The dynamics of dark solitons in a trapped superfluid Fermi gas

TL;DR

This paper investigates the oscillation dynamics of dark solitons in a superfluid Fermi gas across the BEC-BCS crossover, deriving exact relations and validating them with simulations, and suggests experimental tests.

Contribution

It provides an exact equation linking phase jump and energy of solitons and offers a comprehensive analysis of soliton periods across the BEC-BCS crossover.

Findings

Soliton period increases on the BCS side as solitons become shallower.

Derived an exact relation between phase jump and soliton energy.

Supported findings with Bogoliubov-de Gennes simulations.

Abstract

We study soliton oscillations in a trapped superfluid Fermi gas across the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover. We derive an exact equation relating the phase jump across the soliton to its energy, and hence obtain an expression for the soliton period. Our analytic approach is supported by simulations of the time-dependent Bogoliubov-de Gennes equations, which show that the period dramatically increases as the soliton becomes shallower on the BCS side of the resonance. Finally, we propose an experimental protocol to test our predictions.