An efficient spectral method for computing dynamics of rotating two-component Bose--Einstein condensates via coordinate transformation

TL;DR

This paper introduces a spectral numerical method for simulating the dynamics of rotating two-component Bose--Einstein condensates, utilizing coordinate transformation to improve efficiency and accuracy, and extends it to multi-component cases.

Contribution

The paper presents a novel spectral method based on coordinate transformation that simplifies the equations and enhances computational efficiency for rotating BECs, including multi-component systems.

Findings

The method achieves spectral accuracy in all spatial dimensions.

It requires significantly less computational time compared to existing methods.

It successfully models the dynamic properties of rotating two-component BECs.

Abstract

In this paper, we propose an efficient and accurate numerical method for computing the dynamics of rotating two-component Bose--Einstein condensates (BECs) which is described by coupled Gross--Pitaevskii equations (CGPEs) with an angular momentum rotation term and an external driving field. By introducing rotating Lagrangian coordinates, we eliminate the angular momentum rotation term from the CGPEs, which allows us to develop an efficient numerical method. Our method has spectral accuracy in all spatial dimensions and moreover it can be easily implemented in practice. To examine its performance, we compare our method with those reported in literature. Numerical results show that to achieve the same accuracy, our method needs much shorter computing time. We also applied our method to study the dynamic properties of rotating two-component BECs. Furthermore, we generalize our method to solve the vector Gross--Pitaevskii equations (VGPEs) which is used to study rotating multi-component BECs.