An efficient compact splitting Fourier spectral methods for computing the dynamics of rotating spin-orbit coupled spin-2 Bose-Einstein condenstates

TL;DR

This paper introduces a high-order compact splitting Fourier spectral method for simulating the dynamics of rotating spin-2 Bose-Einstein condensates with spin-orbit coupling, offering improved efficiency and accuracy.

Contribution

The paper presents a novel high-order compact splitting Fourier spectral method that efficiently handles rotation and SOC terms in spin-2 BEC dynamics, with exact linear subproblem integration.

Findings

Method is spectrally accurate in space.

Method is high order in time and unconditionally stable.

Effective in simulating vortex lattice dynamics.

Abstract

This paper investigates the dynamics of spin-2 Bose-Einstein condensates (BECs) with rotation and spin-orbit coupling (SOC). In order to better simulate the dynamics, we present an efficient high-order compact splitting Fourier spectral method. This method splits the Hamiltonian into a linear part, which consists of the Laplace, rotation and SOC terms, and a nonlinear part that includes all the remaining terms. The wave function is well approximated by the Fourier spectral method and is numerically accessed with discrete Fast Fourier transform (FFT). For linear subproblem, the handling of rotation term and SOC term poses a major challenge. Using a function mapping based on rotation, we can integrate the linear subproblem exactly and explicitly. This mapping we propose not only helps eliminate the rotation term, but also prevents the SOC term from evolving into a time-dependent form. The nonlinear subproblem is integrated analytically in physical space. Such "compact" splitting involves only two operators and facilitates the design of high-order splitting schemes. Our method is spectrally accurate in space and high order in time. It is efficient, explicit, unconditionally stable and simple to implement. In addition, we derive some dynamical properties and carry out a systematic study, including accuracy and efficiency tests, dynamical property verification, the SOC effects and dynamics of vortex lattice.