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

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. Program summary: Program title: BEC-GP-SPINOR, consisting of: BEC-GP-SPINOR-OMP package, containing programs spin-SO-imre1d-omp.f90 and spin-SO-imre2d-omp.f90, with util.f90. CPC Library link to program files: https://doi.org/10.17632/j3wr4wn946.1 Licensing provisions: Apache License 2.0 Programming language: OpenMP FORTRAN. The FORTRAN programs are tested with the GNU, Intel, PGI, and Oracle compiler. Nature of problem: The present Open Multi-Processing (OpenMP) FORTRAN programs solve the time-dependent nonlinear partial differential Gross–Pitaevskii (GP) equation for a trapped spinor Bose–Einstein condensate, with or without spin–orbit coupling, in one and two spatial dimensions. Solution method: We employ the split-step Crank–Nicolson rule to discretize the time-dependent GP equation in space and time. The discretized equation is then solved by imaginary- or real-time propagation, employing adequately small space and time steps, to yield the solution of stationary and non-stationary problems, respectively.