BEC_Formal_Presentation

Bose-Einstein Condensation in

Weakly Interacting Gases

Dr. Cammerata

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


Definition

BEC

Statistics




interacting gases

Laser Trapping


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?


Definition

BEC

Statistics




interacting gases

Laser Trapping


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”


Definition

BEC

Statistics




interacting gases

Laser Trapping


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!”


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


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.

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BEC_Formal_Presentation