BoseEinstein Condensation in a Dilute Atomic Gas

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Bose-Einstein Condensation in a Dilute Atomic Gas
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BEC
What is it? Why is it interesting?
Its a phase transition (a very special one!)
Statistical Mechanics
Quantum Mechanics
Light-Matter Interactions
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Brief review of basic QM
Particle in a box E(n) h2?2n2/2mL2
For electrons Fermions, S1/2) Fill
according to PEP 2 e-/level
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Filling is different for Bosons
For integer-spin particles (photons, atoms,
etc.) - No limit on occupation
Fill according to Boltzmann factor! F(?)
exp(-?/kT) q Consider value of Q
(V 1 m3, T 300 K)
L
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Translational Partition Function
Atomic (single particle) PF
Ensemble PF (N-particles)
Qens q1q2 qN qN (distinguishable)
Qens qN / N! (indistinguishable)
- still many more states than particles
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Translational Partition Function
At LOW temperature
Qens qN / N! -gt 0 !!
- MANY more particles than states !!
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BEC is a condensation of momentum states into a
single (ground state) wavefunction
at VERY Low T!!

• ? confinement dimension
• kT ltlt ??
• How low T is required?

L
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How low?
Consider confinement dimension L 1 µm M 87
amu (Rb)
Energy difference 10-11 eV (10-30 J)
!! Corresponds to a Temperature 10-8 K
L
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How cold is that?
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Why dont the atoms freeze?
BEC is a metastable state in a forbidden region
of the phase diagram
The trick is to reduce temperature and density at
the same time to avoid regular condensation !!
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Good collisions/Bad collisions

• Maximize GOOD 2-body (elastic) collisions for
  energy exchange
• Minimize BAD 3-body (or surface) collisions

good
BAD!
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How do you measure T in a subkelvin regime?
Spectroscopy!
but atoms dont have rotational structure?
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No-Surface Container The Magneto-Optical Trap
3 counter-propagating beams tuned to doppler
resonance of alkali atom cools to 4 mK
Magnetic quadrupole trap holds them
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The final step Evaporative Cooling

• After reaching doppler limit of laser cooling-
  lasers turned off
• Magnetic trap ramped down (WHY?)

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How do they know its BEC?
look closely at the structure of the central
peak!

• Equipartition theorem demands equal population
  of x, y, z translational states for a system in
  thermal equilibrium
• Its not a thermal state!
• The spatial anisotropy IS the signature of BEC
• - Youre looking at a (macroscopic) wavefunction!

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A macroscopic quantum state
Quantum interference in BEC pairs