Nonlinear Dynamics in a Trapped Atomic Bose--Einstein Condensate Induced by an Oscillating Gaussian Potential

TL;DR

This paper investigates how an oscillating Gaussian potential affects vortex and soliton formation in a trapped Bose-Einstein condensate, revealing dependencies on amplitude and frequency through numerical simulations of the Gross-Pitaevskii equation.

Contribution

It provides a detailed phase diagram, proposes a new critical velocity expression, and analyzes vortex nucleation dynamics in oscillating potentials.

Findings

Large amplitude oscillations nucleate many vortex pairs.

Small amplitude oscillations lead to soliton formation.

Nucleation time diverges near critical parameters.

Abstract

We consider a trapped atomic Bose--Einstein condensate penetrated by a repulsive Gaussian potential and theoretically investigate the dynamics induced by oscillating the Gaussian potential. Our study is based on the numerical calculation of the two-dimensional Gross--Pitaevskii equation. Our calculation reveals the dependence of the characteristic behavior of the condensate on the amplitude and frequency of the oscillating potential. These dynamics are deeply related to the nucleation and dynamics of quantized vortices and solitons. When the potential oscillates with a large amplitude, it nucleates many vortex pairs that move away from the potential. When the amplitude of the oscillation is small, it nucleates solitons through annihilation of vortex pairs. We discuss three issues concerning the nucleation of vortices. The first is the phase diagram for the nucleation of vortices and solitons near the oscillating potential. The second is the mechanism and critical velocity of the nucleation. The critical velocity of the nucleation is an important issue in quantum fluids, and we propose a new expression for the velocity containing both the coherence length and the size of the potential. The third is the divergence of the nucleation time, which is the time it takes for the potential to nucleate vortices, near the critical parameters for vortex nucleation.