with absolute velocities smaller than the critical velocity

vmax =p

2Umax=M; (4.4)

defined by the height of the potential hill Umax(x; y) (cf. fig. 2.6). Here and in thefollowing it is assumed (in accordance with the experimental situation) that the 1=e2

radii of the evanescent-field spot, eq. 2.54, are much larger than the transverse widthof the atom cloud. In that case the value for Umax is the same for all incident atoms.At any instant, the fraction of incident atoms with energies above the barrier is thensimply given by

T =

Z �vmax

�1dv 2pv(v) (4.5)

eqs.2.41;2.42= 1� erf

rUmaxkBT

!; (4.6)

where the factor 2 accounts for the fact that, at any point in time, only half of thelaser-cooled thermal distribution eq. 2.41 is incident on the surface. In the following,


we call T the “translucence” of the mirror for the thermal velocity distribution. Withan increasing potential maximum Umax (this point will be discussed further in the nextparagraph), T gets smaller and and reaches zero asymptotically. The loss rate at thesurface decreases accordingly,

�s;ev(z0) = T �s(z0): (4.7)

In the limit Umax !1 all atoms are reflected from the evanescent field and the lifetimeof the atom cloud, � = (�0 + �s;ev)

�1, is again only determined by collisions with thebackground gas.

Atom-mirror potential in the presence of MOT light. In the absence of MOT light,the properties of the evanescent-field mirror (EWM) for incident atoms are those de-scribed in the second section of this chapter. However, when the resonant MOT light(which couples to the same transition!) is present, the situation changes drastically.Due to the circular polarization of the MOT beams, the electric field takes a finite valueat the mirror surface (the field for a single beam pair at a given instant in time is il-lustrated in fig. 4.4), and the atoms are reflected in a bichromatic light field. The

4z

distance from surface0

0

2

�

lhc

rhc

45Æ

I=Iinc

Figure 4.4: Light field distribution for the reflection of a MOT beam at the mirror surface.While the field components parallel to the surface vanish at the surface (dashed curve), thecomponents normal to the surface take a maximum (dot-dashed curve). The solid line showsthe total field intensity in units of the intensity Iinc of the incident beam.

question is, how does the MOT light affect the potential of the evanescent-wave mir-ror? A simple treatment of this problem in the dressed two-level atom model discussedin chapter 2 is not possible in general as the usual rotating-wave approximation runsinto problems when more than one laser frequency is present, preventing stationaryeigenstates to be constructed. In the case that the MOT light is much weaker thanthe evanescent field, it is however possible to maintain the rotating frame defined by


the evanescent-field frequency while treating the influence of the MOT light as a weaktime-dependent perturbation. In that case it can be shown for a two-level atom (seeappendix A) that the MOT light increases the population �st22 of the attracted state j2i,thereby reduces the absolute value of the dipole force according to (compare eq. 2.21)

hF i = �~@z!2R

ÆL(1� 2�st22): (4.8)

For general parameters, the complications of the bichromatic problem stand in theway of a rigorous yet simple description. However at this point a very crude picture canbe developed. Suppose that the detuning of the evanescent field is sufficiently large toprevent the bare states from being significantly mixed such that j1(N)i � jg;N + 1iand j2(N)i � je;Ni. When the MOT light is added, it drives transitions between theatom’s internal states jgi and jei, leading to a steady-state population �stee;MOT of theexcited state (as defined in eq. 2.25) entirely determined by the MOT light . This valuecoincides with �st22 because of the large EWM detuning, and therefore the MOT lightfield also leads to a cycling between the dressed states (owing to the large detuning ofthe EWM beam, the dressed states readjust quickly after an internal state change). Inthe limit of large MOT saturations, �stee;MOT takes a value close to 1/2 with little spatialvariation over the entire range of the evanescent field. One then obtains for the opticalpotential, using eq. 2.55, the simple steady-state average

Uopt � UEWM;dip (1� 2�stee;MOT ); (4.9)

a value that is much smaller than the “monochromatic” value UEWM , eq. 2.55. There-fore the translucence T for the bichromatic case will be much higher than in themonochromatic case. This picture requires that a steady-state can be reached for themoving atom, which might be problematic as the mean free path between photon scat-tering events for an atom at Doppler velocity is only one order of magnitude belowthe decay length of the evanescent field. Further aspects not taken into account hereinclude the optical potential of the MOT light itself and the possibility of MOT-inducedfluctuations of the dipole force.

To finally calculate the value Umax, one has to include the atom surface interaction.In principle, the model requires the temporal averaging over the interactions for theground and excited state, for the same reasons as for the optical potential. However,if one takes the van-der Waals interaction there is no difference between the two forthe two-level atom. One can then simply add the van-der Waals term, eq. 2.56, to theoptical potential, eq. 4.9 and numerically solve for its maximum value.

4.4 Experiment

The experiments were performed with metastable argon atoms on the 1s5 $ 2p9 tran-sition at 812 nm (IS = 1:29 mW/cm2, � = 2� � 5:27 MHz), using the beam machinedescribed in chapter 2. This section first describes the experimental setup for the re-alization of the 3D MOST configuration. A second part deals with the experimental

4.4. EXPERIMENT 61

results. In our experimental study, we first examined the behavior of a trapped atomcloud as far away from the surface as technically possible, and then studied the changein the parameters of the trap for decreasing heights of the magnetic field zero. Beforestudying the MOST itself, we characterized the atom mirror in the bichromatic lightfield, which exhibits a dramatic attenuation of its reflective behavior compared to themonochromatic case without MOT light.

4.4.1 Experimental Setup

The experimental setup is located in the main chamber of the beam machine as shownin figure 4.5. The MOT beams are generated from a common Gaussian beam and havea 1=e2 diameter of 5.9 mm and a maximum power of of (1:40 � 0:05) mW each. TheEWM beam has a 1=e2 diameter of 2.8 mm. In the experiments on the MOST we usedthe Ti:Sapphire laser for the generation of the EWM light, allowing for powers afterthe fiber of up to 80 mW. The gold-coated prism surface is located on the axis of theatomic beam with horizontal orientation. It is mounted to the electron lens columnof the atom detector. All MOT beams incident on the surface are perfectly circularlypolarized; the admixture of the “wrong-handed” polarization in the reflected beams isbelow 3% of the total beam intensity, as determined in an ellipsometric measurement.Because of limited optical access, a mirror inside the chamber is used to deflect theEWM beam onto the back side of the gold film at the surface plasmon resonance angle.A combination of a quarter- and a half-wave plate is used to generate a linear p polar-ization of the incident EWM beam as required for the excitation of surface plasmons.The magnetic quadrupole coils (”MOT coils”) consist of 1750 turns of coated copperwire (wire diameter 0.3 mm, resistance 27 Ohms) on a water-cooled, sliced coppermount and are located inside re-entrant tubes of diameter 3 cm [209]. The spacing be-tween the coils is 9 cm. At the standard operation current of 700 mA, a field gradientof b = 4:6 G cm�1 is produced along the axial direction that is approximately constantin a range of �1 cm from the center. The offset field coils are located inside the vacuumon the atom detector setup above and below the surface. Their diameter is 3 cm andthey consist of 50 turns of KaptonTM wire (diameter 0.5 mm) each. At the standardquadrupole field gradient, currents of up to 120 mA are needed to produce a field forshifting the cloud in the range of about 1 mm. By measuring the wire resistance underUHV conditions and on the typical experimental time scales, we found no noticeabletemperature increase, so that cooling was not required. Both the quadrupole coils andoffset field coils are connected to homemade constant-current supplies (accuracy 10�4)and can be switched off electronically within 250 �s. Finally, the field compensationof the earth’s magnetic field is done with three orthogonal pairs of homogeneous-fieldcoils that are wound onto the main chamber from the outside.

The atom clouds can be investigated via their fluorescence with the triggerable8-bit CCD camera (Sony CV-M10BX) mounted to a 75mm TV objective (Cosmicar).The objective is located at a distance of 30 cm from the center of the chamber in theplane of the prism surface. A photomultiplier connected to an 8-bit storage oscilloscope


(a) (b)

EWM

ABS

PMCCD1CCD2

MOT

P

M

M

P

Zeeman slower

Figure 4.5: (a) – Experimental setup for the magneto-optical surface trap (top view). Thetrapping beams (MOT) enter the chamber through windows on the top side of the chamberafter traversing a periscope. The atomic-beam slowing laser beam (ABS) passes the prismat grazing incidence. The evanescent-wave mirror beam (EWM) is deflected at a mirror Minside the chamber to the back side of the gold film at the surface plasmon resonance angle. Atriggerable CCD camera (CCD1) and a photomultiplier (PM) are used for measurements of thecloud fluorescence. The surface atom detector (not shown) above the prism (P) can be used tomeasure losses to the surface in situations with no applied magnetic fields. The CCD2 camerais used for additional monitoring of the cloud (the symbols for the optical components areexplained in fig 2.12). (b) – View along the viewing direction of CCD1 into the main chamber.The large tube at the left is the rear end of the Zeeman slower; the two reentrant tubes at 45degrees contain the quadrupole coils for the MOST. The prism is located in the center of thechamber. It is mounted to the lens column of the atom detector, which also carries the offsetcoils.

(Nicolet-450) is used to measure loading and decay curves from the fluorescence. Fi-nally, in order to determine the reflectivity of the atom mirror, the surface atom detectoris used for an investigation of the atomic arrival distribution on the surface for opticalmolasses when the magnetic fields are turned off.

4.4.2 Properties of the Atom Cloud far from the Surface

For a study of the 8-beam MOT we started with a cloud centered at z0 � 1:1 mm abovethe surface, which was the largest possible height at which a stable cloud could beproduced, due to the finite size of the overlap region of the MOT beams. For this height,the lifetime of the cloud for proper beam alignment was roughly 3 s (see below), asexpected from collisions with the background gas, and the loss of atoms to the surfacedid not play a significant role.

4.4. EXPERIMENT 63

Density profile. The cloud fluorescence exhibited a characteristic stationary fringepattern in the 0z direction with a visibility around 30%, as shown in figure 4.6. Bychanging the relative angle of incidence of the MOT beams, the separation of thefringes could be varied widely, while their orientation always remained parallel to thesurface. In the most extreme cases, the cloud could be contained in a single fringe or,alternatively, the fringe separation could be made smaller than the camera resolution of30 �m. In the latter case the cloud fluorescence intensity profile then looked perfectlyGaussian in all three spatial dimensions, and we also observed that the cloud was muchbrighter and more stable against perturbations (e.g. fluctuations of the MOT laser fre-quency). In contrast, for large fringe separations the cloud would typically have fluffyand undefined shapes and sometimes even limply jump between distinct positions.

1.5

1

0.5

Posi

tion

[mm

]

1D dens.

Figure 4.6: CCD camera fluorescence image of a trapped cloud exhibiting characteristic fringesparallel to the surface.

Similar observations of fringes were reported for a 6-beam MOT by Bigelow andPrentiss [146], who showed directly that the fringes not only affect the fluorescencebut are in fact cloud density modulations. They interpreted their findings as the chan-neling and loss of atoms out of the optical potential of the light field formed by theinterference pattern4. However, the authors of a later paper [144] argued that the ef-fect might in fact rather be due to a difference in the diffusion and friction coefficientsin regions of varying polarization, which make the trap “stickier” where Sisyphus cool-ing predominates.

The orientation of the fringe pattern in our case can be deduced starting with thelight field distribution of a single beam pair above the surface (fig. 4.4): The incidentand reflected beams form a standing light wave above the surface that contains bothintensity and polarization gradients with planar symmetry. Altogether four beam pairs

4In the mentioned paper, a density modulation of up to 100% (with larger fringe separation � 1mm)was observed.


with uncontrolled and fluctuating relative phases are present in the setup and the time-averaged light field intensity is the sum of the intensities of the single pairs. In thecase of a deviation between the angles of incidence this results in a 1D intensity beatpattern along z, containing positions where the single-beam field modulations interfereconstructively and others where they average out. We verified the connection to theobserved fluorescence intensity modulation, similarly as in Ref. [146], by changing theangle of incidence of a single beam and comparing the changes in the Fourier spectra ofthe observed distribution and the calculated light field [209]. Moreover we found thefringes of lower density to coincide with the antinodes of the beat pattern (this followsdirectly from an extrapolation of the observed fringe pattern down to the position ofsurface where the light field has the full single-beam intensity modulation depth, i.e.where there is such an antinode).

For all further experiments and characterizations, we always prepared bright andstable Gaussian-shaped clouds with densely-spaced fringes on the order of the cameraresolution5.

