15 research outputs found
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
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
BEC2HPC: a HPC spectral solver for nonlinear Schrödinger and Gross-Pitaevskii equations. Stationary states computation
International audienceWe present BEC2HPC which is a parallel HPC spectral solver for computing the ground states of the nonlinear Schrödinger equation and the Gross-Pitaevskii equation (GPE) modeling rotating Bose-Einstein condensates (BEC). Considering a standard pseudo-spectral discretization based on Fast Fourier Transforms (FFTs), the method consists in finding the numerical solution of the energy functional minimization problem under normalization constraint by using a preconditioned nonlinear conjugate gradient method. We present some numerical simulations and scalability results for the 2D and 3D problems to obtain the stationary states of BEC with fast rotation and large nonlinearities. The code takes advantage of existing HPC libraries and can itself be leveraged to implement other numerical methods like e.g. for the dynamics of BECs
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
Vortex lattice in the crossover of a Bose gas from weak coupling to unitarity
The formation of a regular lattice of quantized vortices in a fluid under
rotation is a smoking-gun signature of its superfluid nature. Here we study the
vortex lattice in a dilute superfluid gas of bosonic atoms at zero temperature
along the crossover from the weak-coupling regime, where the inter-atomic
scattering length is very small compared to the average distance between atoms,
to the unitarity regime, where the inter-atomic scattering length diverges.
This study is based on high-performance numerical simulations of the
time-dependent nonlinear Schrodinger equation for the superfluid order
parameter in three spatial dimensions, using a realistic analytic expression
for the bulk equation of state of the system along the crossover from
weak-coupling to unitarity. This equation of state has the correct
weak-coupling and unitarity limits and faithfully reproduces the results of an
accurate multi-orbital microscopic calculation. Our numerical predictions of
the number of vortices and root-mean-square sizes are important benchmarks for
future experiments.Comment: 23 pages, 4 figures, accepted for publication in Scientific Report
Bright solitons in ultracold atoms
We review old and recent experimental and theoretical results on bright
solitons in Bose-Einstein condensates made of alkali-metal atoms and under
external optical confinement. First we deduce the three-dimensional
Gross-Pitaevskii equation (3D GPE) from the Dirac-Frenkel action of interacting
identical bosons within a time-dependent Hartree approximation. Then we discuss
the dimensional reduction of the GPE from 3D to 1D, deriving the 1D GPE and
also the 1D nonpolynomial Schr\"odinger equation (1D NPSE). Finally, we analyze
the bright solition solutions of both 1D GPE and 1D NPSE and compare these
theoretical predictions with the available experimental data.Comment: 12 pages, 4 figures, tutorial talk at the VI International School and
Conference on Photonics "Photonica 2017", 28 August - 1 September 2017,
Belgrade, Serbia; new version: added one figure and some references,
corrected typo