Thermodynamics of strongly interacting Fermi gases

摘要

These lecture notes review the universal thermodynamics of strongly interacting Fermi gases, experimentally realized with ultracold atoms near Feshbach resonances. These gases serve as a pristine model system for fermionic matter with contact interactions. Over the recent years, their equation of state has been measured to an ever-increasing precision that allows distinguishing between different theoretical approaches to the many-fermion problem. In the spin-balanced, resonant case, the equation of state only depends on temperature and density. The superfluid transition is signaled by a lambda-like feature in the specific heat of the gas. For non-resonant interactions, the scattering length introduces a conjugate extensive thermodynamic quantity, the contact. It encodes the probability to find two particles in close proximity and thus governs the interaction energy of the gas, the tails of the momentum distribution, the wings and the mean transition frequency of radiofrequency spectra, the probability of photoassociation and other experimental quantities. Introducing spin imbalance allows addressing a fifty year old question on the fate of fermionic superfluidity when there are more up spins than down spins and pairing cannot be complete. Phase separation between the superfluid and a mixed normal phase, as well as the eventual breakdown of superfluidity at the Pauli or Clogston-Chandrasekhar limit, have been directly observed. The mixed normal phase is identified as a Fermi liquid of Fermi polarons, dressed quasi-particles with a modified effective mass and energy. Prospects of observing an inhomogeneous superfluid state, the Fulde-Ferrell-Larkin-Ovchinnikov state of mobile Cooper pairs, are briefly discussed.