Experiments with Trapped Potassium Atoms

Robert Brecha

University of Dayton

Outline

Basics of cooling and trapping atoms

Fermionic and bosonic atoms - why do we use potassium?

Parametric excitation and cooling

Sympathetic cooling and BEC

Co-workers and Affiliations

Giovanni Modugno – LENSGabriele Ferrari – LENSGiacomo Roati – Università di TrentoNicola Poli – Università di FirenzeMassimo Inguscio – LENS and Università

di Firenze

In the Lab at LENS

Motivations for Trapping Atoms

Fundamental atomic physics measurements

Condensed matter physics with controllable interactions (“soft” condensed matter)

Tabletop astrophysics – collapsing stars,black holes, white dwarfs

Quantum computing

Atomic Cooling

Laser photons

Physics2000 Demo

Cooling Force

Random emission directions momentum kicks retarding force

Force = (momentum change per absorbed photon) (scattering rate of photons) (Depends on intensity, detuning, relative speed)

Force is not position-dependent no permanent trapping

Laser Cooling and TrappingMagnetic FieldCoils(anti-Helmholtz)

Circularlypolarizedlaser beams

Far Off-Resonance Trap (FORT)

One disadvantage of MOT – presence of magneticfields; only certain internal states trappable

Solution – Use all-optical methodLaser electric field induces an atomic dipole

E

Interaction potential of dipole and field:

0

1 1Re

2 2dipoleU E Ic

FORT Trapping Potential

20

20 0

2 2 /

4 /

tA

R

U M

U Mw

2 2 20, cos exp 2 /U r z U kz r w

Standing-wave in z-direction, Gaussian radially

Oscillation frequencies:

2 21

2U m x

450 K

Fermions vs. Bosons

Spin-1/2 Integer spin

State-occupation limited Gregarious

1

1f

e

1

1f

e

Do not collide* Collide

Fermions vs. Bosons

Bosonic ground-stateoccupation fraction

Fermionic occupationprobabilities

Ensher, et al., PRL 77, 4984 (1996)

Potassium

Three isotopes:39K (93.26%) boson40K (0.01%) fermion41K (6.73%) boson

Potassium Energy Levels

FORT Experimental Schematic

MOT: 5 × 107 atomsT ~ 60K

FORT: 5 × 105 atomsT = 80 K

Absorption beam

Absorption Image from FORT

N =×atoms n = 5 ×cm-3T = 50 – 80 K dT/dt = 40 K/sr = 2× 1 kHz a = 2× 600 kHzU0 = 300 - 600 K

450 K

Elastic Collisions

= p/2ncm

at = 169(9)a0

= 10(3) ms

Inelastic Collisions

Frequency Measurements“Parametric Excitation”

Driving an oscillator by modulating the spring constant leads to resonances for frequencies 20/n.

0

Here we modulatethe dipole-traplaser by a few percent

Parametric Resonances

2a1.8a

Parametric Heating ...and Cooling

2a

1.8a

Tex = 10 ms = 12 %

Tex = 2 ms = 12 %

Trap Anharmonicity

Cooling by Parametric Excitation

Selective excitation of high-lying levels forced evaporation

Occurs on a fast time-scale

Independent of internal atomic structure works on external degrees of freedom

Somewhat limited in effectiveness

The New Experiment

Transfer Tube - MOT1 to MOT2

Sympathetic Cooling

Use “bath” of Rb to cool a sample of K atoms

Goal 1 – Achieve Fermi degeneracy for 40K atoms

Goal 2 – (After #1 did not seem to work)Achieve Bose-Einstein condensationfor 41K

Some Open Questions

Do K and Rb atoms collide? (What is theelastic collisional cross-section?)

Do K and K atoms collide? Is the scattering length positive (stable BEC) or negative (unstable BEC at best)

Some Cold-Collision Physics

Scattered particle wavefunction is written as a sumof “partial waves” with l quantum numbers.

For l > 0, there is repulsive barrier in the correspondingpotential that inhibits collisions at low temperatures.

For identical particles, fermions have only l-odd partial waves, bosons have only l-even waves.

Identical fermions do not collide at low temperatures.

Rubidium Energy Levels87Rb

F´= 3

F´= 2

F´= 1F´= 0

F = 1

F = 26835 MHz

267 MHz

157 MHz

72 MHz

780 nm(4×108 MHz)

Rubidium Ground-State

Apply a B-field:mF = 2

F = 1

F = 2

6835 MHz

mF = -1

“Low-field-seeking states”

BEC ProcedureTrap 87Rb, then 41K in MOT1Transfer first Rb, then K into MOT2Now have 107 K atoms at 300K and

5×108 Rb atoms at 100KLoad these into the magnetic trap after preparing in

doubly-polarized spin state |F=2,mF=2>Selective evaporative cooling with microwave knifeCheck temperature (density) at various stages (a

destructive process)

QUIC Trap

Figure by Tilman Esslinger, ETH Zurich

QUIC Trap Transfer

Figure by Tilman Esslinger, ETH Zurich

Quadrupole field

Magnetic trap field

Microwave “Knife”

(Link to JILA group Rb BEC)

0.1 1 10

1

10

100

1000

10000

Microwave Treshold (MHz)

Ato

m N

um

ber

(10

4 )

1

10

100

Tem

per

atu

re (K

)

Rb

K

Temperature and Number of Atoms

Potassium BEC Transition

(Link to JILA group Rb BEC)

AB C

Optical Density Cross-section

Thermal

Mixed

Condensate

R b K

K

K

K

K

8 7 4 1

Absorption Images

Rb density remainsconstant

K density increases100x

Elastic Collisional Measurements

Return to parametric heating (of Rb) and watch the subsequent temperature increase of K.

13equilt n v

Determined from absorption images

Elastic Collisional Measurements

Ferrari, et al., submitted to PRL

Temperature dependence ofelastic collision rate (Is a >0 or is a < 0?)

Potassium temperatureafter parametricallyheating rubidium

Double Bose Condensate

Future Directions