Bose-Einstein Condensation in Weakly Interacting Gases Dr. Cammerata
Aug 13, 2015
Bose-Einstein Condensation in Weakly Interacting Gases
Definition
BEC
Statistics
Condensation Criteria
Achieving Critical Temperature
Elements of the discovery in weakly
interacting gases
Laser Trapping
Magnetic confinement
Evaporative Cooling
Bose-Einstein Condensation in Weakly Interacting Gases
Definition
BEC
Statistics
Condensation Criteria
Achieving Critical Temperature
Elements of the discovery in weakly
interacting gases
Laser Trapping
Magnetic confinement
Evaporative Cooling
BEC: Definition Bose-Einstein Condensation
is a phase of matter formed by bosons cooled below a critical temperature forming a coherent quantum state. Photons Strongly Interacting
Systems Weakly Interacting Weakly Interacting
Systems Systems
Lasers
Superfluid / SuperconductorAtomic Gases
How do you cool a gas without it condensing to a liquid?
Bose-Einstein Condensation in Weakly Interacting Gases
Definition
BEC
Statistics
Condensation Criteria
Achieving Critical Temperature
Elements of the discovery in weakly
interacting gases
Laser Trapping
Magnetic confinement
Evaporative Cooling
Bose-Einstein Statistics
)(0
)(
1
1
i
i
ii
e e Z
n
nTkB
1
1
1)ln(1)(
ie
Z n i
i
Partition Function
Mean Occupancy
Bose-Einstein Statistics (Continued)
xdpdg
dxdydzdpdpdpg
d zyx
3333 )2()2(
dn dN i
0
)(32
2/3
12
e
dgVm N
dppgV
d3
2
)2(
4
m
p
2
2
Bose-Einstein Condensation
032
2/3
032
2/3
12
)(
12 zTk e
dzzmkTgV
e
dgVm N
B
)()(10
1
xxe
dzz
z
x
Einstein Condensation Temperature: μ = 0
)()(2
)(23
23
32
2/3
mkTgV N
322
612.2
2
BE mk
T
For x >1
612.2)()( 21
23
23
V
N
Bose-Einstein Condensation (Continued)
23
0
ET
TNN
00 NN N
23
10ET
TNN
ET T
ET T T
N
TE
N>0
N=0
ContinuumGround State
Bose-Einstein Condensation: Thermal Wavelength
T
EBTmk
h
2
612.23
322
612.2
2
BE mk
T
612.23 T
A Wavelength larger than the spacing between particles
implies that the wave functions overlap
Wavefunction Extent in momentum space
=>“Wavelength”
Bose-Einstein Condensation: Thermal Wavelength
The overlap is NOT in configuration space but in momentum space
Spacing
Particles described bya single wavefunction
Spacing becomes smaller than “wavelength”
Bose-Einstein Condensation in Weakly Interacting Gases
Definition
BEC
Statistics
Condensation Criteria
Achieving Critical Temperature
Elements of the discovery in weakly
interacting gases
Laser Trapping
Magnetic confinement
Evaporative Cooling
Laser Trapping
Pioneered by Steven Chu, Claude Cohen-Tannoudji, William Phillips.
Shared Nobel Prize in 1997.
Use of lasers to achieve temperatures down to micro-Kelvin.
"Sisyphus cooling" or "optical molasses”
The laser cooling faced a hurdle known as the Doppler limit.
Laser Trapping
Epc
1
How do you trap atoms with lasers?
Recognize that atoms resonantly absorb light at specific frequencies
AND
Light has momentum
112 EE E
Laser Trapping (Continued)
c
1
cc
E p 1
Set the frequency just beneath the resonance frequency.
Equivalent to stopping a bowling ball with N ping pong balls.
c
N 1
N photons
Laser Trapping (Continued)
Cooling can occur down to a Doppler limit. Further cooling requires additional
techniques.
Magneto-Optical Trap (MOT)
Magnetic field helps to further confine the momentum, p, of the atoms.
However, there still exist higher p atoms.
Introduce "Anti-Helmholtz" coils
Evaporative CoolingKleppner and Greytak; Pritchard
Overcomes the Doppler limit as the remaining atoms comprise a
SYSTEM of much lower momentum, p.
“Turn off that light!”
Bose-Einstein Condensation
Cornell and WiemanRubidium vapor, T → 20 nK, N ≈ 2000 atoms
KetterleSodium vapor, T → 100 nK, N ≈ 500000 atoms
Cornell, Wieman and Ketterle shared Nobel Prize in 2001
Bose-Einstein Condensation
Successive occurrence of Bose-Einstein condensation in rubidium. From left to right is shown the atomic distribution in the cloud just prior to condensation, at the start of condensation and after full condensation. High peaks correspond to a large number of atoms. Silhouettes of the expanding atom cloud were recorded 6 ms after switching off the confining forces of the atom trap.