Rotating Bose gas with hard-core repulsion in a quasi-two-dimensional harmonic trap: vortices in Bose-Einstein condensates

Abstract

We consider a gas of N(<~15) Bose particles with hard-core repulsion, contained in a quasi-two-dimensional harmonic trap and subjected to an overall angular velocity Ω about the z axis. Exact diagonalization of the n×n many-body Hamiltonian matrix in given subspaces of the total (quantized) angular momentum L_z, with n~10⁵ (e.g., for L_z=N=15, n=240782) was carried out using Davidson's algorithm. The many-body variational ground-state wave function, as also the corresponding energy and the reduced one-particle density-matrix ρ(r,r')=∑_μλ_μχ_μ(r)χ_μ(r') were determined. With the usual identification of Ω as the Lagrange multiplier associated with L_z for a rotating system, the L_z-Ω phase diagram (or the stability line) was determined that gave a number of critical angular velocities Ω_ci, i=1,2,3,..., at which the ground-state angular momentum and the associated condensate fraction, given by the largest eigenvalue of the reduced one-particle density matrix, undergo abrupt jumps. For a given N, a number of (total) angular momentum states were found to be stable at successively higher critical angular velocities Ω_ci, i=1,2,3,.... All the states in the regime N>L_z>0 are metastable. For L_z>N, the L_z values for the stable ground states generally increased with increasing critical angular velocities Ω_ci, and the condensate was strongly depleted. The critical Ω_ci values, however, decreased with increasing interaction strength as well as the particle number, and were systematically greater than the nonvariational yrast-state values for the L_z=N single vortex state. 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 two-body interaction strength was varied over several (~4) orders of magnitude in the moderately to the weakly interacting regime.