Finite temperature effective field theory for dark solitons in superfluid Fermi gases

TL;DR

This paper develops an analytic finite temperature effective field theory to study dark solitons in superfluid Fermi gases, providing solutions across the BCS-BEC crossover and at various temperatures, with results matching numerical methods.

Contribution

It introduces an analytic approach for dark solitons in superfluid Fermi gases that works across the BCS-BEC crossover and includes Gaussian fluctuations, complementing numerical methods.

Findings

Analytic solutions for the order parameter dip and phase profile.

Exact energy-momentum relation showing solitons behave like classical particles.

Good agreement with numerical Bogoliubov-de Gennes results in strong-coupling and high-temperature regimes.

Abstract

We use a finite temperature effective field theory recently developed for superfluid Fermi gases to investigate the properties of dark solitons in these superfluids. Our approach provides an analytic solution for the dip in the order parameter and the phase profile accross the soliton, which can be compared with results obtained in the framework of the Bogoliubov - de Gennes equations. We present results in the whole range of the BCS-BEC crossover, for arbitrary temperatures, and taking into account Gaussian fluctuations about the saddle point. The obtained analytic solutions yield an exact energy-momentum relation for a dark soliton showing that the soliton in a Fermi gas behaves like a classical particle even at nonzero temperatures. The spatial profile of the pair field and for the parameters of state for the soliton are analytically studied. In the strong-coupling regime and/or for sufficiently high temperatures, the obtained analytic solutions match well the numeric results obtained using the Bogoliubov - de Gennes equations.