Atom number and peak density. For a determination of the atom number via thefluorescence of the cloud, the average coupling of the atoms to the light field (averagingover the population of the magnetic substates and the local light polarization) wasincluded through an effective Clebsch-Gordan coefficient [25] of C2

eff,MOT = 0:7 � 0:2(see Ref. [177]). An intensity of 8 times the peak intensity of a single beam wasassumed. For an axial magnetic field gradient b = 4:6 G/cm and MOT beam parametersIMOT = 6:8 IS (single-beam peak intensity; saturation intensity IS = 1:29 mW/cm2)and Æ = �1:5� (linewidth � = 2� � 5:27 MHz), the typical steady-state atom numberusing the cooled atom source was N = (4 � 1) � 105, corresponding to a Penningcollision-limited peak density of n0 = (3� 1)� 109cm�3. The 1=

pe radius of the cloud

in the 0z direction was �z = 0:23 mm.

Temperatures. The 1D velocity distributions of the cloud normal and parallel to thesurface were measured by the free ballistic expansion of the cloud after release. For thatpurpose the triggerable CCD camera was used. After a free expansion of duration t, theinitial Gaussian cloud (eq. 2.44) with its homogeneous thermal velocity distribution(eq. 2.41), expands into a Gaussian cloud with

�(t) =p�2(0) + (�vt)2; (4.10)

where �(0) and �v =pkBT=M are the initial parameters6. The temperature T can

therefore be deduced from a fit to the experimentally determined function �(t). Wedetermined �(t) in the directions parallel and perpendicular to the surface in the fol-lowing way. First the MOT was loaded. In the decay phase, i.e. after turning off

5This might sound like a piece of cake. In fact it took us almost the entire, nerve-wrecking year 1999to find out how to reliably and reproducibly get to this point with our shaky and extremely drift-friendlybeam machine!

6A derivation can be found in appendix A of Ref. [202].

4.4. EXPERIMENT 65

the atomic and slowing laser beams, the magnetic field and MOT beams were rapidlyswitched off (within 250 �s). After a dark phase of variable duration t (t was succes-sively increased from 25 �s in steps of 250 �s), the MOT beams were then flashed backon for 1 ms, and the fluorescence was recorded with the camera. The 1D distributionswere obtained by summing up the transverse direction in the 2D images, and thenfitting the sums with Gaussians.

The results for different light-shift parameters IMOT=ÆMOT are shown in fig. 4.7.The measured temperatures ranged from 250 �K to about 30 �K for small light-shift

0 2 4 6-I / [I / ]� �

�� S��

0

50

100

150

200

250

tem

per

atu

reT

[µK

]

TD

0.3

0.2 0 1 2 3 4t [ms]

�[m

m]

0.4

0.5

Figure 4.7: Temperatures of the cloud in the directions parallel (�) and perpendicular (�)to the surface for different light-shift parameters �IMOT =ÆMOT . The data points right of thevertical line were taken at a constant intensity IMOT = 6:8 IS for variable detuning. The datapoints left of the vertical line were taken at a constant detuning ÆMOT = �5:7 � for variableintensity. The inset shows a typical result of a measurement of �(t), from which T is extractedas a fit parameter. The single points for �(t) were obtained from a Gaussian fit to single cameraimages. Each of the temperature data points is an average over 10 experimental run series tomeasure �(t).

parameters. The observed linear functional dependence of the temperature belowthe Doppler temperature (TD = 127 �K) is in agreement with polarization-gradientcooling theory. In particular, we were also able to observe the abrupt increasein temperature connected to the breakdown of polarization gradient cooling belowIMOT=jÆMOT j � 0:2IS=�, in agreement with theoretical predictions [154]. A surpris-ing result is the systematic anisotropy. The temperatures perpendicular to the surfaceare consistently lower for light-shift parameters above 0:2IS=�; the difference reducesfor decreasing parameters and finally even seems to revert below 0:2IS=�. A definiteexplanation for this behavior cannot be given at this point, most likely however, thestronger polarization gradients in 0z direction give rise to larger friction coefficients


for Sisyphus cooling of the motion perpendicular to the surface. When the coolingmechanism breaks down the difference in the temperatures consequently vanishes.

4.4.3 Behavior of the Trap for Varying Magnetic-Field Zero Position

In order to characterize the influence of surface losses, we measured the change of thetrap parameters with decreasing height of the cloud above the surface for fixed MOTbeam parameters IMOT = 6:8 IS and ÆMOT = �1:5 � (the atom mirror was not used).For this purpose, a careful MOT beam alignment was required in order to generate asufficiently homogeneous light field over the entire range of heights.

Experimental method. For a translation of the cloud normal to the surface we var-ied the current I1 in the upper quadrupole field coil and the current I3 in the off-set field coils according to the method illustrated in fig. 4.8. Current configurations

(a) (b) (c)

I1

�I1�I1�I1

I2I2

I3

I3

Figure 4.8: Method used to shift the position of the magnetic field zero towards the surfaceby changing the currents in the coils of the MOST setup. In (a) the field zero (full circle) islocated symmetrically between the quadrupole field coils (at 45Æ) on the symmetry axis, whichhave equal but opposite currents. By increasing the current of the upper coil from I1 to I2,the additional field displaces the field zero on the axis towards the lower coil (b). On theaxis of the offset field coils there exists one point where the field vector is parallel to that axis(hollow circle). With the offset field coils (current I3), the total field can then be zeroed at thatpoint (c). Small displacements are linear in the coil currents as the additional fields are nearlyhomogeneous.

fI2; I1 = �700 mA; I3g were calculated for different desired heights z0 of the field zeroby applying Biot-Savart’s law to the coil configuration modeled by current loops [209].Steady-state fluorescence images of the trapped cloud are shown in figure for a seriesof linearly decreasing heights z0. For the highest position shown, the coil currents werefI1 = 708; I2 = �700; I3 = 6g mA, and for the lowest position shown at the far right,f810;�700; 82g mA (for still higher currents in the upper MOT coil, the fluorescencebecame too weak for the detection by the CCD camera7.). When the column sums of

7It should be added here that the waveguide was finally loaded from a MOST with z0 = -0.5 mm

4.4. EXPERIMENT 67

the images are fitted with truncated Gaussians, the positions of the maxima of these fitsagree with the calculated z0 values for the magnetic field zero to within a small errorof 50 �m. The widths perpendicular to the surface agree with the value �z = 230 �mto within an error bar of �30 �m. As expected from the simple model, the steady-stateatom number in the cloud reduces with distance as a result of losses to the surface. Asecond reason for this reduction is the decreasing loading rate; this is discussed furtherbelow.

1m

m

Surface

Figure 4.9: Series of measured cloud fluorescence images for an incremental linear downwardshift of the field zero from z0 = 1:1 mm to z0 = �0:1 mm. The position of the surface ismarked by a horizontal line; below this line the mirror image of the cloud can be seen. Thecloud follows the calculated magnetic field zero to within an error of 50 �m. The atom numberdecreases with the downward shift due to the loss of atoms to the surface (the atom mirror wasoff).

Lifetime. After shuttering the atomic beam and the slowing laser, the trap decay wasmeasured with the photomultiplier. The experimental decay curves were then fittedwith eq. 2.49 with n0, �0 and � � �(z0) as free fit parameters8. The results are shownin fig. 4.10 (a) for the inverse decay rate, i.e. the lifetime of the cloud, �(z0) = �(z0)

�1.The lifetime exhibits a strong dependency on z0, dropping by two orders of magnitudefrom 3:1 s for z0 = 0:96 mm to 50 ms for z0 = 0 mm. The experimental data agreevery well with the model, eq. 4.3, which is shown as a solid line in the figure. Taking� = 3 s as the background-gas collisional value and setting �z = 230 �m (as obtainedfrom the CCD camera measurements), the data can be fitted with the trial rate R asthe single fit parameter, yielding R = (40� 5) s�1.

Temperatures. It is an implicit assumption of the model for the behavior of the life-time that the temperature Tz does not change as z0 is varied (Tz should be homoge-neous over the volume of the cloud, cf. the discussion in the second section of thischapter). An indirect indication for this is the approximate constancy of �z =

pkBT=�

already observed for the shift of the cloud. With the method described in the last sec-tion, we checked the constancy of the temperature in a direct ballistic measurement.

8Eq. 2.49 was derived for the peak density (or equivalently the atom number) of a Gaussian densitydistribution, but it can be shown that it is also valid for other cases if the quantity �0 is accordinglymodified by a geometrical factor.


The results are shown in fig. 4.10(b). The measured temperatures parallel and per-pendicular to the surface indeed stay approximately constant when z0 is varied. Thefluctuations are most likely due to local inhomogeneities in the light field.

Loading rate. The trap loading depends on both the properties of the trap and of theatomic beam and therefore cannot be considered an immediate trap property. Never-theless, under the assumption that the beam is homogeneous in the 0z direction, theloading rate distribution lz(z � z0) should have the symmetry of the cloud, extend-ing radially to a finite capture radius rc (see the discussion of the MOT in chapter2). Therefore, one expects the overall loading rate L(z0) =

Rlz dz to scale linearly

with the remaining capture volume above the surface. The overall loading rates wereextracted from the linear increase of the atom number during the first 30 ms of load-ing. The results are shown in fig. 4.10(c). The measured data can be fit with theintegral over a Gaussian-shaped distribution l(z � z0) characterized by the variance�z;L = (300�30) �m, which can also be interpreted as an effective capture radius. Themaximum loading rate for the large-distance case using an optimized atomic beam (i.e.by cooling the atom source and optimizing the transverse beam collimation) was de-termined to be L = (2:0� 0:6)� 106 s�1. As expected, the rate drops by 50% for z0 = 0when the cloud is cut in half.

4.4.4 Evanescent-Wave Bichromatic Atom Mirror

As discussed in the MOST model, the performance of the evanescent-wave mirror isexpected to depend on the presence of MOT light. In the bichromatic light field, theMOT drives transitions between the evanescent-field dressed states and attenuates theeffective mirror potential. We therefore found it important to study the performanceof the mirror separately before measuring its effect on the lifetime of the MOST. Sucha direct investigation is possible on the basis of our surface atom detection scheme.By counting the secondary electrons from the deexcitation of metastable atoms at thesurface, one has a direct measure of the losses of atoms to the surface.

Experimental characterization method. The interesting quantity is the translucence T of the atom mirror, eq. 4.5. For a measurement of T for different parameters ofthe bichromatic field we proceeded in the following way. First an atomic cloud wasprepared in a MOT near the surface (z0 = 0:2 mm � �z) for standard parametersIMOT = 6:8IS ; ÆMOT = �1:45�. In the trap decay phase, the magnetic field wasswitched off in order to enable the surface detection scheme and simultaneously thelight field parameters of the MOT were switched to the desired values. (For the con-nection with the MOST measurements described below, we measured the temperatureof the optical molasses, which directly influences the translucence, with a ballistic ex-pansion measurement. At ÆMOT = �1:45�, the temperature was 170 �K as for theMOT.) While the signal from the decay to the surface was recorded, the EWM beamwas switched on. For the short time scale required for switching (60 �s) the decay

4.4. EXPERIMENT 69

0.05

0.1

0.5

1

1 0.8 0.6 0.4 0.2 0 -0.2

1 0.8 0.6 0.4 0.2 0 -0.2

0

50

100

150

200

250

Tem

per

atu

reT

[uK

]

1 0.8 0.6 0.4 0.2 0

0

0.2

0.4

0.6

0.8

1

0.5 time [ms]

fluore

scen

ce[a

.u.]

1

time [ms]0 0.5

flu

ore

scen

ce[a

.u.]

(a) (b)

(c)

Life

tim

e

�

[s]

Height of field zero z0 [mm]



perpendicular

parallelLo

adin

gra

te

L

[a.u

.]

Figure 4.10: Properties of the trapped cloud (IMOT = 6:8 IS , ÆMOT = �1:5 �) for differentheights z0 of the magnetic field zero. (a) – Lifetime of the cloud. The insets shows a photo-multiplier decay curve obtained by summing over 10 individual runs from which the lifetimewas extracted as a fit parameter. The dotted curve shows the model calculation for R = 40 s�1.(b) – Temperatures of the cloud as determined from a ballistic expansion measurement withthe CCD camera. The increase of the fit errors close to the surface is due to the decrease inatom number. (c) – Relative loading rate from the atomic beam into the trap. The rates areextracted from the linear increase of the atom number during the first 30 ms of loading. Thedashed curve is a Gaussian error function fitted to the data.

signal is approximately constant, and so the translucence is obtained as T = N1=N0

whereN0 is the count rate immediately before the switching, andN1 immediately after.The experimental scheme is illustrated in fig. 4.11 (a) together with measured signals.Before these signals are discussed, it should be explained that the single data points


that give a measure for the instantaneous count rate are obtained by summing up oversingle, spatially resolved detector pages that are separated by 100 �s. We subdividedthe available set of 64 pages into two 32-page subsets, one for the time window inwhich the EWM beam was turned on and one for the time window in which it wasagain turned off.

