RING-TO-DROPLET TRANSITION IN A TWO-DIMENSIONAL DIPOLAR BOSE–EINSTEIN CONDENSATE: A GROUND-STATE SCAN WITH GPELAB
Keywords:
Gross-Pitaevskii equation, rotational symmetry breaking, droplet lattice, imaginary-time propagation, ground state, GPELab, Dipolar Bose-Einstein condensateAbstract
We use the ready-made simulation model of the MATLAB toolbox GPELab to compute ground states of a two-dimensional dipolar Bose–Einstein condensate (BEC) while the dipolar strength BetaDipole is varied from 5 to 10 at fixed contact strength Beta = 3000. Ground states are obtained by imaginary-time propagation with the BESP scheme. For BetaDipole = 5 and 6 the ground state is a rotationally symmetric set of concentric rings. A hexagonal lattice of density droplets appears between BetaDipole = 6.1 and 6.2, first as a core of about 19 droplets surrounded by faint outer rings, and it grows to about 30 droplets at 6.5 and about 60 to 70 at 10. The energy rises smoothly with BetaDipole, and the difference between the x and y mean-square radii serves as a simple marker of broken rotational symmetry. Among the converged runs, the cost of convergence is highest close to the onset: 55,213 iterations at 6.25, compared with 3,693 at 5. A time-step test shows that Deltat = 1e-2 and Deltat = 1e-3 give the same state, the larger step did converge within 20,000 iterations in the lattice region and gave a saving in CPU time
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