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Physics Letters A

Non-universal thermodynamics of a strongly interacting inhomogeneous Fermi gas using the quantum virial expansion

Shi-Guo Peng, Xia-Ji Liu, Hui Hu, Shiqun Li

Published Jul 4, 2011• 10 citations
Publisher
DOI
10.1016/j.physleta.2011.06.045

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We compare the theoretical predictions for universal thermodynamics of a homogeneous, strongly correlated Fermi gas with the latest experimental measurements reported by the ENS group [S. Nascimb\`ene et al., Nature (London) 463, 1057 (2010)] and the Tokyo group [M. Horikoshi et al., Science 327, 442 (2010)]. The theoretical results are obtained using two diagrammatic theories, together with a virial expansion theory combined with a P\'ade approximation. We find good agreement between theory and experiment. In particular, the virial expansion, using a P\'ade approximation up to third order, describes the experimental results extremely well down to the superfluid transition temperature, Tc 0.16TF{T}_{c}~0.16{T}_{F}Tc​ 0.16TF​, where TF{T}_{F}TF​ is the Fermi temperature. The comparison in this work complements our previous comparative study on the universal thermodynamics of a strongly correlated but trapped Fermi gas. The comparison also raises interesting issues about the unitary entropy and the applicability of the P\'ade approximation.
Quantum virial expansion provides an ideal tool to investigate the high-temperature properties of a strongly correlated Fermi gas. Here, we construct the virial expansion in the presence of spin-population imbalance. Up to the third order, we calculate the high-temperature free energy of a unitary Fermi gas as a function of spin imbalance, with infinitely large attractive or repulsive interactions. In the latter repulsive case, we show that there is no itinerant ferromagnetism when quantum virial expansion is applicable. We therefore estimate an upper bound for the ferromagnetic transition temperature Tc{T}_{c}Tc​. For a harmonically trapped Fermi gas at unitarity, we find that (Tc)upper<TF({T}_{c}){}_{\mathrm{upper}}<{T}_{F}(Tc​)upper​<TF​, where TF{T}_{F}TF​ is the Fermi temperature at the center of the trap. Our result for the high-temperature equations of state may confront future high-precision thermodynamic measurements.