Qualitative signal characteristics. Fig. 4.11 (a) gives typical experimental signalsfor the case that the MOT light was operated at the standard parameters (IMOT =6:8IS ; ÆMOT = �1:45 �) and for the maximum available power of the EWM beam thathad a detuning jÆEWM j = 2� � 500 MHz.

For blue EWM detuning the signal drops as expected when the beam is turned on(black curve). However, as the beam is turned off again, the signal shows an almostinstantaneous increase resulting in a rapidly decaying peak. This peak probably arisesfrom the accumulation of atoms in a thin layer adjoining the evanescent potential. Ifone assumes that the temperature of the atoms in that layer is the same as everywherein the molasses, one can estimate from the duration of the peak that the layer musthave a thickness of order 10 �m. Its emergence is connected to the diffusive atomicmotion in the presence of the reflecting boundary. We did not observe any peak whenthe MOT light was off.

For red EWM detuning the dressed states are interchanged and the effective reflec-tion potential should change from repulsive to attractive; reflection should not occur.The gray curve shows an example that proves this point. When the EWM beam isturned on, a transient increase of the signal can be seen instead of a drop as in the bluecase. This can be attributed to atoms that are in the range of an attractive evanescentpotential and are then “sucked” to the surface, emptying the volume in the range ofthe potential on a fast time scale. The opposite effect, i.e. a small dip, results whenthe beam is turned off again (this is not very well resolved). Apart from these transienteffects, we found the signal to coincide with a reference spectrum, for the case withoutany reflection field at all, to within the counting error. This means that the reflection byradiation pressure from the straylight of the surface plasmon can be ruled out for thelarge chosen value jÆEWM j = 2� � 500 MHz. The difference in the signal behavior forred and blue detunings is a direct proof that the reflection process is due to the opticalpotential of the evanescent wave.

Monochromatic mirror. For a quantitative study of T for different parameters ofthe bichromatic light field, we first checked the performance of the monochromaticatom mirror, i.e. for the case of vanishing MOT light intensity. The result is shownin fig. 4.11 (b). As expected, T drops rapidly with increasing EWM beam intensityas most atoms in the thermal velocity distribution have small kinetic energies9, andthe evanescent potential always wins over the attractive 1s5 van-der-Waals potential at

9The initial potential energy of the atoms can be neglected in comparison to the thermal energy of thecloud.

4.4. EXPERIMENT 71

large enough distances. The data can be fit very well with the model, eq. 4.5, whichis shown as a dashed line (the accumulation layer is ignored in the model, as it is afeature of the “truncation function” u(z)). For the calculation of the optical potential,an effective Clebsch-Gordan coefficient C2

eff,EWM = 0:48 was used (as in previous work,by assuming an unpolarized atomic sample on the J = 2 $ 3 transition [182, 185]).The fit requires an additional 25% reduction of the ensuing potential. This could bedue to a polarization of the atomic sample, to the transverse dislocation of the arrivaldistribution with respect to the surface-plasmon spot center10 (though not accountingfor more than 10%), or to a deviation in the field intensity enhancement factor F . Forlarge EWM intensities, T remains at a finite value around 2% (still for intensities thatare six times higher than the highest one shown in the figure). This is most likelydue to a deexcitation of atoms at spots on the surface where dust particles pierce theevanescent field.

Varying EWM beam intensity; constant MOT intensity. The resulting behavior of T with increasing EWM intensity in the presence of MOT light is shown in fig. 4.11(c). For a comparison, the corresponding monochromatic data are displayed as well(�). The behavior is similar in the sense that with increasing EWM beam intensity, Treduces and finally reaches a value of 3% (the data point for the highest EWM intensityis obtained from the data shown in (a)). This is a crucial result for the operation ofthe MOST as it shows that for the bichromatic light field the mirror can become almostperfectly reflective as well.

There are however two important differences compared to the monochromatic case.First, EWM beam intensities that are two orders of magnitude above those for themonochromatic case are needed to obtain comparable values for T . Comparing corre-sponding T values, one concludes that the height of the potential is effectively reducedby about 97%. Second, T obviously possesses a threshold at small values of IEWM .This does not follow immediately from the model, since the total potential formed bythe exponential optical potential and the atom-surface interaction does not itself pos-sess a threshold for reflection (cf. the monochromatic case). However the behaviorbecomes understandable if one admits the negative, z-dependent light shift Uoffs of thered-detuned saturated MOT standing light wave as illustrated in fig. 4.4, which is ex-pected from eq. 2.22 when only the MOT light is considered. In the bichromatic caseit should locally counteract the repulsive EWM potential in the antinodes of the MOTlight field. Taking the sum of the two potentials, Uoffs has to be overcome first beforeatoms can get reflected.

The dashed line in the figure is the fitted model calculation based on eq. 4.9 andthe 1s5 van der Waals potential, with the following parameters: For the intensity of theevanescent field, the value previously obtained for the monochromatic case is used.

10The position of the EWM spot was measured by reducing the EWM beam diameter, and then releasinga cloud from 1 mm height. In that case, the arrival distribution for late times covered the entire field ofview of the detector. The position of the EWM beam could be localized by the dark spot burnt into thatdistribution and was shifted to the center of the field of view by a parallel translation of the beam.


0 0.05 0.1 0.15

0

0.2

0.4

0.6

0.8

1

0 4 8 12

0

e-

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

0 2 4 6 80

0.2

0.4

0.6

0.8

1

(a)

Time [ms]

Det

ecto

rco

unts

[a.u

.]

EWM

EWM on

N0

N1

(b)

Tran

sluc

ence

T=N0=N1

Tran

sluc

ence

T=N0=N1

Tran

sluc

ence

T=N0=N1

EWM beam intensity IEWM [W/cm2]


ÆEWM = 2� � 687 MHz

(c)

MOT beam intensity IMOT [mW/cm2]

IEWM = 0:17 W/cm2

ÆEWM = 2� � 500 MHz

IMOT = 0

IMOT = 0

(d)IMOT = 8:8 mW/cm2

ÆEWM = 2� � 300 MHz

Figure 4.11: Characterization of the evanescent-wave mirror for a bichromatic light field withdifferent parameters. (a) – Illustration of the experimental measurement method based on thedetection of secondary electrons with the surface atom detector. We measured the change of thecount rate when the EWM beam was turned on and off again. Black curve: blue EWM beamdetuning, gray curve: red EWM beam detuning. (b),(c),(d) – Measured translucences T =N1=N0 of the atom mirror for blue EWM detuning and different parameters of the bichromaticlight field. The detuning of the MOT was ÆMOT = �1:45 � for all measurements. The dashedcurves are model calculations as described in the text.

The fit requires the 30-fold single-beam intensity for the total MOT intensity (which isconsistent with a partial coherence between the four MOT beam pairs), and an offsetterm Uoffs = �0:26 ~� for the effective MOT potential (this value is one order of magni-tude smaller than the values one would calculate from eq. 2.22 for the monochromaticcase). With the offset term included, the fit reproduces the data very well.

4.4. EXPERIMENT 73

Varying MOT intensity; constant EWM intensity. The transition from themonochromatic to the strongly bichromatic case is shown in fig. 4.11 (d). For in-creasing MOT light intensity at ÆMOT = �1:45�, T increases almost linearly. Thedashed curve is the model calculation based on the parameter set obtained from the fitfor fig. 4.11 (c), i.e. it contains no free fit parameters. The offset potential is modeledas Uoffs = �a � ln[1 + !2R;MOT=(Æ

2MOT + 2=4)], where !R;MOT is the Rabi frequency

resulting from the 30-fold single-beam intensity, and a is a proportionality constantthat fixes Uoffs to �0:26 ~� for the parameters of fig 4.11 (c). Of course the model onlyapplies to the Doppler cooling regime where the temperature T of the cloud does notdepend on intensity, cf. eq. 2.43.

4.4.5 Combined MOT–Atom Mirror

At this point of the discussion, the basic properties of the “ingredients” of the magneto-optical surface trap have been characterized. The lifetime of the trapped cloud reduceswhen the magnetic field zero z0 is brought close to the surface as a result of lossesat the surface, while the temperature of the cloud remains unaffected. By adding thelight field of the evanescent-wave atom mirror, atoms are still reflected in the presenceof MOT light, despite severe bichromatic attenuation effects. We have shown that thereflection is due to the optical potential of the evanescent wave. The last point todemonstrate now is that by adding the magnetic field, atoms can actually be trappedin this configuration.

Lifetime. The most direct property to look at as a signature for trapping is the lifetimeof the atom cloud. At a given height z0 the surface loss rate takes a value �s = �s(z0)according to eq. 4.3, and when the mirror is turned on, it should decrease to a value�s;ev = T �s with the translucence T of the atom mirror. The expected lifetime of thecloud is then given by � = (�0 + �s;ev)

�1, where �0 = (3 s)�1 is the background-gasvalue.

For the experiment, we prepared a trap with z0 = 0:0 mm and standard MOT pa-rameters. In that case the surface-collision limited lifetime was (R=2)�1 � ��1s (0)=50 ms, as in the above lifetime-versus-distance measurements. We measured the life-time as a function of the EWM beam intensity for ÆEWM = 2� � 500 MHz, i.e. for thesame parameters as in the measurement of T , fig. 4.11 (c). The result is shown infig. 4.12. At the highest achievable EWM beam intensity, the lifetime rises to a valueof around 400 ms. Being an order of magnitude above the value for vanishing inten-sity, this clearly demonstrates the functionality of the MOST. For the model calculation(dotted curve) the parameters are those of the T measurement except for the offsetpotential which was chosen as a free fit parameter, yielding Uoffs = �0:57 ~�. The insetin the figure shows the expected saturation of the lifetime on a semi-logarithmic plot.

To verify the evanescent nature of the reflection process, we measured the lifetimeof the trap at 500 MHz red detuning of the EWM beam at maximum power. Within thefit error of 5 ms, the lifetime remained at its zero-intensity value of 50 ms, in agreement


0.05

4 6 8 10

Lif

etim

et

[s]

00

0

0.5

0.5

1

1

1.5 2

2

2.5

0.1

0.10.2

0.3

0.4


Figure 4.12: Lifetime of the MOST (z0 = 0:0 mm) as a function of the EWM beam intensity.The light field parameters are IMOT = 6:8IS ; ÆMOT = �1:45 � and ÆEWM = 2� � 500 MHz.The inset (with the same units as the main plot) shows the extrapolation of the lifetime forhigher powers of the EWM beam.

with the measurement of T .

Other properties. The cloud temperature for the operating MOST could not be di-rectly measured with the CCD camera due to technical problems associated with theintense straylight of the EWM surface plasmons. It is very unlikely, however, that thetemperature of the cloud is affected by, e.g., diffusive heating in the evanescent field:The damping rate in the MOT� 105 s�1 is orders of magnitude larger than the trial rateR with which trapped atoms probe the evanescent field, such that atoms rethermalizequickly. Also the scattering rate from the straylight of the evanescent field is orders ofmagnitude smaller than the scattering rate of the saturated MOT. Therefore, it shouldbe relatively safe to assume an averaged temperature around 200 �K.

We also measured the loading rate in the presence of the reflection field and foundno difference to the case without the field, to within an error of 5%. This was asexpected since the evanescent field is not strong enough to reflect atoms that are muchfaster than those in the trap, and also since the atoms from the beam were incidentparallel to the surface.

The equilibrium between loading and decay determines the steady-state atom num-ber in the trap. At the highest possible EWM beam intensity, we measured an atomnumber of

N = (1:3 � 0:4) � 105 (4.11)

with the calibrated photomultiplier. For this number, the peak atom density is on theorder of 109 cm�3. The exact value depends on the trapping volume above the surface

4.5. CONCLUSIONS 75

which could not be determined directly with the CCD camera as a result of the intensestraylight from the surface plasmons. Such a density is already in the regime wherePenning collisions become important; therefore the achievable steady-state atom num-ber cannot be expected to be much higher, even for perfect reflectivity of the atommirror.

4.5 Conclusions

We have demonstrated and characterized the magneto-optical surface trap (MOST),which is a combination of an 8-beam MOT with an optical evanescent-wave (surface-plasmon) atom mirror. In this trap, the atoms are in contact with an evanescent fieldthat separates the atomic cloud from the mirror surface by a fraction of an opticalwavelength. In the experiment, we were able to trap (1:3 � 0:4) � 105 atoms with alifetime of (390� 30) ms in the situation where the zero z0 of the magnetic quadrupolefield was located at the surface.

