Rotating Bose gas with hard-core repulsion in a quasi-2D harmonic trap: vortices in BEC

We consider a gas of N(=6, 10, 15) Bose particles with hard-core repulsion, contained in a quasi-2D harmonic trap and subjected to an overall angular velocity $\mathrm{\Omega }$ about the z-axis. Exact diagonalization of the $n\times n$ many-body Hamiltonian matrix in given subspaces of the total (quantized) angular momentum L${}_z$, with $n\sim {10}^5$(e.g. for L${}_z$=N=15, n =240782) was carried out using Davidson’s algorithm. The many-body variational ground state wavefunction, as also the corresponding energy and the reduced one-particle density-matrix were calculated. With the usual identification of $\mathrm{\Omega }$ as the Lagrange multiplier associated with L${}_z$ for a rotating system, the $L_z-\mathrm{\Omega }$ phase diagram (or the stability line) was determined that gave a number of critical angular velocities $\Omega_{{\bf c}i}, i=1,2,3,… ,$ at which the ground state angular momentum and the associated condensate fraction undergo abrupt jumps. A number of (total) angular momentum states were found to be stable at successively higher critical angular velocities $\Omega_{{\bf c}i},
i=1,2,3,…$foragivenN\mathrm{.}For$L_{z}>N$, the condensate was strongly depleted. The critical ${\mathrm{\Omega }}_{\mathbf{c}i}$ values, however, decreased with increasing interaction strength as well as the particle number, and were systematically greater than the non-variational Yrast-state values for the single vortex state with L${}_z$ =N. We have also observed that the condensate fraction for the single vortex state (as also for the higher vortex states) did not change significantly even as the 2-body interaction strength was varied over several $(\sim 4)$ orders of magnitude in the moderately to the weakly interacting regime.