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arXiv:1008.1457 · Physical Review A

Virial expansion for a strongly correlated Fermi gas with imbalanced spin populations

Xia-Ji Liu, Hui Hu

Published Oct 26, 2010• 28 citations
arXivHTMLPDF

Abstract

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 ${T}_{c}$. For a harmonically trapped Fermi gas at unitarity, we find that $({T}_{c}){}_{\mathrm{upper}}<{T}_{F}$, where ${T}_{F}$ 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.

DOI
10.1103/physreva.82.043626

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We briefly review current research progress in the field of strongly correlated atomic Fermi gases. A deep understanding of strongly correlated quantum gases is plagued by the lack of either exact solutions or a controllable small interaction parameter. In this work, we present a systematic virial expansion method to study the high-temperature thermodynamics of a strongly correlated Fermi gas,where the controllable parameter is given by the fugacity,exp (μkBT),with μ being the chemical potential. A practical way is proposed to obtain the expansion coefficients for both homogeneous and harmonically trapped Fermi gases. We calculate, for the first time accurately, the third-order virial coefficient. The resulting equation of states at high temperatures is compared with a recent thermodynamic measurement and with Monte Carlo simulations.
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 b{3}(T) at finite temperatures T. At resonance, a T-independent coefficient b{3,infinity};{hom} approximately -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.
We analytically determine the properties of three interacting fermions in a harmonic trap subject to an external rotation. Many-body thermodynamic quantities such as the entropy and energy are calculated from the third-order quantum virial expansion. As the external rotation is increased, the regime over which the virial expansion is valid is extended to lower temperatures. By parameterizing the solutions in the rotating frame we find that the energy and entropy are universal for all rotations in the strongly interacting regime. Additionally, we find that rotation suppresses the onset of itinerant ferromagnetism in strongly interacting repulsive three-body systems.
Three fermions with strongly repulsive interactions in a spherical harmonic trap constitute the simplest nontrivial system that can exhibit the onset of itinerant ferromagnetism. Here, we present exact solutions for three trapped, attractively interacting fermions near a Feshbach resonance. We analyze energy levels on the upper branch of the resonance where the atomic interaction is effectively repulsive. When the sss-wave scattering length aaa is sufficiently positive, three fully polarized fermions are energetically stable against a single spin-flip, indicating the possibility of itinerant ferromagnetism, as inferred in the recent experiment. We also investigate the high-temperature thermodynamics of a strongly repulsive or attractive Fermi gas using a quantum virial expansion. The second and third virial coefficients are calculated. The resulting equations of state can be tested in future quantitative experimental measurements at high temperatures and can provide a useful benchmark for quantum Monte Carlo simulations.
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Using a second-order quantum virial expansion, we theoretically study the high-temperature thermodynamics of spin-polarized Fermi gases with ppp-wave interaction confined in two-dimensional harmonic traps. The second virial coefficient is calculated based on the energy spectrum of two harmonically trapped fermions. We find that the two-body spectrum can correctly be evaluated only when the ppp-wave effective range is properly considered, which is referred to as the well-known Wigner's bound. According to the quantum virial expansion, the high-temperature thermodynamics of the system is then discussed based on the two-body solutions. In addition, we investigate the high-temperature behavior of ppp-wave contacts in harmonic traps within the quantum virial expansion, which characterize a set of universal relations of strongly interacting spin-polarized Fermi gases. Our results can provide an accurate benchmark at high temperature for future numerical simulations as well as high-precision thermodynamic measurements of harmonically trapped spin-polarized Fermi gases in two dimensions.