experiments with trapped potassium atoms robert brecha university of dayton
TRANSCRIPT
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