Numerical simulation of nonequilibrium states in a trapped Bose-Einstein condensate

TL;DR

This paper presents numerical simulations of a perturbed trapped Bose-Einstein condensate, reproducing experimental phenomena such as vortex formation, turbulence, and granular states through solving the 3D nonlinear Schrödinger equation.

Contribution

It introduces a numerical approach that accurately models nonequilibrium states in a trapped Bose-Einstein condensate, aligning well with experimental observations.

Findings

Regular vortices are observed in simulations.

Transition to quantum vortex turbulence occurs with increased excitation.

Granular states emerge at higher perturbation levels.

Abstract

In this work we present numerical study of a trapped Bose-Einstein condensate perturbed by an alternating potential. The relevant physical situation has been recently realized in experiment, where the trapped condensate of $^{87}$Rb, being strongly perturbed, exhibits the set of spatial structures. Firstly, regular vortices are detected. Further, increasing either the excitation amplitude or modulation time results in the transition to quantum vortex turbulence, followed by a granular state. Numerical simulation of the nonequilibrium Bose-condensed system is based on the solution of the time-dependent 3D nonlinear Schr\"{o}dinger equation within the static and dynamical algorithms. The damped gradient step and time split-step Fourier transform methods are employed. We demonstrate that computer simulations qualitatively reproduce the experimental picture, and describe well the main experimental observables.