Collective oscillations of one-dimensional Bose-Einstein gas in a time-varying trap potential and atomic scattering length

TL;DR

This paper investigates the collective oscillations of a one-dimensional Bose gas under time-varying trap potentials and scattering lengths, revealing bistability in the mean field regime and parametric resonance in the Tonks-Girardeau regime.

Contribution

It provides a comparative analysis of oscillation behaviors in two regimes and introduces analytical expressions for soliton dynamics under rapid nonlinear modulations.

Findings

Bistability observed in mean field regime oscillations

Linear parametric resonance in Tonks-Girardeau regime

Analytical formulas derived for soliton width and secondary oscillation frequency

Abstract

The collective oscillations of 1D repulsive Bose gas with external harmonic confinement in two different regimes are studied. The first regime is the mean field regime when the density is high. The second regime is the Tonks-Girardeau regime when the density is low. We investigate the resonances under periodic modulations of the trap potential and the effective nonlinearity. Modulations of the effective nonlinear coefficient result from modulations of the atomic scattering length by the Feshbach resonance method or variations of the transverse trap frequency. In the mean field regime we predict the bistability in the nonlinear oscillations of the condensate. In the Tonks-Girardeau regime the resonance has the character of a linear parametric resonance. In the case of rapid strong modulations of the nonlinear coefficient we find analytical expressions for the nonlinearity managed soliton width and the frequency of the slow secondary oscillations near the fixed point.