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Physical Review A

Effect of the induced interaction on the superfluid-transition temperature of ultracold Fermi gases within the T -matrix approximation

Xiao-Xia Ruan, Hao Ran Gong, Long Du, Weimin Sun, Hong-Shi Zong

Published Apr 9, 2013• 13 citations
Publisher

Abstract

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 $T$-matrix approximation. The result shows that the transition temperature is reduced by about $10%$ at unitarity due to the induced interaction. In the Bardeen-Cooper-Schrieffer (BCS) limit, the critical temperature is about $0.45{T}_{c}^{\text{BCS}}$ 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.

DOI
10.1103/physreva.87.043608

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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.
We study the effect of the induced interaction on the superfluid transition temperature of a Fermi gas with a Bose-Einstein condensation--Bardeen-Cooper-Schrieffer (BEC-BCS) crossover. The Gorkov-Melik-Barkhudarov theory about the induced interaction is extended from the BCS side to the entire crossover and the pairing fluctuation is treated in the approach by Nozi\`eres and Schmitt-Rink. At unitarity, the induced interaction reduces the transition temperature by about 20%. In the BCS limit, the transition temperature is reduced by a factor of about 2.22, as found by Gorkov and Melik-Barkhudarov. Our result shows that the effect of the induced interaction is important both on the BCS side and in the unitary region.
We theoretically investigate the specific heat at constant volume C V in the BCS(Bardeen-Cooper-Schrieffer)-BEC(Bose-Einstein-condensation)-crossover regime of an ultracold Fermi gas, below the superfluid phase transition temperature T c . Within the strong-coupling framework developed by Nozières and Schmitt-Rink, we show that the temperature dependence of C V drastically changes as one passes through the crossover region, and is sensitive to strong fluctuations in the Cooper channel near the unitarity limit. We also compare our results to a recent experiment on a 6 Li unitary Fermi gas. Since fluctuation effects are a crucial key in the BCS-BEC-crossover phenomenon, our results would be helpful in considering how the fermionic BCS superfluid changes into BEC with increasing the interaction strength, from the viewpoint of specific heat.
We theoretically investigate the isothermal compressibility ${\ensuremath{\kappa}}_{T}$ in the normal state of an ultracold Fermi gas. Including pairing fluctuations, as well as preformed-pair formations, within the framework of the self-consistent TTT-matrix approximation, we evaluate the temperature dependence of this thermodynamic quantity over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. While ${\ensuremath{\kappa}}_{T}$ in the weak-coupling BCS regime is dominated by Fermi atoms near the Fermi surface, correlations between tightly bound Cooper-pair molecules are found to play crucial roles in the strong-coupling BEC regime. In the latter region, besides a two-body molecular interaction, a three-body one is shown to sizably affect ${\ensuremath{\kappa}}_{T}$ near the superfluid phase-transition temperature. Our results indicate that the strong-coupling BEC regime of an ultracold Fermi gas would provide a unique opportunity to study multibody correlations between Cooper-pair molecules.
We investigate the uniform spin susceptibility ${\ensuremath{\chi}}_{\mathrm{s}}$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas. Including pairing fluctuations within the framework of an extended TTT-matrix approximation, we show that ${\ensuremath{\chi}}_{\mathrm{s}}$ exhibits nonmonotonic temperature dependence in the normal state. In particular, ${\ensuremath{\chi}}_{\mathrm{s}}$ is suppressed near the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​ due to strong pairing fluctuations. To characterize this anomalous behavior, we introduce the spin-gap temperature Ts{T}_{\mathrm{s}}Ts​ as the temperature at which ${\ensuremath{\chi}}_{\mathrm{s}}$ takes a maximum value. Determining Ts{T}_{\mathrm{s}}Ts​ in the whole BCS-BEC crossover region, we identify the spin-gap regime in the phase diagram of a Fermi gas in terms of the temperature and the strength of a pairing interaction. We also clarify how the spin-gap phenomenon is related to the pseudogap phenomenon appearing in the single-particle density of states. Our results indicate that an ultracold Fermi gas in the BCS-BEC crossover region is a very useful system to examine the pseudogap phenomenon and the spin-gap phenomenon in a unified manner.
We investigate the Gorkov--Melik-Barkhudarov (GM) correction to superfluid transition temperature in two-dimensional Fermi gases with Rashba spin-orbit coupling (SOC) across the SOC-driven BCS-BEC crossover. In the calculation of the induced interaction, we find that the spin-component mixing due to SOC can induce both of the conventional screening and additional antiscreening contributions that interplay significantly in the strong SOC regime. While the GM correction generally lowers the estimate of transition temperature, it turns out that at a fixed weak interaction, the correction effect exhibits a crossover behavior where the ratio between the estimates without and with the correction first decreases with SOC and then becomes insensitive to SOC when it goes into the strong SOC regime. We demonstrate the applicability of the GM correction by comparing the zero-temperature condensate fraction with the recent quantum Monte Carlo results.
We investigate magnetic properties and effects of pairing fluctuations in the Bardeen-Cooper-Schrieffer--Bose-Einstein condensation (BCS-BEC) crossover regime of an ultracold Fermi gas. Recently, Liu and Hu [Europhys. Lett. 75, 364 (2006)], and Parish et al. [Nat. Phys. 3, 124 (2007)], pointed out that the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink (NSR), which has been extensively used to successfully clarify various physical properties of cold Fermi gases, unphysically gives negative spin susceptibility in the BCS-BEC crossover region. The same problem also exists in the ordinary non-self-consistent TTT-matrix approximation. In this paper, we clarify that this serious problem comes from incomplete treatment in term of pseudogap phenomena originating from strong pairing fluctuations, as well as effects of spin fluctuations on the spin susceptibility. Including these two key issues, we construct an extended TTT-matrix theory which can overcome this problem. The resulting positive spin susceptibility agrees well with the recent experiment on a 6{}^{6}6Li Fermi gas done by Sanner et al. [Phys. Rev. Lett. 106, 010402 (2011)]. We also apply our theory to a polarized Fermi gas to examine the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​, as a function of the polarization rate. Since the spin susceptibility is an important physical quantity, especially in singlet Fermi superfluids, our results would be useful in considering how singlet pairs appear above and below Tc{T}_{\mathrm{c}}Tc​ in the BCS-BEC crossover regime of cold Fermi gases.