Electric field sensing near atom chips using cold Rydberg atoms

J. Carter, Jim MartinDepartment of Physics and Astronomy

Gerlach's postcard, dated 8 February 1922, to Niels Bohr. It shows a photograph of the beam splitting, with the message, in translation: "Attached [is] the experimental proof of directional quantization. We congratulate [you] on the confirmation of your theory." (see Physics Today Dec. 2003.)

W. Gerlach

The Stern-Gerlach demonstration of “space quantization”

Magnetic dipole moment

The Stern-Gerlach experiment and the magnetic dipole force

Energy of magnetic dipole in a magnetic field:

Gradients in magnetic field generate forces:

Magnetic field

Space quantization of angular momentum gives “low and high field seekers”:

ener

gy

magnetic field

low field seeker

high field seeker

from plaque at the Frankfurt institute

Can the Stern-Gerlach force be used to “trap” atoms?

• review of mechanism of force.

• necessity for laser cooling.

• demonstration.

• miniaturization (atom chips!).

• Rydberg atom surface interactions with atom chips.

Magnetic dipoles: the simplest magnets

a small circular loop of current.

IR a = πR2

area

in a constant magnetic field the dipole experiences no net force:

~m = Iaz

magnetic moment:

F

all forces cancel

I

B~F = q~v × ~B

A changing magnetic field exerts a force on a dipole

Cylindrical symmetry:

B

∂Bz∂z

+ 2∂Br∂r

= 0

No sources or sinks:

∂Br∂r

= − 12∂Bz∂z

~∇ · ~B = 0

Total force on dipole:

I

Fz = −Br I 2πR

Fz = −R∂Br

∂r I 2πR

Fz =12R

∂Bz

∂z I 2πR

Fz =∂Bz

∂z I πR2

Fz =∂Bz

∂z m

~F = −∇(− ~B · ~m)a changing

magnetic field generates a force on dipole.

special case of

Magnetic dipole moment is related to angular momentumimagine each current loop consists of a point particle moving in a circle:

v

R q

the average is:~μ ~μ = aI z

= πR2 qTz

= πR2 q2πR/v z

= 12qRv z

we can write in terms of the angular momentum of the moving charge:

Rv

~c = ~r × ~p

(in this case)= mRv z

Magnetic dipole moment is related to angular momentum -- cont’d

~μ = 12qm~c

combining our 2 expressions involving gives:Rv

nice … we don’t need to know velocity, radius etc…

now we might suppose that a given atom has some fraction of angular momentum which does not involve motion of charged particles.

introduce : a dimensionless “fudge factor”.

~μ = g 12qm~c

g

quantization of the projection of angular momentum gives quantization of the projection of magnetic moments.

Even holds for spin!

Stern-Gerlach Experiment was later used to determine the magnetic moment of the proton

It is very laudable that you are making such an effort to measure the magnetic moment of the proton. Don’t you think that is really superfluous, since we know perfectly well what the result will be -- W. Pauli

Magnetic moment of proton is different from electron …

Dirac theory does not apply, proton has structure !!!!

“… But the important step was to reduce our reliance on theoretical predictions” -- I. Estermann

gproton ≈ 5.6gelectron ≈ 2

Can we use Stern-Gerlach type force to trap atoms???Originally proposed by Segre in 1930’s.A uniform magnetic field and the field from a current carrying wire form a local minima in |B|:

I

~B0 ~B = μ02π

Ir φ

1 A, 2 G, 1.4 MHz/G

Trap depth given by bias field.

300 K -> 400 T; too large!

need cold gas – laser cooling!

Wire trap demonstrated by Schmiedmayer et al., 1999

Potential minimum

Denschlag, Cassettari, Chenet, Schneider and Schmiedmayer, Appl. Phys. B, 69, 291 (1999).

Fields can be provided by microfabricated wires:“Atom Chips”

Single wire with external bias field

Miniaturize trapping wires by fabricating them on a substrate – gives very high trapping gradients.

Atom clouds can be positioned by varying wire currents and bias field (which can be provided by wires).

Three wire guide

Review article: J. Fortagh, C. Zimmermann, RMP, 79, 235 (2007).