We have investigated the behavior of the trapped cloud for varying distances fromthe surface (in the absence of the evanescent field) and found a dramatic decrease ofthe lifetime by two orders of magnitude to about 50 ms when z0 was reduced from1 mm above the surface down to zero. For large distances, the behavior of the trapresembles that of a standard MOT. However a characteristic modulation of the clouddensity normal to the surface can be observed, and the velocity distribution of the cloudis clearly anisotropic. For a cloud with z0 = 0 with a lifetime of 50 ms we have shownthat the evanescent field of the atom mirror can increase the lifetime by one order ofmagnitude, which can be expected to be limited by the available power for the atommirror. We have investigated the atom mirror in the presence of the MOT light andfound a drastic reduction of its reflectivity compared to the case without MOT light,due to a bichromatic effect. We have characterized this effect for different parametersof the bichromatic light field. A simple model of the MOST has been developed whichis consistent with the experimental observations.

Chapter 5

Continuous Loading andManipulation of Atoms in a SurfaceWaveguide

We have demonstrated the continuous loading of a planar waveguide for atomsin sub-�m distance from a metallic surface. The loading of the waveguide, whichis formed by the optical potential of a red-detuned standing light wave above amirror surface, is achieved via evanescent-field optical pumping from a magneto-optical surface trap (MOST). We have demonstrated light-induced elements for themanipulation of atoms in the waveguide geometry, including a continuous atomsource, a switchable channel guide, an atom detector and an optical surface lattice.We have combined the source, the channel and the detector to form a simple atom-optical integrated circuit.

5.1 Introduction

In the well-established field of integrated optics, optical circuits have been built thatcombine a number of miniaturized, interconnected optical components on a commonsubstrate such as light sources, optical waveguides, modulators and detectors [134].These devices find widespread use in telecommunication and instrumentation tech-niques. The atom-optical analogue to integrated optics, i.e. the realization of atom-optical setups in a miniaturized, substrate-based geometry, offers intriguing prospectsfor atom interferometry [8] and quantum computing [135,136] and also is of interestfor the study of atomic gases in low-D [72,71] and close to surfaces [44,109].

Over the last years, techniques to guide laser-cooled atoms over macroscopic dis-tances have been developed, based on optical potentials in hollow-core optical fibersand laser beams [116, 117, 118, 119] and magnetic potentials along current-carryingwires [120, 121, 122]. This has recently been extended to the use of microfabri-cated wires on substrates for which isolated components such as weakly confining

77

78 CHAPTER 5. CONTINUOUS LOADING AND MANIPULATION OF ATOMS...

linear [124, 125, 126] and (switchable) Y-branch atom guides [127, 128], magnetictraps [129] and a conveyor belt [130] above a substrate have been demonstrated. Onthe other hand several schemes have been proposed for the realization of surface trapswith tightly confining 1D optical and magnetic potentials [105,106,107,108,112] thatcan be interpreted as planar waveguides for atoms. One of these schemes, in whichlaser-cooled atoms are transferred into a single potential layer of a standing light wave(SLW) in sub-�m distance from a reflecting surface via evanescent-wave optical pump-ing [107] has been demonstrated by us in earlier work on metastable argon [110,111].

The present work addresses the manipulation of atoms in our planar waveguide.This opens a novel route to integrated atom optics. The waveguide provides a planargeometry above a substrate surface into which atom-optical components are subse-quently integrated, and transverse guiding inside the waveguide is achieved by later-ally structuring the waveguide potential. This all-optical approach is in close analogyto the realization of integrated optics [134]. One of the central issues of the presentwork is the continuous loading of the waveguide, which allows for the realization of aCW atom source in the planar waveguide geometry. Such a continuous loading schemealso is of interest for scenarios to reach quantum degeneracy in low-dimensional, opensystems [92,100,112].

This chapter is divided into two main parts. The first part discusses some basicconcepts of continuous loading and the implementation of atom-optical components,and the second part describes our experimental work and results.

5.2 Basic Concepts

5.2.1 Overview

Our experimental schematic is shown in fig. 5.1, together with the relevant levelsand transitions in argon. As in our earlier work, Ref. [110], the waveguide potentialfor 1s3 atoms is generated by a 1D standing light wave (SLW) that is red detuned withrespect to the 1s3 $ 2p4 transition. The SLW itself is generated by reflecting a Gaussianlaser beam at the gold-coated prism surface. Parallel to the surface, the atoms in theSLW are weakly confined and behave classically (on the order of 104 bound statesare populated), while perpendicular to it there exist only a few bound states. TheSLW waveguide is an atom-optical analogue to planar optical waveguides known fromintegrated optics1 [134].

The scheme for the continuous loading of the waveguide combines the magneto-optical surface trap (MOST) with an evanescent field for optical pumping to 1s3 (OP).The MOST serves a reservoir of 1s5 atoms in contact with an evanescent-wave mirror(EWM) in which the trapped atoms approach the surface to within a fraction of the

1The analogy is based on the formal equivalence of Helmholtz’s equation to the (time-independent)Schrödinger equation [4]: For an electromagnetic wave E (of freq. !) in a medium with index n onehas (r2 + k2)E = 0, where k = !=(c=n). For the wavefunction one has (r2 + k2) = 0, wherek =p(2M(E � U)=~; in which E is the energy of the atom and U the optical potential.

5.2. BASIC CONCEPTS 79

Ar* (1s3)

OPEWM

820 nm

MOST

De

tec

tio

n

e-

WG

1s5 1s3

WGD

1.5 mm

42p

WGWGD

MOT

EWM

OP

2p

51s1s3

9

**

(a) (b)

812 nm715 nm

795 nm

Figure 5.1: (a) Scheme for experiments on “integrated atom optics” and (b) relevant levelsand transitions in argon. An array of tightly confining planar waveguide layers for 1s3 atoms isformed by the optical potential of a red detuned standing light wave (WG). Atoms are loadedinto the lowest waveguide layer 820 nm from the surface via evanescent-field optical pumping(OP) from the steady-state MOST for 1s5 atoms, which is realized by combining a modifiedMOT at the surface with an evanescent-wave atom mirror (EWM). The MOST is loaded froma slow atomic beam. This CW loading scheme realizes a source of 1s3 atoms inside the wave-guide. Atoms propagate in the waveguide until they reach the detection area (WGD) wherethey hit the surface and are detected via secondary electrons. The detection scheme is basedon the deformation of the confining potential with an attractive evanescent field.

optical wavelength by diffusive motion. The OP field is used to transfer 1s5 atoms tothe state 1s3 in a short range above the surface. The optically pumped 1s3 atoms scatterlocally into the few waveguide potential layers that are in the range of this field2.Owing to the large difference in the wavelengths of the 1s5 $ 2p9 and 1s3 $ 2p4transitions of 17 nm, the atoms in the waveguide are completely decoupled from theMOST light, and vice versa.

For detection, we let the metastable 1s3 atoms collide with the gold-coated surfaceand detect the secondary electrons ejected upon impact with the atom detector de-scribed in chapter 2.1.3. Making use of this method, we have implemented a schemefor an integrated atom detector. It is based on the deformation of the lowest wave-guide layer with an attractive evanescent field in a small spot (WGD) that results in therelease of atoms towards the surface.

The implementation of the source and the detector at separate positions in thewaveguide layer allows for the realization of an elementary atomic beam experimentin the quasi-2D geometry of the lowest waveguide layer as shown in fig. 5.1.

2The CW loading mechanism allows to couple atoms into the waveguide, directly from an atomicbeam. One might therefore be led to interpreting it instead as the realization of an input coupler foratoms. However, the waveguide field only interacts with atoms in the 1s3 state, which are produced byoptical pumping in the evanescent field. Therefore the term source is appropriate for those atoms.


5.2.2 The Waveguide

Optical potential. In the far-detuned limit, the confining optical potential generatedby the intensity distribution I(r) of the SLW is given by

UWG;dip(r) =~A2

795

8Is;795

I(r)

ÆWG; (5.1)

where A795 = 18:6 � 106s�1 is the Einstein coefficient, Is;795 = 0:77 mW/cm2 is theeffective saturation intensity, and ÆWG the detuning of the beam with respect to the1s3 $ 2p4 transition. Because of the red detuning ÆWG < 0, the minima of the opticalpotential coincide with the antinodes of the SLW. For the s-polarization of the WG beamthe intensity distribution of the SLW is given by

I(r) = I0(x; y) sin2(k0 z) (5.2)

with

I0(x; y) = 4IWG exph� 2x2

(wWG= cos �i)2� 2y2

w2WG

iand k0 =

2� cos �i�WG

; (5.3)

where IWG is the center intensity, �WG = 796 nm the wavelength (for ÆWG = �2� �600 GHz red detuning, for which the increase in wavelength �WG = 1:25 nm), wWG

the waist and �i = 45Æ the angle of incidence of the waveguide beam.Close to the surface the attractive atom-surface interaction becomes important. The

total potential of the waveguide in a good approximation is given by

UWG = UWG;dip + UCP ; (5.4)

where UCP (z) is the Casimir-Polder term, eq. 2.57, in which the static polarizabilityfor the state 1s3 is given by �0;1s3 = 4��0 � (49:5 � 1) � 10�30m [175]. The resultingtotal potential is illustrated in fig. 5.2 for typical experimental parameters. As a resultof the atom-surface interaction, the WG layer closest to the surface (i = 0) is stronglydeformed and does not provide confinement while the interaction does not affect theconfinement in higher layers. The distance of the potential minimum in layer i = 1from the surface is 820 nm 3, and the layers are separated by 560 nm.

Guided modes. In the optical potential, the motion of atoms perpendicular to thesurface is described by the 1D Schrödinger equation

h� ~

2

2M@2z + UWG;dip(z)

i = E (5.5)

3The gold film on the prism surface for 796 nm has a measured dielectric number " = �27:9 + i0:90(cf. chapter 2). As a result, in-plane vector of the reflected beam is phase shifted by 1:08� (instead of �for a perfect metal). This results in a 23 nm shift of the SLW towards the surface, compared to the idealcase.


2.521.510.50

-20

-40

-60

0

Distance from surface [µm]z

WG

po

ten

tial

[µK

]

s-pol.WG

i=1 i=2 i=3 i=4

(i=0)

795nm

42p

1s3

Figure 5.2: Waveguide potential for a WG beam with intensity IWG = 44 W/cm2 and 1.25 nmred detuning. While the motion of atoms is quasi-free parallel to the surface, it is quantized inthe normal direction (shown are levels in the harmonic approximation), confining the atomsin planar waveguide layers i. Close to the surface, the optical potential is deformed by theatom-surface interaction.

for the atomic wavefunction . Because of the periodic sinusoidal form of UWG;dip(z),this equation is equivalent to Mathieu’s differential equation [170] whose eigenvaluesform an energy band structure. In the harmonic approximation sin2(k0z) � (k0z)

2,which is a crude but sufficient approximation for our purposes4, one obtains from eq.5.5 harmonic-oscillator states j�i with eigenvalues

E� =

�� +

1

2

�~osc;z with osc;z = k0

p2U0=M; (5.6)

where U0 is the potential (as defined in eq. 5.1) that corresponds to the maximumintensity I0. For typical experimental WG parameters, osc;z = 2��80 kHz = kB=(2~)�7:8 �K, which corresponds to a number of five bound harmonic-oscillator states (i.e.guided modes) perpendicular to the surface.

Losses. Another important aspect of the waveguide is the loss of guided atoms fromthe WG potential.

Photon scattering on the 1s3 $ 2p4 transition is connected to heating of atoms outof the WG potential as well as to optical pumping to untrapped internal atomic states(with a branching ratio of 0.44 in the state 2p4). The rate for photon scattering is givenby

�sc;� =A2795�2p48Is;795

hIi�Æ2WG

; (5.7)

where the mean intensity hIi� = h�jIj�i is determined by the overlap of the state j�iof the atom with the WG light field. For red detuning ÆWG < 0, the scattering rate

4Band structures have been studied previously in a 3D blue optical lattice experiment [210] that wasrealized with our beam machine in 1996 and is described in detail in Ref. [184]. Cf. also Ref. [185] for adiscussion of the case of the 1D waveguide potential.


is highest for the ground state and decreases with the excitation �. Since �sc;� /IWG=Æ

2WG and UWG;dip / IWG=ÆWG, it is possible to suppress the scattering rate while

maintaining the WG potential by increasing both the intensity and the detuning of theWG beam. For our experimental parameters, the photon scattering losses are on theorder of 10 s�1.

Collisional losses arise from inelastic collisions (1) between WG atoms and ambientbackground gas atoms, (2) between WG atoms and impurities on the surface, or (3)between WG atoms themselves. This is expressed by the loss rate

�coll = �0 + �33nWG; (5.8)

where �0 includes the first two contributions, �33 is a rate constant for two-body col-lisions between 1s3 atoms and nWG is the density of atoms in the WG potential. Inthe presence of the MOST for CW loading, the background-gas density of 1s5 atomsreached a level for which the collisional loss rate �0 became comparable to the rate forphoton scattering.

