Virial Expansion for a Strongly Correlated Fermi Gas

Using a high temperature virial expansion, we present a controllable study of the thermodynamics of strongly correlated Fermi gases near the BEC-BCS crossover region. We propose a practical way to determine the expansion coefficients for both harmonically trapped and homogeneous cases, and calculate the third order coefficient b₃(T) at finite temperatures T. At resonance, a T-independent coefficient b_3,∞^hom⁡≈-0.290 952 95 is determined in free space. These results are compared with a recent thermodynamic measurement of ⁶Li atoms, at temperatures below the degeneracy temperature, and with Monte Carlo simulations.