Universal thermodynamics of a strongly interacting Fermi gas: theory versus experiment

Strongly interacting, dilute Fermi gases exhibit a scale-invariant, universal thermodynamic behavior. This is notoriously difficult to understand theoretically because of the absence of a small interaction parameter. Here, we present a systematic comparison of theoretical predictions from different quantum many-body theories with recent experimental data of Nascimbne et al (2010 Nature 463 1057). Our comparisons have no adjustable parameters, either theoretically or experimentally. All the model approximations seem to fluctuate rather than converge on the experimental data. It turns out that a simple Gaussian pair fluctuation theory gives the best quantitative agreement, except at the critical superfluid transition region. In the normal state, we also calculate the equation of state by using a quantum cluster expansion theory and explore in detail its applicability to low temperatures. Using the accurate experimental result for the thermodynamic function S(T), we determine the temperature T of a trapped Fermi gas at unitarity as a function of a non-interacting temperature T_i, which can be obtained by an adiabatic sweep to the free gas limit. By analyzing the recent experimental data, we find a characteristic temperature (T/T_F)₀=0.19±0.02 or (T_i/T_F)₀=0.16±0.02 in a harmonic trap, below which there are deviations from normal Fermi-liquid-like behavior that may be attributed to pairing effects. Here, T_F is the Fermi temperature for a trapped ideal, non-interacting Fermi gas. Our thorough comparison may shed light on the further theoretical development of strongly interacting fermions.