Dynamics of bright matter wave solitons in a quasi 1D Bose-Einstein condensate with a rapidly varying trap

TL;DR

This paper investigates how rapid periodic modulations of the trapping potential affect the stability and dynamics of bright matter wave solitons in a quasi-1D Bose-Einstein condensate, revealing stabilization effects and bifurcations.

Contribution

It derives an averaged Gross-Pitaevskii equation accounting for rapid trap modulations and demonstrates stabilization and bifurcation phenomena in soliton dynamics.

Findings

Effective potential can stabilize unstable GP equations.

Bifurcation from single to triple well potential occurs.

Stabilization of BEC on-site state in modulated optical lattice.

Abstract

The dynamics of a bright matter wave soliton in a quasi 1D Bose-Einstein condensate with periodically rapidly varying trap is considered. The governing equation is derived based on averaging over fast modulations of the Gross-Pitaevskii (GP) equation. This equation has the form of GP equation with effective potential of more complicated structure than unperturbed trap. For the case of inverted (expulsive) quadratic trap corresponding to unstable GP equation, the effective potential can be stable. For the bounded in space trap potential it is showed that the bifurcation exists, i.e.,the single well potential bifurcates to the triple well effective potential. Stabilization of BEC cloud on-site state in the temporary modulated optical lattice is found. (analogous to the Kapitza stabilization of the pendulum). The predictions of the averaged GP equation are confirmed by the numerical simulations of GP equation with rapid perturbations.