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arXiv:0905.1023 · Physical Review A

Induced interaction in a Fermi gas with a BEC-BCS crossover

Zeng-Qiang Yu, Kun Huang, Lan Yin

Published May 22, 2009• 37 citations
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Abstract

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.

DOI
10.1103/physreva.79.053636

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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.
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 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 study the superfluid critical temperature in a two-band attractive Fermi system with strong pairing fluctuations associated with both interband and intraband couplings. We focus specifically on a configuration where the intraband coupling is varied from weak to strong in a shallow band coupled to a weakly interacting deeper band. The whole crossover from the Bardeen-Cooper-Schrieffer (BCS) condensation of largely overlapping Cooper pairs to the Bose-Einstein condensation (BEC) of tightly bound molecules is covered by our analysis, which is based on the extension of the Nozi\`eres-Schmitt-Rink approach to a two-band system. In comparison with the single-band case, we find a strong enhancement of the critical temperature, a significant reduction of the preformed pair region where pseudogap effects are expected, and the entanglement of two kinds of composite bosons in the strong-coupling BEC regime.
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 determine the size of the critical region of the superfluid transition in the Bardeen-Cooper-Schrieffer--Bose-Einstein condensation (BCS-BEC) crossover of a three-dimensional fermion gas, using a renormalization-group approach to a bosonic theory of pairing fluctuations. For the unitary Fermi gas, we find a sizable critical region $[{T}_{G}^{\ensuremath{-}},{T}_{G}^{+}]$, of order Tc{T}_{c}Tc​, around the transition temperature Tc{T}_{c}Tc​ with a pronounced asymmetry: $|{T}_{G}^{+}\ensuremath{-}{T}_{c}|/|{T}_{G}^{\ensuremath{-}}\ensuremath{-}{T}_{c}|\ensuremath{\sim}8$. The critical region is strongly suppressed on the BCS side of the crossover but remains important on the BEC side.
We investigate the specific heat at constant volume CV{C}_{V}CV​ in the Bardeen-Cooper-Schrieffer--Bose-Einstein-condensate (BCS-BEC)-crossover regime of an ultracold Fermi gas above the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​. Within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that this thermodynamic quantity is sensitive to the stability of preformed Cooper pairs. That is, while ${C}_{V}(T\ensuremath{\gtrsim}{T}_{\mathrm{c}})$ in the unitary regime is remarkably enhanced by metastable preformed Cooper pairs or pairing fluctuations, it is well described by that of an ideal Bose gas of long-lived stable molecules in the strong-coupling BEC regime. Using these results, we identify the region where the system may be viewed as an almost ideal Bose gas of stable pairs, as well as the pseudogap regime where the system is dominated by metastable preformed Cooper pairs, in the phase diagram of an ultracold Fermi gas with respect to the strength of a pairing interaction and the temperature. We also show that the calculated specific heat agrees with the recent experiment on a 6Li^{6}\text{Li}6Li unitary Fermi gas. Since the formation of preformed Cooper pairs is a crucial key in the BCS-BEC-crossover phenomenon, our results would be helpful in considering how fluctuating preformed Cooper pairs appear in a Fermi gas to eventually become stable as one passes through the BCS-BEC-crossover region.