Bose-Einstein Condensation Ultracold Quantum Coherent Gases

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

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

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

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

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

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

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.

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

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

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

Pauli Pressure Fermi Boltzmann Gaussian Fit