Bell Soliton in Ultra-cold Atomic Fermi Gas

TL;DR

This paper reports the theoretical discovery and analysis of supersonic bell solitons in ultra-cold Fermi gases across the BCS-BEC crossover, including their stability and behavior in different regimes.

Contribution

It introduces an exact solution for bell solitons in superfluid Fermi gases using a density transformation of the hydrodynamic equations.

Findings

Bell solitons exist as exact solutions in the BCS-BEC crossover.

Soliton stability is confirmed through numerical analysis.

Maximum contrast of solitons occurs in the BEC regime.

Abstract

We demonstrate the existence of supersonic bell soliton in the Bardeen-Cooper-Schrieffer-Bose-Einstein condensate (BCS-BEC) crossover regime. Starting from the extended Thomas-Fermi density functional theory of superfluid order parameter, a density transformation is used to map the hydrodynamic mean field equation to a Lienard type equation. As a result, bell solitons are obtained as exact solutions, which is further verified by the numerical solution of the dynamical equation. The stability of the soliton is established and its behaviour in the entire crossover domain is obtained. It is found that, akin to the case of vortices, the bell solitons yield highest contrast in the BEC regime.