FORTRESS: FORTRAN programs to solve coupled Gross-Pitaevskii equations for spin-orbit coupled spin-f Bose-Einstein condensate with spin f = 1 or 2

Abstract

We provide here the updated versions of OpenMP parallelized FORTRAN 90/95 programs to numerically study the ground states and/or the dynamics of homogeneous or trapped spin-1 or spin-2 Bose-Einstein condensates (BECs) with anisotropic spin-orbit (SO) coupling. The coupled sets of three or five Gross-Pitaevskii (GP) equations, respectively, for a spin-1 or a spin-2 Bose-Einstein condensate (BEC) are solved using a time-splitting Fourier spectral method. New version program summaryProgram Title: FORTRESSCPC Library link to program files:https://doi.org/10.17632/st7md3ss85.2Developer's repository link:https://github.com/arko87/FORTRESSLicensing provisions: MITProgramming language: OpenMP Fortran 90/95Supplementary material: The key details to solve the five coupled Gross-Pitaevskii equations for an SO-coupled spin-2 BEC are presented in the supplementary file. In addition, some sample numerically obtained ground state solutions of SO-coupled spin-2 BECs and OpenMP performance results of the software with spin f=2 are provided.Journal reference of previous version: Comput. Phys. Commun. 259 (2021) 107671Does the new version supersede the previous version?: YesReasons for the new version: The previous version can be used to numerically study an SO-coupled spin-1 BEC only, whereas the new version extends the applicability of the software to the SO-coupled spin-2 BECs.Summary of revisions: The new features and augmentations in the package are as follows:(i) Input parameters relevant to the problem under investigation are now read via an input file. Three sample input files corresponding to quasi-one-dimensional (q1D), quasi-two-dimensional (q2D), and three-dimensional (3D) spinor BECs have been provided. The user can edit these files as per the requirement of the problem. Details of the parameters in the sample input files are described in the README.md file provided with the software.(ii) The software has been augmented to solve the five coupled Gross-Pitaevskii equations for SO-coupled spin-2 BECs. The users can now employ the software to study SO-coupled spin-2 [1] as well as spin-1 [2,3] BECs by merely providing the integer ‘SPIN’ parameter equal to 1 for a spin-1 or 2 for a spin-2 BEC in the input file.(iii) A Makefile has been provided to compile the programs with multiple (intel, GNU, and f95) compiler options. Depending on the availability or the choice of user, any of the above compiler options can be used. The user can furthermore choose the variable DIMENSION = 1D, 2D or 3D in the Makefile to simulate, respectively, q1D, q2D or 3D spinor BECs. Depending on the value of DIMENSION, the relevant input file will be read. All the details about using the Makefile are given in the README.md file.(iv) The double precision reals and arrays have been declared in a processor-independent manner.(v) The various arrays have been declared with ALLOCATABLE attribute to assign the memory dynamically and thus more efficiently manage the memory requirement of the software. For a particular allocatable array, memory is allocated using an ALLOCATE statement and deallocated by using a DEALLOCATE statement.(vi) OpenMP parallelization has been improved further.(vii) A few other minor modifications to the codes, e.g. inclusion of convergence criterion based on energy in addition to the criterion based on the absolute value of the wavefunctions in the previous version, directing error messages to a file, etc.Nature of problem: To solve the coupled Gross-Pitaevskii equations (CGPEs) for an SO-spin-f BEC with f=1 or 2.Solution method: We use a time-splitting Fourier spectral method to solve the CGPEs. The resulting equations are evolved in imaginary time to obtain the ground state of the system or in real time to study the dynamics. Additional details of the solution method applicable to spin-2 BEC are provided in the supplementary material.