Tunneling effects may crudely be estimated in the WKB approximation as

�tunn � osc;z exp

ZE�<UWG

dzh2M(E� � UWG)

i1=2; (5.9)

for the higher modes. For the lower modes, band-structure calculations based on Math-ieu’s equation and a numerical treatment of the time-dependent Schrödinger equationof the system [185] show that the tunneling rates are negligible compared to photonscattering, which is consistent with our experimental observations.

Thermal contact with the surface. A recent paper discusses the thermal contact ofparticles in surface traps with room-temperature surfaces [109]. The coupling dependson the mode density of thermal electromagnetic field fluctuations at the trap frequen-cies, the type of interaction and the distance from the surface. Spinless neutral atomssuch as argon in the 1s3 state are only affected by time-dependent distortions of thevan-der-Waals potential due to thermal surface oscillations. At distances above 100 nm,the corresponding heating rates are below 10�6 s�1 [109] i.e. negligible.

5.2.3 Continuous Loading

In earlier work we have demonstrated a pulsed loading scheme in which 1s5 atomswere collected and then dropped from a standard 6-beam MOT half a centimeter abovethe surface [110], from which they expanded ballistically. Atoms incident on the sur-face were decelerated in the EWM potential and optically pumped by the OP, ideally attheir classical turning point in the EWM. This has been modeled in Ref. [107] on thebasis of a Quantum Monte Carlo simulation that tracked the motion of the atoms in theconservative potential until optical pumping occurred.

For the present loading scheme (cf. fig. 5.3 (a)), the situation is qualitativelydifferent. Since the waveguide is loaded from the steady-state MOST, atoms that enterthe range of the OP field do not have a nearly uniform velocity but are subject to


diffusive motion while cycling between 1s5 and 2p9 in the bichromatic EWM light field.Here, a comparable simulation of the atomic motion would not only be much moredemanding numerically but would also require an exact theoretical understanding ofthe simultaneous interaction with the (spatially modulated) bichromatic light field,which goes far beyond the simple model presented in chapter 4. Based on the MOSTmodel, a crude description can however be given.

EWM

MOST

OP

}MOT

WG

(a) (b)

OP

inte

nsi

ty

MOST

0

n

WG pot.

�715

1s5

2p4

1s3

A795

S�

� = 1� = 0

�44

Figure 5.3: Scheme for continuous loading (a) and simple model of the loading process (b).1s5 Atoms from a slow atomic beam are collected and cooled in the magneto-optical surfacetrap (MOST). In this trap, which is the combination of a surface-MOT and an evanescent-waveatom mirror (EWM), atoms approach the surface to within a fraction of an optical wavelengthby diffusion. In the short range of the OP field for optical pumping to 1s3, atoms are locallytransferred from the MOST into the potential of the waveguide via optical pumping (see text).

The MOST density n is modeled as spatially uniform over the length scale of theevanescent fields5. As illustrated in fig. 5.3 (b), this spatially flat reservoir of atoms is”tapped” at the surface by the evanescent OP field,

Iop(r) � F715IOP e�z=�715 ; (5.10)

where �715 and F715 is the decay length and field intensity enhancement of the sur-face plasmons and IOP the power in the OP beam. The coupling to the light field onresonance is expressed by the Rabi frequency

!R;OP � A715

qIop(r)=(2Is;715); (5.11)

where A715 = 6:25 � 105 s�1 and Is;715 = 0:036 mW/cm2. This coupling leads to apopulation �44 of the state 2p4, from which the atoms then decay to 1s3. For weakcoupling, this rate is given by

�OP = A795 �44 ; and �44 � !2R;OP=(�22p4 + 4Æ2eff ) (5.12)

5Very close to the surface this is certainly a very crude approximation since n should vanish near theEWM potential maximum.


The linewidth �2p4 = 33 � 106 s�1 is the full with of the state 2p4, and the effectivedetuning Æeff that accounts for the coupling to the other light fields 6. By being op-tically pumped, 1s3 atoms can scatter into a bound (harmonic) state j�i of the locallyoverlayed WG layer. For an atom in momentum state jpi this probability is given bythe Franck-Condon factor S�p = jhpj�ij2. For the thermal momentum distribution ofthe MOST reservoir, a thermally averaged FCF [92] can be calculated, which can bewritten as

S� = h S�pi = 2 cos �i�WG

�dB

2��!p�

Z 1

�1da H2

� (a) e�a2=(2�2); (5.13)

where �dB = h=p2�MkBTz � 20 nm is the thermal de Broglie wavelength (for Tz =

200 �K), the H� are Hermite polynomials and � = [2 + ~osc;z=(~kBTz)]1=2. For the

standard MOST and WG parameters, with kBTz � ~osc;z, the Franck-Condon factorsall have comparable values7 S� � 10�2. Provided that the MOST reservoir can beregarded infinite (such that n is not reduced much by loss from optical pumping), theloading rate into a waveguide layer i centered about zi can be written as

lWG;i � n(zi)�OP (zi)X�

S� (5.14)

For weak coupling to the other fields (Æeff � �2p4) the loading rate therefore shoulddrop exponentially from one layer to the next, and it should be proportional to the OPbeam intensity and the lifetime of the MOST.

5.2.4 Surface-Sensitive Detection.

The scheme for an integrated atom detector is illustrated in fig. 5.4 (a). A beam thatis split from the WG beam is incident from below the surface at the surface-plasmonresonance angle. It is used to generate an additional attractive evanescent potential(“waveguide deformation”, WGD) which simply adds to the WG potential, providedthat the polarization of the evanescent light field is orthogonal to that of the WG.

The effect of the evanescent field is illustrated in fig. 5.4 b: when the WGD beam ison, the attractive potential bends down the WG potential such that atoms are releasedtowards the surface8. The number of layers that lose their confinement depends on thepower available in the WGD beam (the evanescent field intensity has a decay length�796 = 316 nm, and so going from layer i to i+ 1 requires a power increase by a factor

6The effective detuning can be expected to arise from light shifts of the state 1s5 due to the EWMand the MOT as well as of the state 2p4 due to the WG [107]. Yet another additional contribution canbe expected from the cycling transitions 1s5 $ 2p9 that destroy the coherent internal evolution of theRabi oscillation between 1s5 and 2p4, similar as the decay from 2p4 to 1s3 itself: The state 1s5 acquiresa “width” �sc=2 that adds to the linewidth �2p4 , thereby slowing the decay to 1s3 via 2p4 further (this issimilar to the Quantum Zeno effect [211]).

7For much lower reservoir temperatures Tz the lower states are more likely to be populated.8This scheme was devised by the author already for earlier work [111], where it was used to charac-

terize the spatial selectivity of the pulsed loading scheme.

5.3. EXPERIMENT 85

of six). In the experiments we probed the population of the “surface waveguide layer”i = 1, as illustrated in the figure.

p-pol.

WGD

s-pol.WG2.521.510.50

-20

-40

-60

0

Distance from surface [µm]z

WG

po

ten

tial

[µK

]

WG+WGD

WG

i=1 i=2 i=3

(a) (b)

Figure 5.4: Surface-sensitive detection. The attractive optical potential of the WGD beam(exponential decay length �796 = 316 nm) deforms the WG potential, such that guided atomsare released towards the surface.

5.3 Experiment

5.3.1 Experimental Setup

The setup for our experiments is depicted in figs. 5.5 and 5.6. It is a straightforwardextension of that described in chapter 4, additionally including beams for the wave-guide (WG) and detection (WGD) at 796 nm and optical pumping (OP) at 715 nm.The WGD and OP beams were incident on the gold-coated surface at their surface-plasmon resonance angles, at which the evanescent-field parameters are �715 = 277 nm,�796 = 316 nm, F715 = 32 and F796 = 111, cf. chapter 2.

5.3.2 Continuous Loading

The first step towards integrated atom optics in our system was the realization of aCW loading scheme for the waveguide, which in a more general context is also thefirst-time demonstration of CW loading of an optical trap.

For the demonstration and a study of the loading mechanism we chose the waistof the WG beam at the surface as wWG = 0:43 mm, which was comparable to thetransverse waist of the atom cloud in the MOST. For the initial alignment of the setup,the position of the MOST cloud was taken as a fixed parameter9. To align the OP beam(wOP = 0:72 mm, IOP = 6:1 mW/cm2) we then released a cloud of 1s5 atoms froma MOT with z0 = 1 mm, which gave rise to a broad arrival distribution that coveredthe entire field of view of the surface atom detector. The OP spot could be localized

9As remarked earlier, the MOST proved to be an extremely fragile object that needed a lot of time-consuming beam alignment to be sufficiently stable.


Figure 5.5: Experimental configuration for the experiments on trapping and manipulationof atoms in the waveguide. The configuration is an extension of that of the MOST depictedin fig. 4.2, including additional beams for the waveguide (WG), optical pumping (OP) andsurface-sensitive detection (WGD). The EWM, OP and WGD beams are incident at the respec-tive surface-plasmon resonance angles.

by turning on the EWM, suppressing the 1s5 atoms but transmitting all pumped 1s3atoms. After aligning the OP, we optimized the relative alignment of the OP, EWM andWG spots by using the pulsed loading mechanism demonstrated in earlier work, cf.Ref. [110], and maximizing the number of atoms in the WG potential.

The TOF signal. In the aligned setup, we switched to the configuration for continu-ous loading by starting with a steady-state MOST (z0 = �0:5 mm, IEWM = 1:0 W/cm2,ÆEWM = 2� � 687 MHz) to which we added the OP and WG beams (�WG = 1:25 nm,IWG = 60 mW/cm2). After about 90 ms, the OP beam was turned off to stop loading,followed by the MOST about 10 ms later. When the WG was subsequently switchedoff, we observed a rapidly decaying TOF peak with a width of about 300 �s, as shownin fig. 5.7 (the EWM was left on as a shield for residual 1s5 atoms during the detectionphase). The appearance of this signal clearly shows that the CW loading mechanismworks10.

10In some initial experimental runs we observed overlayed spectra that varied slowly on the time scaleof the WG signal peak [212]. These could be minimized by lowering the MOST cloud, while the WGpeak itself remained nearly unaffected, or by realigning the beams. Probably they were due to intense

5.3. EXPERIMENT 87

(b)

P

M1

M2

M3

M4

(a)

EWM

OP

WG

WGD

ABS

MOT

Zeeman slower

M1 M

2M3

P

M4

Figure 5.6: (a) – Experimental setup for the experiments with the waveguide (top view). Theatomic-beam slowing laser beam (ABS) passes the prism (P) at grazing incidence. The MOTbeams enter the chamber through windows on the top side of the chamber. The EWM, OP andWGD beams are deflected at mirrors M1 and M2 inside the chamber to the back side of the goldfilm. The EWM and WGD are separated with a polarizing beam splitter cube behind the fiber.The waveguide (WG) beam is incident on the surface at 45Æ. For this purpose, two deflectionmirrors M3 and M4 above the prism are used which are mounted to the atom detector setup.The elements in the dashed rectangle in the bottom (cyl. lens and thin wire/ razor blade) areused for the realization of a channel waveguide and a switch, and the retroreflecting mirror inthe other dashed rectangle for is used for the realization of a surface lattice. The symbols forthe optical components are explained in fig 2.12. (b) – View into the main chamber. The largetube at the left is the rear end of the Zeeman slower; the two reentrant tubes at 45 degreescontain the MOT coils.

Loading rate. For a characterization of the loading process, we measured the loadingcurve of the waveguide. For that purpose, the loading time was increased successivelyin steps of 5 ms and the TOF signal was recorded each time. The measurement se-quence is illustrated in fig. 5.8, and the measured loading curve (for IWG = 44 W/cm2,IOP = 6 mW/cm2 and IEWM = 1 W/cm2) is shown in fig. 5.8. The increase of theatom number NWG in the loading phase can be fit by

NWG(t) =LWG

�WG

�1� e��WGt

�: (5.15)

The quantity LWG is the overall loading rate for 1s3 atoms in the WG potential, and�WG is the overall one-body loss rate from the waveguide. The fit of eq. 5.15 to thedata yields a loading rate of LWG = (1:6� 0:5)� 103 s�1 into the waveguide potential,of which a fraction of 25% is loaded into the lowest populated layer i = 1 for the

OP straylight near local surface scatterers that lead to significant optical pumping of atoms in the MOSToutside the range of the evanescent field, i.e. into the “bulk” layers i � 1. Apart from these initial runs,optical pumping by surface-plasmon straylight was however not an issue.


