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(= 6, 10, 15) Bose particles with hard-core repulsion, contained in a quasi-2D 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 Lz, with n ∼ 10 5 (e.g. for Lz=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 ρ (r, r ′ ) = µ λµχ * µ (r) χµ (r ′ ) were calculated. With the usual identification of Ω as the Lagrange multiplier associated with Lz for a rotating system, the Lz − Ω phase diagram (or the stability line) was determined that gave a number of critical angular velocities Ωci, 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. A number of (total) angular momentum states were found to be stable at successively higher critical angular velocities Ωci, i = 1, 2, 3, · · · for a given N. All the states in the regime N > Lz > 0 are metastable. For Lz >N, the Lz values for the stable ground states generally increased with the increasing critical angular velocities Ωci, and the condensate was strongly depleted. The critical Ωci 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 Lz=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(∼ 4) orders of magnitude in the moderately to the weakly interacting regime.

Many-body quantum dynamics in the decay of bent dark solitons of Bose–Einstein condensates

“…Weak [46], moderate [53], and rapid [47] rotating regimes have been explored, leading to the formation of one to few singly quantized vortices, and progressively (with increased stirring) of regular vortex patterns forming canonical polygons and vortex lattices. For the MB treatment of these coherent structures, diagonalization techniques have been developed [53,54] which, however, bear the limitation of tackling few boson systems. The MB effects on vortex formation in rotating BECs for larger bosonic ensembles have been considered very recently [55,56] where modes of hidden vorticity not visible in the total density of the system, have been identified.…”

Vortex patterns in moderately rotating Bose-condensed gas

“…The simultaneous eigenstate of Hamiltonian and total angular momentum minimizes the free energy at zero-temperature in the corotating frame to become the ground state of the system. With the usual identification of Ω as the Lagrange multiplier associated with the total angular momentum L z for the rotating system, the L z -Ω stability line has a series of critical angular velocities Ω ci , i = 1, 2, 3, · · ·, at which total angular momentum of the condensed many-body ground state takes quantum jump (undergoes quantum phase transition) [31]. The ground state corresponding to critical angular velocity Ω ci , is referred to as quantum mechanically stable phase-coherent vortical state [24][25][26].…”

Ground and Low-Lying Collective States of Rotating Three-Boson System

“…Restricting to n r = 0 and taking m ≥ 0 in the above equation corresponds to the LLL approximation. Taking n r ≥ 0 and allowing m to take positive as well as negative values corresponds to going beyond LLLs [39,40]. The N -body variational wavefunction is…”