Trapping wire fabrication

Develop resist

Deposit Cr adhesion layer and Au

Strip resist, gold pattern remains

Coat wafer with resist and expose through mask

SEM image of wires patterned with ShipleyAZ 2035 nLOF and e-beam gold

Lift-off photolithography:

7 μm

Gold wire bonds (25 x 250 μm)

UW atom chip

Macor spacer

Chamber OverviewChamber Overview

Absorption images in various stages of loading

after MOT andmolasses

in macroscopic trap

in chip trap

afterevaporative

cooling

Surface interaction studies using atom chips

Lin, Teper, Chin, and Vuletic, PRL, v. 92, 050404 (2004):

in our case, use this control to do Rydberg excitation at variable atom-surface distances.

Rydberg atoms

loosely bound electron circling ionic core.

Ionization continuum

Infinitely many bound states

these states have long lifetimes (eg. 17p of Na: 50 μs ).properties scale with n and can be exaggerated.

for Na

ioni

zatio

n pot

entia

l

quantum defect (depends on core)

Rydb

erg c

onsta

nt (1

3.5 eV

)

Measurement of the “size” of Rydberg atoms

(Fabre et al., J. Phys. B: At. Mol. Phys. 16, L671 (1983)).

Scanning electron microscope image

“tilted”

“normal”

Transmission as a function of nshows Rydberg states are like hard spheres of size:

that must “fit” through slits.

Tran

smis

sion

10 μm

Rydberg atom size revisited-- what really happens?

Rydberg electron generates image Rydberg atom.

towardsmetal

effective potential for Rydberg electron:

ion core

saddle point

field ionization by image predicts: vs.

but …

Rydberg atom surface interactions – with atom chipsz

+-

-+

?

Dunning et al., Nucl.Instr. And Meth. B. 203,69 (2003).

Carter and Martin, PRA83, 032902 (2011).

Atom destroyed by image field-ionization:

z = a0 n2

Perturbative dipole-dipole interaction with image

ΔE= - n4 / z3

E

n=14

?

E

?

EDunning et al., Nucl.Instr. And Meth. B. 203,69 (2003).

?

E

O. Cherry, R. Al-Dahleh (CIRFE Group)

Atom chip with planarizing and shield layer

4.5 μm of polyimide flattens 1.5 μm wires to 240 nm.room for improvement (etch back).

Initial studies with unshielded chip- relevant to interactions of atomic systems with

“surface devices”Our unshielded chip:

Experimental sequence and 87Rb excitation scheme

5s1/2

5p3/2

36s1/2

F=2

F=3 780 nm

(imaging)

480 nm (doubled Ti:sapph)

B-fieldto lock ti:sapph we use transfer cavity and injection locked current modulation …

E-field

δE = −3 MHz(V/cm)2F

2

energy

Rydberg excitation spectra, 36s1/2

turn off chip wires, but not B bias field

4 MHz width(< 6 MHz 5p lifetime)Coherence narrowing?

Plate voltage scans can be used to null E field

E-field

36s1/2

energy

Microwave/selective field ionization calibration of electric field strength far from surface

36s1/2

36p1/2

E field

Energy

Compensating field as a function of atom surface distance

No absorbates? See Rydberg EIT work over planarized chip: Tauschinsky PRA, 81, 063411 (2010) [Spreeuw, Amsterdam]

wire voltage biasing significantly influences observed fields.

Time dependence of positive wire bias charging

initially we thought this was due to e- charging. But negative biasing shows similar time-scale behavior – desorption???

Summary // Overview

laser cooled atoms are held fixed distances above surfaces using atom chips and excited to Rydberg states to determine E-fields due to surface (wire structure in our case).

how the wires are voltage biased influences fields once they are shut-off. Negative biasing significantly reduces residual fields.

mechanism is not clear … more experiments needed.

next: time varying fields – relevant for

ion trapping heating. Spin echo on Rydberg microwave transition

Muller et al.http://arxiv.org/abs/1104.2739

patch (based on ion trap heating)

Thanks:J. Carter, P. Bohlouli-Zanjani, L. Jones, C. Liekhus-Schmaltz, M. Mazurek,

M. Torabifard, O. Cherry, R. Mantifel, J. Petrus, K. Afrousheh, A. Mugford, J. Keller, M. Fedorov

Funding: NSERC, CFI, OITUniversity of Waterloo

Apparatus

Injection locked diode lasers can be current modulated at RF frequencies to add sidebands

Kobayashi and Kimura, NTT, Electronics Letters, v 18, 210 (1982)

By sinusoidally modulating current to LD2 you sinusoidally modulate phase, which is equivalent to frequency modulation (at least for constant modulation frequency).

Rydberg laser locking scheme

arXiv/1109.0338despite amplitude modulation

secondary sidebands are symmetric.