0

Inte

gra

ted

cou

nts

WGOP

OP 0 1 32 4 5 6

CW MOST EWM

EWMtime [ms]

WG

MOT x [mm]

y[m

m]

1.5

1.5

-1.5

-1.5

-0.75

-0.75

0.75

0.75

0

0

cts.

cts.

Figure 5.7: Experimental TOF signal of the CW loaded atom waveguide. The spatially resolvedimage gives the lateral distribution in the waveguide. The projections on the x and y axes canbe fit with Gaussians, yielding waists wx = 0:30 mm and wy = 0:33 mm.

chosen loading parameters (see below). In other experimental runs, we were able tooptimize the loading further by realigning the various beams, and we achieved steady-state atom numbers up to NWG � 130. Assuming the same loss rate, this correspondsto an increase of the loading rate to LWG � 4:8 � 103 s�1.

Loss rate. In the loading curve, the atom number reaches a steady state valueNWG =LWG=�WG. With NWG = 36, one obtains a loss rate �WG = (45 � 3) s�1, whichexceeds the photon-scattering rate on the open 1s3 $ 2p4 transition, �sc = 32 s�1. Toinvestigate this further, we measured the decay of the WG population after the loadingphase. In this measurement, the loading time was held fixed at 200 ms while thedecay time in the measurement sequence was sequentially increased. We measured anexponential decay with rate �WG;dec = (31�2) s�1, consistent with the rate for photonscattering11. This measurement shows that the additional losses during the loadingphase, ��WG = (14�4) s�1, are due to collisions between atoms in the WG and atomsin the MOST, which act as a background gas12.

11Non-exponential decay due to collisions between 1s3 atoms in the WG potential was observed for WGdensities 109 cm�3 [110], whereas in our case the densities were of order 108 cm�3 (the 3D density iscalculated by approximating the distribution in the direction perpendicular to the surface as a Gaussianwith waist 796 nm=(2

p2)).

12The collisional contribution �c � ��WG can be used to deduce a lower limit for the rate constant�35 = n�1��c. With the MOST density being of order n � 109 cm�3 (cf. chapter 4), one obtains�35 � 10�8 cm3s�1. (Qualitatively similar collisional losses were also observed by J. Stuhler et al. [103]

5.3. EXPERIMENT 89

AB/ABS

EWM

70

1 64

302.5�tL 5

loadingMOST/OPPhase

Duration [ms]

decay det.

MO

ST

MOT

B

OP

WGdet. trig.

detector signal pages

125µs 125µs

gateopen

{

{

NWG

Figure 5.8: Single sequence step for measuring the WG loading curve. The loading isstarted after an initial MOST/OP phase by switching on the WG beam. After a variable time� tL = 0 : : : 200 ms, the OP and MOT beams are switched off to stop loading, and the 1s3 atomdistribution in the WG potential is subsequently detected. During detection, the EWM beamis on in order to suppress counts from residual 1s5 MOST atoms. The detector is gated for a2.5 ms time window by turning off the magnetic field. This gating was used to store data fordifferent values of � tL in the same image sequence.

0 50 100 150 200

0

10

20

30

40

Ato

mnu

mbe

r

NWG

loading time �tL [ms]

Figure 5.9: WG loading curve determined from the summation over 200 sequential runs. Errorbars are due to the signal background (MOST atoms and atom beam). The dashed line is anexponential fit with time constant �L = (45� 3) s�1.

for the case of a MOT overlapped with a magnetic trap.)


Parameter dependence and spatial selectivity. To characterize the steady state fur-ther, we measured the dependence of the total atom number and of the population ofthe lowest layer i = 1 on the intensities of the EWM and OP fields. For that purpose,the surface-sensitive detection scheme was used.

The waveguide first was loaded from the MOST for 200 ms, with given intensitiesIOP and IEWM . After loading, the WGD beam (wWGD = 0:55 mm) was flashed onfor 500 �s before switching off the WG itself (this time was long enough for all atomsin layer i = 1 to be released yet short compared to the decay time of the WG). Tocheck the detection method experimentally, we recorded the WGD signal for differentintensities IWGD after the WG was loaded with a fixed set of loading parameters. Forlow intensities the signal first increased and then saturated for intensities above 80%of the final value IWGD = 33 W/cm2. This shows that the deformation of the higherlayers remained small enough to prevent noticeable loss, while layer i = 1 was emptiedcompletely.

Fig. 5.10 (a) shows a set of data, containing (1) the peak resulting from the releaseof atoms from the single layer when the WGD beam is turned on, followed by (2) thepeak of remaining atoms in higher layers when subsequently the WG is turned off. Peak(3) is from a reference run without WGD. The relative population P1 of layer i = 1 canbe determined by comparing the number of counts in the “depleted” peak N2 (i.e. afterthe loss of the atoms from layer i = 1) to the number of counts in the reference peakN3

that contains all atoms, as P1 = 1 �N2=N3. The results for the relative population P1are shown in fig. 5.10 (b) and (c). In both cases, P1 remains above 20% and typicallyis around 30%. The dependence of the total atom number N3 on the intensities IEWM

and IOP is also shown in figs. 5.10 (b) and (c) 13 . The atom number increases aboutlinearly with the OP and EWM intensity, which is in rough qualitative agreement withthe simple model discussed above. The coupling to the evanescent OP field is weak,which can be seen from the constancy of P1 when IOP is increased. Increasing IEWM

increases the MOST density, and with it the local pumping rate (note that the WGsignal does not vanish completely at zero EWM intensity, as well as the density in theMOST). The experimentally observed spatial selectivity is considerably smaller thanexpected value (P1;th � 85%). This might be due to a reduction of the MOST density(or alternatively an increase of Æeff , as explained in footnote 6) in the range of theevanescent fields.

Comparison with pulsed loading and possible improvements. It is interesting tocompare the performance of CW loading to that of the pulsed scheme realized previ-ously [110]. One benchmark is the loading flux F , i.e. the loading rate per area, for

13For these measurements, an equivalent measurement sequence was used in which the reference peakitself was referenced to the atom number in the MOST. This was done in order to minimize effects oftemporal drifts in the performance of the atom source. — For a direct comparison of the WGD and WGpeaks it is important to note that, while for the WGD case all atoms are released towards the surface, inthe WG case one half of the atomic distribution ballistically escapes upward without being detected in theobservation time window, such that for a determination of the atom number corresponding to the WGpeak, the signal has to be multiplied by a factor of two [182].

5.3. EXPERIMENT 91

(a)

time [ms]

TO

Fco

unts

WG

WGD

(1)

time [ms]

(3)

(2)

0 1 2 30 1 2 30

(b)

0

0.2

0.4

0.6

0.8

1

0 0.5 1

(c )

0 3 60

IEWM [W/cm2] IOP [mW/cm2]

IOP = 6:1 mW/cm2 IEWM = 1:1 W/cm2

Rel

.po

p.

P1=(1�N2= N3)

Atom

number

N�3

Figure 5.10: Dependence of the total atom number and the relative population P1 of layeri = 1 on the EWM and OP intensities. (a) – TOF data obtained for loading parameters IEWM =1 W/cm2 and IOP = 3 mW/cm2. Turning on the WGD beam gives rise to a peak (1) from atomsreleased from layer i = 1. When the WG beam is subsequently turned off, the atoms storedin the higher layers are released (2). This signal (2) is compared to a reference measurementwithout WGD beam (3). (b) and (c) – Dependence of the total atom number N�

3 (filled boxes,determined from a separate set of experimental runs, see text) and relative population P1 =(1 � N2=N3) of layer i = 1 (open boxes) on IEWM and IOP . N2 and N3 are determined asthe sum of counts between 1.9 ms and 2.5 ms, minus the average of counts between 2.6 and3.2 ms which is taken as a physical offset level after the decay of the peak.

layer i = 1. For that purpose one can relate the loading rate to the area A = �wxwy ofthe atomic distribution in the waveguide (cf. fig. 5.7). For the pulsed loading scheme,up to 103 1s3 atoms were tapped in the WG layer on an area Ap = 1:5� 10�2 cm2 aftera 20 ms loading pulse, which leads to a loading flux Fp � 106 cm�2 s�1 for the shortduration of the pulse. For the present scheme, the area of the WG is Ac = 3�10�3 cm2,such that Fc � LWG=Ac � (105:::106) cm�2 s�1, this time in for CW operation. Thesituation looks even more favorable for the new scheme when the loading efficiency� � LWG=L is compared, defined as the ratio of the loading rate LWG of the WG tothe loading rate L of the atom reservoir. For the CW loading parameters, the loadingrate L of the MOST (z0 = �0:5 mm, IMOT = 6:8Is) is on the order of 105 s�1 (cf.chapter 4). This yields a loading efficiency �c = LWG=L � 10�2. On the other hand,for the pulsed scheme, the loading rate into the MOT was around 107 s�1, which yieldsa corresponding efficiency �p � 10�3, which is one order of magnitude smaller (in thatcase, the lower efficiency is due to losses from the transverse ballistic expansion of theatom cloud [111]).

Our CW loading scheme has been discussed in connection with the realization of aCW atom laser for argon [92,100,111]. This presumes a loading flux of > 109 cm�2s�1

[111], which is still far out of reach for the present, proof-of-principle realization. Sig-nificantly higher loading rates might however be reached with optimized parameters,


as suggested by the data in fig. 5.10. In the present realization, we were severely lim-ited by the maximum powers of the OP, EWM and MOT laser beams. Without theserestrictions, it should be possible to better match the temperature of the MOST to thedepth of the WG potential and to increase the optical pumping rate in the evanescentfield. This way it should be possible to reach higher loading efficiencies � ! 1. For highOP intensities, optical pumping by straylight outside the range of the evanescent fieldmay eventually become significant as a shielding effect; however this can be suppressedby further improving the quality of the surface. It should also be possible to increasethe loading rate into the MOST by at least one order of magnitude by improving theflux of the Zeeman-slowed atomic beam with an another transverse cooling stage. Al-together, a WG loading flux of the required order might therefore be reachable withimproved experimental apparatus.

5.3.3 Integrated Atom Source and Switchable Channel Guide

The CW loading scheme can readily be used as an atom source for integrated atomoptics. In this context it is sufficient to realize that, while the CW loading is limited tothe overlap area of the MOST and the OP field (“source region”), the WG profile canbe much larger (“beam region”). By using an elliptically deformed Gaussian beam spot(waist ratio � 1=10, long axis waist 2 mm), we have realized a planar channel atomguide into which source was placed about 1.5 mm off center along the long axis.

(b)

(a)

source beam

MOST/OPShadow

WG

WG

1 mm

1m

m1

mm

1 mm

1m

m

MOST/OP

Figure 5.11: Guided atomic motion in a channel guide as observed with the surface atomdetector using the TOF technique. The planar channel is formed by an elliptically shapedWG spot in which the atom source is put off center. (a) Measured lateral distribution for CWoperation of the source (the image was taken after 100 ms). (b) Measured lateral distributionfor CW operation obtained with a beam blocker (formed by the imaged shadow of a thin wire)behind the source region. The source and beam regions can be clearly identified.

The distribution of atoms in the channel is shown in fig. 5.11 (a) for CW operation

5.3. EXPERIMENT 93

0 ms

10 ms

20 ms

MOST/OP

WGShadow

remove (t=0)load (t<0)

5 ms

15 ms

25 ms

Figure 5.12: Sequence of TOF images showing the propagation of atoms in the channel. TheCW source is first turned off, and then an “opto-atomic” switch behind the source region isquickly activated (by pulling a razor blade out of the WG beam profile), allowing the atomsinto the channel. The dynamic range of the single images is normalized to the brightest pixel.

of the source. The image, which was obtained with the TOF technique after turningoff the WG beam, shows a distribution of atoms stretching along the entire field ofview of the detector. In order to locate the source and beam regions physically and todemonstrate the flow of atoms, we first created a beam blocker behind the source. Thiswas done by imaging the shadow of a thin wire onto the surface that was placed intothe WG beam along the short axis of the ellipse. The shadow, which had a transverseextension of less than 500 �m, gave rise to a potential barrier that the atoms in the WGcould not penetrate. We first placed this beam blocker into the source region and thendisplaced it downstream until the atom density in the remaining channel vanished, asshown in fig. 5.11 (b). This is a clear proof that the atoms in the right half of the fieldof view of fig. 5.11 (a) must have originated from a spatially separated source.


