Pinning and collective modes of a vortex lattice in a Bose-Einstein condensate

TL;DR

This paper investigates the ground state configurations and collective excitations of vortex lattices in rotating Bose-Einstein condensates within optical lattices, revealing phase transitions, lattice geometries, and mode dispersions depending on system parameters.

Contribution

It introduces a method to determine the phase diagram of vortex arrangements in BECs under optical lattices, including novel pinned and half-pinned phases, and analyzes their collective mode spectra.

Findings

Transition from unpinned to pinned vortex lattices with increasing optical potential

Identification of square, triangular, and half-pinned vortex lattice phases

Calculation of anisotropic, gapped or gapless collective modes

Abstract

We consider the ground state of vortices in a rotating Bose-Einstein condensate that is loaded in a corotating two-dimensional optical lattice. Due to the competition between vortex interactions and their potential energy, the vortices arrange themselves in various patterns, depending on the strength of the optical potential and the vortex density. We outline a method to determine the phase diagram for arbitrary vortex filling factor. Using this method, we discuss several filling factors explicitly. For increasing strength of the optical lattice, the system exhibits a transition from the unpinned hexagonal lattice to a lattice structure where all the vortices are pinned by the optical lattice. The geometry of this fully pinned vortex lattice depends on the filling factor and is either square or triangular. For some filling factors there is an intermediate half-pinned phase where only half of the vortices is pinned. We also consider the case of a two-component Bose-Einstein condensate, where the possible coexistence of the above-mentioned phases further enriches the phase diagram. In addition, we calculate the dispersion of the low-lying collective modes of the vortex lattice and find that, depending on the structure of the ground state, they can be gapped or gapless. Moreover, in the half-pinned and fully pinned phases, the collective mode dispersion is anisotropic. Possible experiments to probe the collective mode spectrum, and in particular the gap, are suggested.