Bose-Einstein Condensation Ultracold Quantum Coherent Gases

1. Bose-Einstein Condensation Ultracold Quantum Coherent Gases

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

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

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

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

6. RF@1.660 MHz: N=1.4x105, T<Tc RF@1.725 MHz: N = 6.4x105, T~Tc RF@1.740 MHz: N = 7.3x105, T>Tc 87Rb BEC

7. RF@1.660 MHz: N=1.4x105, T<Tc RF@1.725 MHz: N = 6.4x105, T~Tc RF@1.740 MHz: N = 7.3x105, T>Tc Surprise! Reach Tc with only a 30x loss in number. (trap loaded with 2x107 atoms)  Experimental cycle = 5 - 15 seconds 87Rb BEC

10. “Iceberg” BEC Fermi Sea Fermions: Sympathetic 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. We cool our fermionic 40K atoms sympathetically with an 87Rb BEC.

11. 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 The Problem with Fermions Identical ultra-cold fermions do not interact

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

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. Fermi Boltzmann Gaussian Fit Pauli Pressure