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Modern Physics Letters B

The energy of a unitary Fermi gas in the normal phase including the effect of induced interaction

Hao Ran Gong, Xiao-Xia Ruan, Pang Hou-Rong, Hong-Shi Zong

Published Nov 17, 2015• 2 citations
Publisher

Abstract

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].

DOI
10.1142/s0217984915502073

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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].
In this paper, taking into account the effect of the induced interaction, we calculate the superfluid-transition temperature of ultracold Fermi gases within the framework of the non-self-consistent TTT-matrix approximation. The result shows that the transition temperature is reduced by about 1010%10 at unitarity due to the induced interaction. In the Bardeen-Cooper-Schrieffer (BCS) limit, the critical temperature is about 0.45TcBCS0.45{T}_{c}^{\text{BCS}}0.45TcBCS​ and it is the same as the result of the usual Gorkov and Melik-Barkhudarov correction, whereas in the Bose-Einstein condensate (BEC) limit, the influence of the induced interaction can be neglected and the critical temperature turns out to be the transition temperature of ideal Bose gases. Our results show that the induced interaction cannot be neglected in the study of the BCS-BEC crossover.
Taking into account the effect of the generalized Gor'kov and Melik—Barkhudarov (GMB) approximation, we calculate the radio-frequency spectra of balanced and homogeneous ultracold Fermi gases within the framework of the non-self-consistent T-matrix approximation at unitarity in the normal phase. The corresponding equations are numerically calculated on the real frequency axis directly. It is found that our results agree well with the experimental result of the radio-frequency spectroscopy [Phys. Rev. Lett. 101 (2008) 140403].
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.
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.