Hetero pairing and component-dependent pseudogap phenomena in an ultracold Fermi gas with mass imbalance

TL;DR

This paper clarifies the superfluid transition in mass-imbalanced ultracold Fermi gases, showing it always occurs and reveals component-dependent pseudogap phenomena, with implications for hetero pairing systems like Li-K mixtures.

Contribution

It demonstrates that the superfluid transition always exists in mass-imbalanced gases using SCTMA, correcting previous ETMA results, and explores component-dependent pseudogap phenomena.

Findings

Superfluid transition persists regardless of mass imbalance.

Pairing fluctuations cause different pseudogap behaviors in light and heavy components.

Li-K mixtures are promising for hetero pairing and pseudogap studies.

Abstract

We investigate the superfluid phase transition and single-particle excitations in the BCS (Bareen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas with mass imbalance. In our recent paper [R. Hanai, et. al., Phys. Rev. A 88, 053621 (2013)], we showed that an extended $T$-matrix approximation (ETMA) can overcome the serious problem known in the ordinary (non-self-consistent) $T$-matrix approximation that it unphysically gives double-valued superfluid phase transition temperature $T_{\rm c}$ in the presence of mass imbalance. However, at the same time, the ETMA was also found to give the vanishing $T_{\rm c}$ in the weak-coupling and highly mass-imbalanced case. In this paper, we inspect the correctness of this ETMA result, using the self-consistent $T$-matrix approximation (SCTMA). We show that the vanishing $T_{\rm c}$ is an artifact of the ETMA, coming from an internal inconsistency of this theory. The superfluid phase transition actually always occurs, irrespective of the ratio of mass imbalance. We also apply the SCTMA to the pseudogap problem in a mass-imbalanced Fermi gas. We show that pairing fluctuations induce different pseudogap phenomena between the the light component and heavy component. We also point out that a $^6$Li-$^{40}$K mixture is a useful system for the realization of a hetero pairing state, as well as for the study of component-dependent pseudogap phenomena.