Sound velocity and dimensional crossover in a superfluid Fermi gas in an optical lattice

TL;DR

This paper investigates how interactions and lattice geometry affect sound velocity and dimensional crossover in superfluid Fermi gases within optical lattices, revealing the smoothing of van Hove singularities and signatures of dimensional transitions.

Contribution

It demonstrates the impact of interactions on van Hove singularities and characterizes dimensional crossover effects on sound velocity in non-cubic optical lattices.

Findings

Interactions smooth out van Hove singularities in the Fermi gas.

Sound velocity shows clear signatures of dimensional crossover.

Dimensional effects are observable in both 1D and 2D limits.

Abstract

We study the sound velocity in cubic and non-cubic three-dimensional optical lattices. We show how the van Hove singularity of the free Fermi gas is smoothened by interactions and eventually vanishes when interactions are strong enough. For non-cubic lattices, we show that the speed of sound (Bogoliubov-Anderson phonon) shows clear signatures of dimensional crossover both in the 1D and 2D limits.