1. Bose-Einstein Condensation Ultracold Quantum Coherent Gases

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

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

4. EiEi NiNi 1 EFEF Quantum Statistics Bosons Fermions symmetric  symmetric multi-particle wavefunction.  Integer spin: photons, 87 Rb.  probability of occupying a state |i> with energy E i. anti-symmetric  anti-symmetric multi-particle wavefunction.  ½-integer spin: electrons, protons, neutrons, 40 K.  probability of occupying a state |i> with energy E i. EiEi NiNi N BEC

5. Bose-Einstein Condensation of 87 Rb Evaporation Efficiency BEC thermal atoms magnetic trapping evap. cooling MOT 10 -13 110 -6 10 5 PSD

6. 87 Rb BEC RF@1.740 MHz: N = 7.3x10 5, T>T c RF@1.725 MHz: N = 6.4x10 5, T~T c RF@1.660 MHz: N=1.4x10 5, T<T c

7. 87 Rb BEC Surprise! Reach T c with only a 30x loss in number. (trap loaded with 2x10 7 atoms)  Experimental cycle = 5 - 15 seconds RF@1.740 MHz: N = 7.3x10 5, T>T c RF@1.725 MHz: N = 6.4x10 5, T~T c RF@1.660 MHz: N=1.4x10 5, T<T c

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

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

11. Sympathetic Cooling Cooling Efficiency 10 8 10 6 10 4 10 2 10 0 10 2 10 4 10 5 10 6 10 7 10 8 10 6 10 4 10 2 10 0 10 2 10 4 10 5 10 6 10 7 10 8 10 6 10 4 10 2 10 0 10 2 10 4 10 5 10 6 10 7

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

13. Fermi Boltzmann Gaussian Fit Pauli Pressure