Collective modes of vortex lattices in two-component Bose-Einstein condensates under synthetic gauge fields

TL;DR

This paper investigates the collective excitation modes of vortex lattices in two-component Bose-Einstein condensates under synthetic magnetic fields, revealing universal low-energy behaviors and complex effects of intercomponent interactions.

Contribution

It introduces a comprehensive numerical analysis of vortex lattice excitations in two-component BECs under synthetic gauge fields, highlighting the impact of intercomponent interactions and lattice symmetry.

Findings

Two distinct low-energy modes with linear and quadratic dispersion are found.

Rescaling relations connect spectra under parallel and antiparallel fields when vortices overlap.

Interlaced vortex lattices show breakdown of rescaling, indicating complex vortex displacement effects.

Abstract

We study collective modes of vortex lattices in two-component Bose-Einstein condensates subject to synthetic magnetic fields in mutually parallel or antiparallel directions. By means of the Bogoliubov theory with the lowest-Landau-level approximation, we numerically calculate the excitation spectra for a rich variety of vortex lattices that appear commonly for parallel and antiparallel synthetic fields. We find that in all of these cases, there appear two distinct modes with linear and quadratic dispersion relations at low energies, which exhibit anisotropy reflecting the symmetry of each lattice structure. Remarkably, the low-energy spectra for the two types of fields are found to be related to each other by simple rescaling when vortices in different components overlap owing to an intercomponent attraction. These results are consistent with an effective field theory analysis. However, the rescaling relations break down for interlaced vortex lattices appearing with an intercomponent repulsion, indicating a nontrivial effect of an intercomponent vortex displacement beyond the effective field theory. We also find that high-energy parts of the excitation bands exhibit line or point nodes as a consequence of a fractional translation symmetry present in some of the lattice structures.