Stability of Quantized Vortices in a Bose-Einstein Condensate Confined in an Optical Lattice

TL;DR

This study explores the stability of quantized vortex states in Bose-Einstein condensates within optical lattices, revealing stability conditions for different vortex charges and potential types through linear stability analysis.

Contribution

It provides a detailed analysis of vortex stability in BECs with periodic potentials, including the effects of potential shape and vortex charge, and discusses the stability thresholds.

Findings

Single-charged vortices are stable in cosinusoidal potentials.

Higher charge vortices tend to be unstable and break into single vortices.

Stability depends on the potential's shape and strength.

Abstract

We investigate the existence and especially the linear stability of single and multiple-charge quantized vortex states of nonlinear Schroedinger equations in the presence of a periodic and a parabolic potential in two spatial dimensions. The study is motivated by the examination of pancake-shaped Bose-Einstein condensates in the presence of magnetic and optical confiement. A two-parameter space of the condensate's chemical potential versus the periodic potential's strength is scanned for both single- and double-quantized vortex states located at a local minimum or a local maximum of the lattice. Triply charged vortices are also briefly discussed. Single-charged vortices are found to be stable for cosinusoidal potentials and unstable for sinusoidal ones above a critical strength. Higher charge vortices are more unstable for both types of potentials and their dynamical evolution leads to breakup into single-charged vortices.