In order to observe the motion of atoms in the channel directly, we extended thebeam blocker concept to allow for switching. In principle this could have been doneby quickly removing the wire from the WG beam in a controlled way. We decidedhowever for a simpler technique that was physically equivalent for our purpose byusing a razor blade mounted to an electro-mechanical relay that was placed in the WGbeam (replacing the wire). In analogy to integrated optics, this might be called an“opto-atomic” switch 14. In the “open” status, only the source region was exposed toWG light, whereas in the “closed” status, no part of the beam profile was chopped,enabling the flow of atoms out of the source region. The switching time, i.e. the timerequired to remove the blade from the beam, was approximately 2 ms.

In the experiment we first operated the source CW with open switch in order toaccumulate 1s3 atoms in the source region. After turning off the source, the switch wasclosed. This resulted in atoms propagating downstream the channel whose motioncould be tracked using the TOF technique. Results are shown in fig. 5.12. The motionis an accelerated ballistic expansion (there is a potential gradient towards the center ofthe WG beam spot) with velocities on the order of a few centimeters per second.

5.3.4 Integrated Atom Detector and Simple Integrated Circuit

In the above experiments on the channel, atoms were detected by turning off the WGbeam and recording spatially resolved TOF images. This detection method, which relieson the spatial resolution of the surface atom detector’s MCP, necessarily releases atomseverywhere in the waveguide potential. An alternative scheme can be implementedusing the surface-sensitive potential deformation (WGD) method. As illustrated in fig.5.1 the position and size of the detection are are determined by the parameters ofthe WGD beam and therefore can be easily adjusted. The scheme is intrinsically localand does not require, as such, the spatial resolution of the MCP. At the same time italso allows to probe atoms in the operating waveguide. It is therefore an atom-opticalanalogue to an integrated optical detector15.

In the experimental demonstration of this integrated atom detector, the WGD spot(WGD beam waist 0.32 mm) was located in the channel at a lateral distance of 1.5 mmfrom the atom source as illustrated in fig. 5.1, and the results are shown in fig. 5.13(b). The upper image of the figure displays the recorded background distribution forthe operating WG. As shown in the lower image of the figure, an additional flashing ofthe WGD beam (for 500 �s) resulted in electrons being locally ejected from the surface,as expected.

We also used the detector to determine the fraction of atoms in WG layer i = 1, asdone already for the characterization of CW loading. For this purpose, the image for

14Integrated electro-optic switches [213] locally change the transmission of a waveguide via its indexof refraction, using the Pockels and Kerr effects. In our case the shadow changes the index of refractionfor atoms, n =

p1� U=E [4], where U is the optical potential and E is the kinetic energy of the atom

incident on the barrier.15Integrated optical detectors commonly are realized by semiconductor photodiodes that are incorpo-

rated into or grown on top of the integrated waveguide [214,215].

5.3. EXPERIMENT 95

local detection was compared to a reference image as in fig. 5.11 (a). Evaluated in thearea of the detector, the data yield a relative population P1 = 27%.

WG

MOST/OP WGD

WG on

WG on, flash WGD

Figure 5.13: Demonstration of an integrated atom detector. The images show the recordedlateral distributions for the operating WG immediately before (top) and while (bottom) theWGD beam is flashed on for 500 �s. The detector (WGD) is located at a distance of about 1.5mm from the source. The combination of source, guide and detector realizes an elementaryintegrated circuit.

The setup shown in fig. 5.13 used to demonstrate the atom detector incorporates,in the planar geometry of the waveguide, the source and detector as interconnectedfunctional elements. In analogy to integrated optics, this setup can thus be viewed as asimple atom-optical integrated circuit. Our circuit realizes an elementary atomic beamexperiment in the lowest WG layer at a distance of 820 nm from the surface, as is alsosketched in fig. 5.1 (a).

5.3.5 Optical Surface Lattice

One of the advantages of our optical system over the realization of atom optics in mag-netic potentials is the large flexibility to modulate and reshape the confining potential.This was already exploited for the integrated atom detection. Another example is therealizability of an optical “surface lattice”.

Principle. As illustrated in fig. 5.14, the optical surface lattice is realized by retrore-flecting the (elliptical) WG beam. This gives rise to a WG intensity modulation alongthe long axis (0y) which, together with the modulation perpendicular to the surface,produces a periodic array of quasi-1D channel waveguides16. The modulation of theoptical potential along the surface is given by

UOL;dip = U0

h1 + %� 2

p% cos(k0yy)

i; (5.16)

16The term channel waveguide is appropriate here, since the atomic motion is quantized in the radialdirection, with only a small number of bound states.


Ar* (1s3)

OP

MOT

EWM

Mirro

r

AttenuatorWG

P1

P2

Figure 5.14: Experimental scheme for an optical surface lattice. A periodic array of quasi-1D channels is produced by retroreflecting a fraction (power P2) of the s-polarized WG beam(power P1). The modulation depth can be adjusted with an attenuator in front of the retrore-flection mirror. The lattice is loaded via evanescent-field optical pumping (OP) from the MOST.

where U0 is the depth of the single-beam waveguide potential, % = P2=P1 is the ratiobetween the powers (intensities) of the reflected beam (P2) and the original WG beam(P1), and k0y = 2� sin �i=�WG is the wave vector along 0y. For the incidence angle�i = 45Æ, k0y coincides with the wave vector for the modulation along 0z, which leadsto equal oscillation frequencies in the channel waveguides parallel and perpendicularto the surface. Depending on the ratio % (which can be adjusted with an attenuator),the depth of the modulation can be varied from 0 to 4 U0.

Experiment and interpretation of results. In a simple experiment we operated thelattice and atom source CW for 200 ms for different ratios % = P2=P1, which werechosen between 0 and 1, covering a range of four orders of magnitude, and then tookTOF data for the distribution of 1s3 atoms in the lattice potential. A set of experimentalTOF images is shown in fig. 5.15 (a). With increasing depth of the intensity modula-tion, 1s3 atoms increasingly accumulate in the source area while the number of thosein the “beam area” reduces. For full modulation, the atoms are completely confined inthe source area. Even though the modulation period (560 nm) is much too small toobserve the channel structure directly, this transverse confinement is clear evidence forthe atom localization in the array of channel waveguides at the surface.

To interpret the data further one can exploit that, in the absence of a heating mech-anism in the optical potential, atoms in the beam area must be those atoms from thethermal distribution in the source area (after optical pumping to 1s3) whose kineticenergy exceeds the modulation depth of the lattice 17. The fact that these atoms spill

17A second possibility for an escape from the source area (neglecting tunneling as a third possibility)is diffusion due to a Langevin force, cf. eq. 2.39, which arises from photon scattering: by absorbinglattice photons, atoms can accumulate enough energy to hop to adjoining lattice sites [216, 217]. In ourcase, however, photon scattering on the open 1s3 $ 2p4 transition leads to a loss to the ground state 2p1

5.3. EXPERIMENT 97

�� 2MOST/OP

WG

(a)

P P2 1/ = 0

1

2 x 10-3

1 x 10-2

1 x 10-1

(b)

0.01 0.02 0.05 0.1 0.2 0.5 1

0

0.2

0.4

0.6

0.8

1

0A

B

x

x�

Relative modulation depthpP2=P1

Loca

lized

frac

tion

A=(A+B)

Figure 5.15: Localization of atoms in the optical surface lattice. (a) Atom distribution for CWsource operation for different ratios P2=P1 of the beam powers (and intensities) measured 200ms after the WG beam is turned on (the dynamic range of the single images is normalized to thebrightest pixel). With increasing depth of the intensity modulation, an increasing fraction of 1s3atoms accumulate in the source area, which is indirect evidence for the transverse localizationof these atoms in the array of channels. (b) Fraction f = A=(A + B) of localized atoms inthe source area versus relative modulation depth % =

pP2=P1. The fraction f is obtained as

illustrated in the inset (see text). The solid curve is the model with maximum modulation depthUOL;max = 6:5 kBTy.

out ballistically into the neighboring beam area is, of course, a trivial statement in thelimiting case % = 0, but it also holds for the other cases % 6= 0 in which a variable frac-tion of the thermal distribution in the beam area does remain localized in the lattice.For a given modulation depth UOL;1 � p%UOL;max, this fraction is given by

f = erf

sUOL;1kBTy

!(5.17)

where Ty is the transverse temperature, in direct analogy to the treatment of thetranslucence of the atom mirror’s potential barrier for a thermal distribution, eq. 4.6.

already after two scattering events. An influence of diffusion on the (conservative) atom dynamics in thewaveguide due to photon scattering can therefore be neglected.


The fraction f can be extracted from the experimental TOF data in the followingway. The total atom number NS in the source area is the sum of a localized atomnumber A and a ballistic background B, which is the same as in a neighboring beamarea of equal size (the average of the regions left and right of the source is taken).Then f is given by

f =NS �B

NS=

A

A+B: (5.18)

An example (for % = 2� 10�3) is illustrated in the inset of fig. 5.15 (b).Fig. 5.15 (b) also summarizes the results of our measurements. The experimental

values for f agree very well with the model, eq. 5.17, which is shown as a solid curve.In the model, the absolute value of the full (% = 1) modulation depth, UOL;max, istaken as a single fit parameter, resulting in UOL;max = (6:5 � 0:5) kBTy (unfortunatelyneither Ty nor UOL;max are not known well enough to allow for a direct comparison).

Further experiments. The surface lattice can readily be transformed into a conveyorbelt for atoms. Such a device could e.g. be used to deliver atoms to other functionalelements for atom manipulation with high accuracy18. The easiest realization is tomove the retroreflection mirror along the beam axis: this shifts the array of channelsalong the prism surface19. Still another possibility would be to frequency-shift theretroreflected beam to obtain a moving standing-wave surface lattice. Other possibleapplications include studies of single-atom dynamics in (temporally modulated) opticallattices, complementary to work on single ions [217].

5.4 Conclusions

In our experiments with metastable argon, we have demonstrated the continuous load-ing of atoms into a surface atom waveguide. The optical waveguide potential for 1s3metastable argon atoms is formed by a red-detuned standing light wave (SLW) above agold-coated prism surface. In this planar system the atomic motion is quasi free parallelto the surface while normal to it only a few bound states exist. The CW loading mech-anism is based on the combination of the magneto-optical surface trap (MOST) withan evanescent field that pumps the atoms from 1s5 to the other metastable state 1s3in its short range above the surface. Experimentally, we have achieved a loading rateon the order of 103 atoms/s, which corresponds to a flux of 105 atoms/(s cm2). This is

18An optical conveyor belt has been realized recently for free space [218].19We have indeed tried to demonstrate the conveyor belt experimentally. For that purpose we mounted

a 1-inch retroreflecting diameter mirror to a large loudspeaker coil at 1 m from the surface that wasdriven by a sawtooth function generator. In order to maintain the overlap of the WG spots on the sur-face over the whole translation length of 3 mm, a stability of order 10�4 in the angle would have beenrequired. Experimentally, however, we managed to achieve only down to 10�3 with the help of a mechan-ical stabilization mechanism. Despite some indications of operation, we have not anymore been able toconvincingly demonstrate the conveyor belt in time.

5.4. CONCLUSIONS 99

roughly comparable to the peak loading flux of our previously realized pulsed loadingscheme. The evanescent loading mechanism led to a relative population of around 30%for the lowest confining waveguide layer centered at 820 nm from the surface, ordersof magnitude closer than achieved in the work on atoms trapped in magnetic potentialsat surfaces.

Based on the continuous loading scheme for the waveguide, we have implementeda local atom source in its planar geometry. We have realized a switchable channel guideconnected to the source and have directly observed the propagation of atoms in thisguide. We have realized an atom detector in the channel guide via a local deformationof the confining waveguide potential with another evanescent light field. The combi-nation of the source, the guide and the detector forms a simple atom-optical integratedcircuit that realizes an atomic beam experiment in the waveguide geometry. Finally, wehave demonstrated and studied the localization of atoms in an optical surface lattice.

Our scheme for integrated atom optics is extremely flexible since the confiningoptical potential of the waveguide can be modulated easily both in space and time. Infuture applications, one might envision using addressable liquid crystal pixel arrays astransmission masks in the waveguide beam that are combined with a high-resolutionimaging system. In this way, miniaturized and time-dependent atom-optical setupscould be realized, paving the way to novel integrated elements and complex integratedcircuits. In addition, the extreme closeness to the surface makes our system interestingfor the probing of atom-surface interactions.

Appendix A

Dressed Atom in a BichromaticLight Field

The optical potential acting on a two-level atom in a bichromatic light field L1 = (!0+ÆL;1; !R;1) and L2 = (!0 + ÆL;2; !R;2) is of immediate interest for the magneto-opticalsurface trap. The dressed-atom model can give an intuitive insight into the underlyingphysical processes as long as !R;1 � !R;2. It is then possible to construct dressedstates from the coupling to the strong field, and the weak field then merely acts a time-dependent perturbation that induces transitions between those states. The treatmentpresented here (for details, see Ref. [212]) is based on a suggestion in Ref. [219]; asimilar approach can be found in Refs. [220,221].

