Traveling Dark Solitons in Superfluid Fermi Gases

TL;DR

This paper studies dark solitons in superfluid Fermi gases, deriving their properties analytically and numerically across the BEC-BCS crossover, revealing their oscillation behavior and dispersion relations.

Contribution

It introduces a combined analytical and numerical approach to characterize dark solitons in superfluid Fermi gases, especially at unitarity and across the BEC-BCS crossover.

Findings

Solitons oscillate sinusoidally at a reduced trap frequency of 1/√3.

Dispersion relations are consistent with scaling arguments at unitarity.

Numerical profiles match analytical predictions across the crossover.

Abstract

Families of dark solitons exist in superfluid Fermi gases. The energy-velocity dispersion and number of depleted particles completely determines the dynamics of dark solitons on a slowly-varying background density. For the unitary Fermi gas we determine these relations from general scaling arguments and conservation of local particle number. We find solitons to oscillate sinusoidally at the trap frequency reduced by a factor of $1/\sqrt{3}$. Numerical integration of the time-dependent Bogoliubov-de Gennes equation determines spatial profiles and soliton dispersion relations across the BEC-BCS crossover and proves consistent with the scaling relations at unitarity.