Vortex patterns in moderately rotating Bose-condensed gas

TL;DR

This paper uses exact diagonalization to study vortex pattern formation in a rotating Bose-condensed gas, revealing stable polygonal vortex arrangements and mechanisms of vortex nucleation and pattern transition.

Contribution

It provides detailed analysis of vortex patterns and their internal structure in a finite Bose gas, highlighting the transition mechanisms and symmetry properties of vortex configurations.

Findings

Stable polygonal vortex patterns with 5- and 6-fold symmetry observed.

Hexagonal vortex pattern is a precursor to triangular vortex lattice.

Unstable states show quantum melting of vortex patterns.

Abstract

Using exact diagonalization, we investigate the many-body ground state for vortex patterns in a rotating Bose-condensed gas of $N$ spinless particles, confined in a quasi-two-dimensional harmonic trap and interacting repulsively via finite-range Gaussian potential. The $N$-body Hamiltonian matrix is diagonalized in given subspaces of quantized total angular momentum $L_{z}$, to obtain the lowest-energy eigenstate. Further, the internal structure of these eigenstates is analyzed by calculating the corresponding conditional probability distribution. Specifically, the quantum mechanically stable as well as unstable states in a co-rotating frame are examined in the moderately rotating regime corresponding to angular momenta $4N \le L_{z} < 5N$ for $N=16$ bosons. In response to externally impressed rotation, patterns of singly quantized vortices are formed, shaping into canonical polygons with a central vortex at the trap center. The internal structure of unstable states reveals the mechanism of entry, nucleation and pattern formation of vortices with structural phase transition, as the condensate goes from one stable vortical state to the other. The stable polygonal vortex patterns having discrete $p$-fold rotational symmetry with $p=5$ and $p=6$ are observed. The hexagonal vortex pattern with $p=6$ symmetry is a precursor to the triangular vortex lattice of singly quantized vortices in the thermodynamic limit. For unstable states, quantum melting of vortex patterns due to uncertainty in positions of individual vortices, is also briefly discussed.