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Physical Review A

Induced interaction in a spin-polarized Fermi gas

Zeng-Qiang Yu, Lan Yin

Published Jul 8, 2010• 11 citations
Publisher

Abstract

We study the effect of the induced interaction on the superfluid transition temperature of a spin-polarized Fermi gas. In the BCS limit, the polarization is very small in the superfluid state, and the effect of the induced interaction is almost the same as in the spin-balanced case. The temperature ${T}_{t}$ and the polarization ${P}_{t}$ of the tricritical point are both reduced from mean-field results by a factor about $2.22$. This reduction is also significant beyond the BCS limit. In the unitary limit, we find $({P}_{t},{T}_{t}/{T}_{F})=(0.42,0.16)$, in comparison with mean-field and experimental results.

DOI
10.1103/physreva.82.013605

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We study the effect of the induced interaction on the superfluidtransition temperature of a spin-polarized Fermi gas. In the BCS limit, the polarization is very small in the superfluid state, and the effect of the induced interaction is almost the same as in the spin-balanced case. The temperature Tt and the polarization Pt of the tricritical point are both reduced from mean-field results by a factor about 2.22. This reduction is also significant beyond the BCS limit. In the unitary limit, we find (Pt,Tt/TF)=(0.42,0.16), in comparison with mean-field and experimental results.
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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.
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We study the effects of induced interactions on the pairing gap, transition temperature, and chemical potential of a quasi-two-dimensional Fermi gas of atoms with spin-orbit coupling. We find that these mean-field parameters are significantly modified when induced interactions are taken into account. We also investigate the implications of induced interaction corrections for the BEC-BCS crossover driven by spin-orbit coupling, which happens even for small (compared to the Fermi energy) values of the binding energy.
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