Vortex lattice solutions to the Gross-Pitaevskii equation with spin-orbit coupling in optical lattices

TL;DR

This paper investigates vortex lattice solutions in Bose-Einstein condensates with spin-orbit coupling in optical lattices, using numerical methods to analyze the Gross-Pitaevskii equation and identify various vortex states.

Contribution

It introduces numerical analysis of vortex lattice solutions in spin-orbit coupled BECs within optical lattices, highlighting the emergence of diverse vortex states under strong coupling.

Findings

Numerical Bloch states for the linear equation were obtained.

Stationary solutions with nonlinear terms were compared to linear states.

Various vortex lattice states appear when spin-orbit coupling is strong.

Abstract

Effective spin-orbit coupling can be created in cold atom systems using atom-light interaction. We study the BECs in an optical lattice using the Gross-Pitaevskii equation with spin-orbit coupling. Bloch states for the linear equation are numerically obtained, and compared with stationary solutions to the Gross-Pitaevskii equation with nonlinear terms. Various vortex lattice states are found when the spin-orbit coupling is strong.