1. Bose-Einstein Condensation Ultracold Quantum Coherent Gases

2. What’s Ultra-Cold Matter ?mK μK nK
Very Cold
 Typically nanoKelvin – microKelvin
 Atoms/particles have velocity ~ mm/s – cm/s
Very Dense … in Phase Space x p x p x p
Different temperatures
Same phase space density
Higher
phase space density

3. Ultra-cold Quantum Mechanics
Quantum mechanics requires x p Dx Dp
 fundamental unit of phase space volume
 Quantum physics is important when
Boltzmann régime
Quantum régime
Equivalent:
deBroglie wavelength ~ inter-particle separation

4. Quantum Statistics Bosons Fermions
symmetric multi-particle wavefunction.
Integer spin: photons, 87Rb.
probability of occupying a state |i> with energy Ei.
anti-symmetric multi-particle wavefunction.
½-integer spin: electrons, protons, neutrons, 40K.
probability of occupying a state |i> with energy Ei. Ei Ni
NBEC Ei Ni 1 EF

5. Bose-Einstein Condensation of 87Rb
10-13
10-6 1
105
thermal
atoms
MOT
magnetic
trapping
evap.
cooling
BEC
PSD
Evaporation Efficiency

6. 87Rb BEC RF@1.725 MHz: RF@1.660 MHz: RF@1.740 MHz: N = 6.4x105, T~Tc

7. 87Rb BEC Surprise! Reach Tc with only a 30x loss in number.
MHz:
N = 7.3x105, T>Tc
MHz:
N = 6.4x105, T~Tc
MHz:
N=1.4x105, T<Tc
Surprise! Reach Tc with only a 30x loss in number.
(trap loaded with 2x107 atoms)
 Experimental cycle = seconds

10. Fermions: Sympathetic Cooling
Problem:
Cold identical fermions do not interact due to Pauli Exclusion Principle.
 No rethermalization.
 No evaporative cooling.
Fermi Sea
“Iceberg”
BEC
Solution: add non-identical particles
 Pauli exclusion principle does not apply.
We cool our fermionic 40K atoms sympathetically with an 87Rb BEC.

11. The Problem with Fermions
Identical ultra-cold fermions do not interact
At very low temperatures,
If , then two atoms must scatter as an s-wave:
s-wave is symmetric under exchange of particles:
as = 0 for fermions

12. Sympathetic Cooling Cooling Efficiency 108 106 104 102 100 105 107 108

13. Below TF 0.9 TF 0.35 TF For Boltzmann statistics and a harmonic trap,
For ultra-cold fermions, even at T=0,

14. Pauli Pressure
Fermi
Boltzmann
Gaussian Fit