Cooper pairing and BCS-BEC evolution in mixed-dimensional Fermi gases

TL;DR

This paper explores the phase diagram of mixed-dimensional Fermi gases, revealing stable gapless superfluid phases during the BCS-BEC crossover, with potential implications for quantum simulation and superfluidity research.

Contribution

It introduces a novel stable gapless superfluid phase in mixed-dimensional Fermi gases, expanding understanding of superfluid phases in reduced-dimensional systems.

Findings

Discovery of a stable gapless superfluid phase.

Identification of phase-separated and normal regions.

Analysis of BCS-BEC evolution in mixed dimensions.

Abstract

Similar to what has recently been achieved with Bose-Bose mixtures [Lamporesi et al., Phys. Rev. Lett. 104, 153202 (2010)], mixed-dimensional Fermi-Fermi mixtures can be created by applying a species-selective one-dimensional optical lattice to a two-species Fermi gas ($\sigma \equiv \{\uparrow, \downarrow \}$), such a way that only one of the species feel the lattice potential and is confined to a quasi-two-dimensional geometry, while having negligible effect on the other, that is leaving it three dimensional. We investigate the ground state phase diagram of superfluidity for such mixtures in the BCS-BEC evolution, and find normal, gapped superfluid, gapless superfluid, and phase separated regions. In particular, we find a stable gapless superfluid phase where the unpaired $\uparrow$ and $\downarrow$ fermions coexist with the paired (or superfluid) ones in different momentum space regions. This phase is in some ways similar to the Sarma state found in mixtures with unequal densities, but in our case, the gapless superfluid phase is unpolarized and most importantly it is stable against phase separation.