C programs for solving the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

We present C programming language versions of earlier published Fortran programs (Muruganandam and Adhikari, Comput. Phys. Commun. 180 (2009) 1888) for calculating both stationary and non-stationary solutions of the time-dependent Gross-Pitaevskii (GP) equation. The GP equation describes the properties of dilute Bose-Einstein condensates at ultra-cold temperatures. C versions of programs use the same algorithms as the Fortran ones, involving real- and imaginary-time propagation based on a split-step Crank-Nicolson method. In a one-space-variable form of the GP equation, we consider the one-dimensional, two-dimensional, circularly-symmetric, and the three-dimensional spherically-symmetric harmonic-oscillator traps. In the two-space-variable form, we consider the GP equation in two-dimensional anisotropic and three-dimensional axially-symmetric traps. The fully-anisotropic three-dimensional GP equation is also considered. In addition to these twelve programs, for six algorithms that involve two and three space variables, we have also developed threaded (OpenMP parallelized) programs, which allow numerical simulations to use all available CPU cores on a computer. All 18 programs are optimized and accompanied by makefiles for several popular C compilers. We present typical results for scalability of threaded codes and demonstrate almost linear speedup obtained with the new programs, allowing a decrease in execution times by an order of magnitude on modern multi-core computers.Comment: 8 pages, 1 figure; 18 C programs included (to download, click other and download the source

OpenMP Fortran programs for solving the time-dependent dipolar Gross-Pitaevskii equation

In this paper we present Open Multi-Processing (OpenMP) Fortran 90/95 versions of previously published numerical programs for solving the dipolar Gross-Pitaevskii (GP) equation including the contact interaction in one, two and three spatial dimensions. The atoms are considered to be polarized along the z axis and we consider different cases, e.g., stationary and non-stationary solutions of the GP equation for a dipolar Bose-Einstein condensate (BEC) in one dimension (along x and z axes), two dimensions (in x-y and x-z planes), and three dimensions. The algorithm used is the split-step semi-implicit Crank-Nicolson scheme for imaginary- and real-time propagation to obtain stationary states and BEC dynamics, respectively, as in the previous version [R. Kishor Kumar et al., Comput. Phys. Commun. 195, 117 (2015)]. These OpenMP versions have significantly reduced execution time in multicore processors

Symmetry breaking, Josephson oscillation and self-trapping in a self-bound three-dimensional quantum ball

We study spontaneous symmetry breaking (SSB), Josephson oscillation, and self-trapping in a stable, mobile, three-dimensional matter-wave spherical quantum ball self-bound by attractive two-body and repulsive three-body interactions. The SSB is realized by a parity-symmetric (a) one-dimensional (1D) double-well potential and (b) a 1D Gaussian potential, both along the $z$ axis and no potential along the $x$ and $y$ axes. In the presence of each of these potentials, the symmetric ground state dynamically evolves into a doubly-degenerate SSB ground state. If the SSB ground state in the double well, predominantly located in the first well ($z>0$), is given a small displacement, the quantum ball oscillates with a self-trapping in the first well. For a medium displacement one encounters an asymmetric Josephson oscillation. The asymmetric oscillation is a consequence of SSB. The study is performed by a variational and numerical solution of a non-linear mean-field model with 1D parity-symmetric perturbations

Faraday and Resonant Waves in Dipolar Cigar-Shaped Bose-Einstein Condensates

Faraday and resonant density waves emerge in Bose-Einstein condensates as a result of harmonic driving of the system. They represent nonlinear excitations and are generated due to the interaction-induced coupling of collective oscillation modes and the existence of parametric resonances. Using a mean-field variational and a full numerical approach, we studied density waves in dipolar condensates at zero temperature, where breaking of the symmetry due to anisotropy of the dipole-dipole interaction (DDI) plays an important role. We derived variational equations of motion for the dynamics of a driven dipolar system and identify the most unstable modes that correspond to the Faraday and resonant waves. Based on this, we derived the analytical expressions for spatial periods of both types of density waves as functions of the contact and the DDI strength. We compared the obtained variational results with the results of extensive numerical simulations that solve the dipolar Gross-Pitaevskii equation in 3D, and found a very good agreement.Comment: 18 pages, 10 figure

FORTRESS II: FORTRAN programs for solving coupled Gross-Pitaevskii equations for spin-orbit coupled spin-2 Bose-Einstein condensate

We provide here a set of three OpenMP parallelized FORTRAN 90/95 programs to compute the ground states and the dynamics of trapped spin-2 Bose-Einstein condensates (BECs) with anisotropic spin-orbit (SO) coupling by solving a set of five coupled Gross-Pitaevskii equations using a time-splitting Fourier spectral method. Depending on the nature of the problem, without any loss of generality, we have employed the Cartesian grid spanning either three-, two-, or one-dimensional space for numerical discretization. To illustrate the veracity of the package, wherever feasible, we have compared the numerical ground state solutions of the full mean-field model with those from the simplified scalar models. The two set of results show excellent agreement, in particular, through the equilibrium density profiles, energies and chemical potentials of the ground-states. We have also presented test results for OpenMP performance parameters like speedup and the efficiency of the three codes