Spin-1 spin-orbit- and Rabi-coupled Bose-Einstein condensate solver

TL;DR

This paper introduces OpenMP-accelerated FORTRAN programs for solving the Gross-Pitaevskii equation to study the properties and dynamics of spin-1 Bose-Einstein condensates with various couplings in 1D and 2D.

Contribution

The authors develop and provide optimized FORTRAN programs with OpenMP for simulating spin-1 BECs, including multiple forms of spin-orbit coupling, enabling efficient stationary and dynamic studies.

Findings

Programs successfully compute stationary states and dynamics of spinor BECs.

Inclusion of various spin-orbit coupling forms enhances simulation versatility.

Outputs include wave functions, energies, and density profiles.

Abstract

We present OpenMP versions of FORTRAN programs for solving the Gross-Pitaevskii equation for a harmonically trapped three-component spin-1 spinor Bose-Einstein condensate (BEC) in one (1D) and two (2D) spatial dimensions with or without spin-orbit (SO) and Rabi couplings. Several different forms of SO coupling are included in the programs. We use the split-step Crank-Nicolson discretization for imaginary- and real-time propagation to calculate stationary states and BEC dynamics, respectively. The imaginary-time propagation programs calculate the lowest-energy stationary state. The real-time propagation programs can be used to study the dynamics. The simulation input parameters are provided at the beginning of each program. The programs propagate the condensate wave function and calculate several relevant physical quantities. Outputs of the programs include the wave function, energy, root-mean-square sizes, different density profiles (linear density for the 1D program, linear and surface densities for the 2D program). The imaginary- or real-time propagation can start with an analytic wave function or a pre-calculated numerical wave function. The imaginary-time propagation usually starts with an analytic wave function, while the real-time propagation is often initiated with the previously calculated converged imaginary-time wave function.