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Modern Physics Letters B

The pressure and entropy of a unitary Fermi gas with particle-hole fluctuation

Hao Ran Gong, Xiao-Xia Ruan, Hong-Shi Zong

Published Nov 28, 2017• 0 citations
Publisher

Abstract

We calculate the pressure and entropy of a unitary Fermi gas based on universal relations combined with our previous prediction of energy which was calculated within the framework of the non-self-consistent T-matrix approximation with particle-hole fluctuation. The resulting entropy and pressure are compared with the experimental data and the theoretical results without induced interaction. For entropy, we find good agreement between our results with particle-hole fluctuation and the experimental measurements reported by ENS group and MIT experiment. For pressure, our results suffer from a systematic upshift compared to MIT data.

DOI
10.1142/s021798491750364x

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We calculate the pressure and entropy of a unitary Fermi gas based on universal relations combined with our previous prediction of energy which was calculated within the framework of the non-self-consistent T-matrix approximation with particle-hole fluctuation. The resulting entropy and pressure are compared with the experimental data and the theoretical results without induced interaction. For entropy, we find good agreement between our results with particle-hole fluctuation and the experimental measurements reported by ENS group and MIT experiment. For pressure, our results suffer from a systematic upshift compared to MIT data.
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.
In this paper, taking into account the effect of the induced interaction, we calculate the energy of ultracold Fermi gases at unitarity in the framework of non-self-consistent T-matrix approximation (nTMA) above the critical temperature and compare the result with the experimental data and other theoretical calculation without induced interaction. Our calculated chemical potential is higher than the experimental data, but our calculated energy obtains a good agreement with Tokyo experiment for temperature range between [Formula: see text] and [Formula: see text].
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.
The finite-temperature thermodynamics of a unitary Fermi gas is studied in detail. The chemical potential, energy density, and entropy are given analytically with the quasilinear approximation. The ground-state energy agrees with previous theoretical and experimental results. Recently, the generalized exclusion statistics is applied to the discussion of the finite-temperature unitary Fermi-gas thermodynamics. A concrete comparison between the two different approaches is performed. Emphasis is made on the behavior of the entropy per particle. In physics, the slope of entropy gives the information on the effective fermion mass ${m}^{\ensuremath{\ast}}/m$ in the low-temperature strongly degenerate region. Compared with ${m}^{\ensuremath{\ast}}/m\ensuremath{\approx}0.70<1$ given in terms of the generalized exclusion statistics, our quasilinear approximation determines that ${m}^{\ensuremath{\ast}}/m\ensuremath{\approx}1.11>1$.