Dark matter-wave solitons in the dimensionality crossover

TL;DR

This paper investigates the behavior of dark matter-wave solitons during the transition from three-dimensional to one-dimensional regimes, revealing deviations from classical frequency predictions using advanced mean-field models.

Contribution

It introduces a nonpolynomial Schrödinger mean-field model to accurately analyze soliton dynamics across the dimensionality crossover, highlighting deviations from traditional 1D predictions.

Findings

The anomalous mode frequency matches the soliton oscillation frequency in the crossover regime.

Significant deviations from the expected frequency occur even in the 1D limit.

The model captures the complex dynamics not accounted for by simpler 1D theories.

Abstract

We consider the statics and dynamics of dark matter-wave solitons in the dimensionality crossover regime from 3D to 1D. There, using the nonpolynomial Schr\"{o}dinger mean-field model, we find that the anomalous mode of the Bogoliubov spectrum has an eigenfrequency which coincides with the soliton oscillation frequency obtained by the 3D Gross-Pitaevskii model. We show that substantial deviations (of order of 10% or more) from the characteristic frequency $\omega_{z}/\sqrt{2}$ ($\omega_{z}$ being the longitudinal trap frequency) are possible even in the purely 1D regime.