The evolution of the system, including spontaneous emission, is again given by themaster equation 2.15, where the Hamiltonian of the total system is now

H = HAL2 + �VAL1 : (A.1)

Here HAL2 describes the coupling of the atom to the mode L2 as discussed in chapter2, and �VAL1 (0 � � � 1) describes the additional perturbation due to L1,

VAL1 =~!R;12

he�i(!0+Æ1)tL+ + ei(!0+Æ1)tL�

i: (A.2)

The density of the system can be expanded into a perturbation series

� = �(0) + ��(1) + �2�(2) + : : : (A.3)

that is expressed in the unperturbed dressed-state basis by the density matrix elements

�(n)ii =

XN

hi (N)j�(n)ji (N)i; �ij(�)(n) =XN

hi (N�1)j�(n)jj (N)i (i 6= j): (A.4)

Steady-state solutions for �ii and �ij(�) to the different orders in � can then be foundin a straightforward way starting from the zeroth-order solution discussed in chapter

101

102 APPENDIX A. DRESSED ATOM IN A BICHROMATIC LIGHT FIELD

2. Setting � = 1, the result for the steady-state population difference �st � (�22� �11)is

�st;(0) =cos4 �2 � sin4 �2

cos4 �2 + sin4 �2(A.5)

�st;(1) = 0 (A.6)

�st;(2) = ��st;(0) !2R;1

"cos4 �2

�2coh;2 + (2 + ÆL;2 � ÆL;1)2+ (A.7)

sin4 �2�2coh;2 + (2 + ÆL;1 � ÆL;2)2

#�coh;2=�

sin4 �2 + cos4 �2; (A.8)

where �coh;2 and �2 are given by the coupling to the mode L2 and are defined asin section 2.1.1. This means that the coupling to the weak mode L1 acts as reducethe population difference in second order by �st;(2), proportional to its intensity. Thephysical interpretation of this is therefore that the mode L1 drives additional transitionsbetween the dressed states. These then lead to an attenuation of the optical dipole forcehFdipi (cf. eq. 2.21) exerted by the field L2.

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Zusammenfassung

Diese Dissertation beschreibt Experimente zur Speicherung und Manipulationlasergekühlter metastabiler Argon-Atome an einer Oberfläche. Die einzelnen Punkteder Arbeit lassen sich wie folgt zusammenfassen:

Magneto-optische Oberflächenfalle. Eine neuartige magneto-optische Oberflächen-falle (MOST) wurde realisiert und charakterisiert. Bei der MOST handelt es sich umdie Kombination einer oberflächennahen magneto-optischen Falle (MOT) mit einemoptisch-evaneszenten Atomspiegel. Die in der MOT gespeicherte Atomwolke wirddurch das evaneszente Lichtfeld, dessen Reichweite ein Bruchteil einer optischenWellenlänge beträgt, von der metallischen Oberfläche des Spiegels ferngehalten. ImExperiment konnten so (1:3�0:4)�105 Atome bei einer Lebensdauer von (390�30) msgespeichert werden.

Die Eigenschaften der gespeicherten atomaren Wolke wurden, zunächst ohnedas evaneszente Feld, für verschiedene Abstände der Wolke zur Oberfläche un-tersucht. Insbesondere wurde, bei einer Abstandsverringerung des Quadrupol-Magnetfeldnullpunks z0 der MOT von 1 mm über der Oberfläche auf Null, einedramatische Abnahme der Lebensdauer um zwei Größenordnungen auf etwa 50 msbeobachtet. Die Eigenschaften des Atomspiegels in der Gegenwart des MOT-Lichtswurden untersucht; hierbei wurde eine starke Reduktion der Reflektivität im Vergleichzum Fall ohne MOT-Licht festgestellt. Dieser bichromatische Effekt wurde für ver-schiedene Parameter der Lichtfelder charakterisiert. Für eine Falle mit z0 = 0 konnteschließlich nachgewiesen werden, daß die Lebensdauer der gefangenen Wolke mithilfedes evaneszenten Felds des Atomspiegels um mindestens eine Größenordnung ver-längert werden kann. Die Eigenschaften der MOST werden anhand eines einfachenModells erklärt.

Kontinuierliches Laden eines planaren Wellenleiters für Atome. Durch Verwen-dung der MOST als Atomreservoir an der Oberfläche konnte ein kontinuierlicher Lade-mechanismus für einen planaren Atomwellenleiter demonstriert werden. Der Wellen-leiter wird durch das periodische optische Potential einer stehenden Lichtwelle überder Oberfläche gebildet, die gegen einen optischen Übergang rotverstimmt ist. DiesesSystem ist durch quasi-freie atomare Bewegung parallel zur Oberfläche charakterisiert,während senkrecht dazu nur wenige gebundene Zustände existieren. Ein kontinuier-

119

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licher, oberflächensensitiver Lademechanismus für den Wellenleiter konnte experi-mentell demonstriert werden. Der Mechanismus basiert auf der MOST als Reservoirlasergekühlter Atome an der Oberfläche, aus dem Atome innerhalb der kurzen Abfal-länge eines evaneszenten Lichtfelds optisch in den Wellenleiter gepumpt werden. DerLademechanismus wurde für verschiedene Parameter charakterisiert; hierbei wurdeeine maximale Laderate der Größenordnung 103 Atome/s, entsprechend einem Lade-fluß von 105 Atomen/(s cm2) erreicht. Der evaneszente Lademechanismus führte zueiner etwa 30%igen relativen Besetzung der untersten besetzbaren Wellenleiterschicht,deren mittlerer Abstand von der Oberfläche 820 nm betrug.

Manipulation von Atomen im Wellenleiter: integrierte Atomoptik. Auf der Basisdes kontinuierlichen Ladeschemas konnte eine lokale Atomquelle in der Wellenleiter-geometrie implementiert werden. In einem schaltbaren, an die Quelle anschließendenlinearen Kanal konnte die Propagation von Atomen im Wellenleiter direkt beobachtetwerden. Ein im Wellenleiter integrierter Atomdetektor wurde über eine lokale Ver-formung des Wellenleiterpotentials realisiert. Quelle, Kanal und Detekor wurden zueinem integrierten Schaltkreis für ein einfaches miniaturisiertes Atomstrahlexperimentin der untersten Wellenleiterschicht kombiniert. In einem weiteren Experiment kon-nte die Lokalisierung von Atomen in einem quasi-eindimensionalen Oberflächengitterdemonstriert werden.

Nachweis metastabiler Atome an einer Oberfläche. Der Nachweis der metasta-bilen Atome an der Oberfläche erfolgte durch die elektronenoptische Abbildung vonSekundärelektronen, die bei der Abregung einzelner Atome an der Oberfläche aus-gelöst werden. Der Oberflächenatomdetektor wurde mit atomoptischen Methodencharakterisiert und kalibriert. Die Detektionseffizienzen für die in den Experimentenverwendeten Zustände 1s5 (MOST) und 1s3 (Wellenleiter) von Argon wurden be-stimmt. Dies ermöglichte einen Zugang zu der bisher nicht bekannten Elektronenaus-lösewahrscheinlichkeit von 1s3 an einer Goldoberfläche, für die mit einem Wert von� 14% eine Übereinstimmung mit der für den Zustand 1s5 gefunden wurde. Basierendauf der räumlichen und zeitlichen Auflösung des Detektors konnte eine Methode zurdreidimensionalen Flugzeitspektroskopie demonstriert werden.

Danksagung

An dieser Stelle möchte ich mich bei allen bedanken, die zum Gelingen dieser Arbeitbeigetragen haben.

Ich danke Professor Jürgen Mlynek für die Möglichkeit, mich in der stimulierendenAtmosphäre seines Konstanzer Lehrstuhls mit Atomoptik beschäftigen zu können, undinsbesondere für die uneingeschränkte und vertrauensvolle Unterstützung meiner Ar-beit, die mir immer ein großer Ansporn zum Erfolg war. Ich danke weiterhin ProfessorTilman Pfau (Universität Stuttgart) für viele gemeinsame Überlegungen und Diskussio-nen in seiner Zeit als Leiter der Konstanzer Atomoptik-Gruppe, sowie seinem Nachfol-ger Dr. Markus Oberthaler für klärende Diskussionen, sein Interesse und seine Geduldbis zum Abschluß der Arbeit.

Bei der täglichen Arbeit an der nun Geschichte gewordenen Strahlmaschine ISABELdanke ich zunächst meinen Vorgängern Michael Hartl und Harald Gauck für die invieler Hinsicht interessante gemeinsame Zeit. Harald Schnitzler schuf mit seinerKamerasoftware während seiner Diplomarbeit eine extrem zuverlässige Voraussetzungfür die Durchführung unserer Experimente, hierfür nochmals vielen Dank. Kay Orgassadanke ich für seinen großen Einsatz während seiner Diplomandenzeit, die vom gemein-samen harten Ringen um die Reproduzierbarkeit der MOST geprägt war. Ein großerDank gilt Dr. Masahiro Hasuo (Gastwissenschaftler von der Universität Kyoto) undThomas Anker, zunächst HiWi und dann Diplomand, für die exzellente Zusammen-arbeit während des letzten experimentellen Jahres, in dem eine Vielzahl von Ergebnis-sen entstanden sind. Schließlich danke ich Dr. Richard Adams, Postdoc an der Nachbar-maschine, für seinen unnachahmlichen Humor, der viel zu einem heiteren Arbeitsklimaim Labor beigetragen hat.

Die Optimierung der Oberberfläche war eine wichtige Voraussetzung für unsere Ex-perimente. Ich danke Professor Paul Leiderer und Dr. Clemens Bechinger für wertvolleInformationen zu Oberflächenplasmonen und Schichtsystemen, sowie Stefan Walheimund Erik Schäffer für die Hilfe bei der Charakterisierung unserer aufgedampften Gold-schichten mit dem AFM, und nochmals Stefan Walheim für einen überaus wertvollenTip zur Behandlung unserer Glasprismen. Jean-Philippe Deschamps (Ecole Polytech-nique, Paris) danke ich für Experimente zum optimierten Aufdampfen von Schichtenwährend eines Praktikums in unserer Gruppe und Dr. Vahid Sandoghdar und seinerNanooptik-Gruppe am Lehrstuhl für das Bereitstellen von Infrastruktur in ihrem Labor.Weiterhin danke ich Dr. Carsten Henkel (Universität Potsdam) für die Zusammenarbeit

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bei der Steulicht-Charakterisierung und -Modellierung. Dr. Peter Marzlin danke ichfür wertvolle Hinweise zur störungstheoretischen Behandlung des Zweifarbenproblemsder MOST.

Der Atomoptikgruppe und allen Kollegen auf P8 danke ich für das freundschaftlicheund hilfsbereite Miteinander, und insbesondere auch den ”Chromis” Jürgen Stuhler,Piet Schmidt und Sven Hensler für den Erfahrungsaustausch von MO(S)T zu MOT. Un-serem Elektronik-Guru Stefan Eggert danke ich für seine bewundernswert schnellenLösungsvorschläge und für seine Engelsgeduld bei der Feinjustage von Schaltkreisen.Stefan Hahn war nicht nur Ansprechpartner für verzwickte mechanische Fragen, son-dern hat auch als Infrastrukturspezialist nicht unerheblich zum reibungslosen Ablaufder Arbeit beigetragen, hierfür vielen Dank. Ute Hentzen und Waltraud Heinzen dankeich für ihre große Hilfsbereitschaft bei organisatorischen Dingen und den Werkstättender Uni Konstanz für die schnelle und hochwertige Bearbeitung zahlreicher Aufträge.

Beim Verfassen der schriftlichen Arbeit konnte ich von hilfreichen Anmerkungender Probeleser Dr. Björn Brezger, Dr. Masahiro Hasuo, Dr. Markus Oberthaler, Dr. JoBellanca und Thomas Anker profitieren, denen ich hierfür herzlich danke. Ein großerDank gilt hier auch Professor Wolfgang Ketterle und Professor David Pritchard, in derenGruppe am Massachusetts Institute of Technology ich die schriftliche Arbeit zu Endebringen durfte.

Den Mitmusikern der Lehrstuhl-Jazzcombo, darunter Hannes Schniepp, PeterMarzlin, Stefan Eggert, sowie als Very Special Guests Tilman Pfau und Jürgen Mlynek,danke ich für musikalische Sternstunden rund um die Konstanzer Physik...

Schließlich, aber nicht zuletzt, danke ich von Herzen meiner Familie und meinerFrau Elisa, die meinetwegen den Sprung über den Atlantik hin und wieder zurückgewagt hat, für die unbeschreibliche Unterstützung und Rückendeckung während allder Jahre.

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