Dark soliton oscillations in Bose-Einstein condensates with multi-body interactions

TL;DR

This paper derives an analytical expression for dark soliton oscillation frequencies in Bose-Einstein condensates with multi-body interactions, revealing their dependence on background density and interaction strengths, unlike the standard cubic case.

Contribution

It provides a new analytical formula for dark soliton oscillations in BECs with arbitrary nonlinearities, especially cubic-quintic, and demonstrates how these oscillations depend on interaction parameters.

Findings

Oscillation frequency depends on background density and interaction strengths in cubic-quintic BECs.

Analytical results agree well with numerical simulations.

The approach enables potential measurement of interaction parameters from soliton dynamics.

Abstract

We consider the dynamics of dark matter solitons moving through non-uniform cigar-shaped Bose-Einstein condensates described by the mean field Gross-Pitaevskii equation with generalized nonlinearities, in the case when the condition for the modulation stability of the Bose-Einstein condensate is fulfilled. The analytical expression for the frequency of the oscillations of a deep dark soliton is derived for nonlinearities which are arbitrary functions of the density, while specific results are discussed for the physically relevant case of a cubic-quintic nonlinearity modeling two- and three-body interactions, respectively. In contrast to the cubic Gross-Pitaevskii equation for which the frequencies of the oscillations are known to be independent of background density and interaction strengths, we find that in the presence of a cubic-quintic nonlinearity an explicit dependence of the oscillations frequency on the above quantities appears. This dependence gives rise to the possibility of measuring these quantities directly from the dark soliton dynamics, or to manage the oscillation via the changes of the scattering lengths by means of Feshbach resonance. A comparison between analytical results and direct numerical simulations of the cubic-quintic Gross-Pitaevskii equation shows good agreement which confirms the validity of our approach.