Vortex lattice stability and phase coherence in three-dimensional rapidly rotating Bose condensates

TL;DR

This paper develops equations for vortex lattice modes in 3D rotating Bose-Einstein condensates, analyzing their stability, excitations, and phase coherence, predicting vortex lattice melting at finite temperatures.

Contribution

It extends the understanding of vortex lattice dynamics to three dimensions, including elastic and bending energies, and analyzes thermal effects on order and correlations.

Findings

Tkachenko mode frequency becomes linear at long wavelengths in 3D

Vortex displacement correlations grow with separation at finite temperature

Predicted vortex lattice melting at higher temperatures and lower particle numbers

Abstract

We establish the general equations of motion for the modes of a vortex lattice in a rapidly rotating Bose-Einstein condensate in three dimensions, taking into account the elastic energy of the lattice and the vortex line bending energy. As in two dimensions, the vortex lattice supports Tkachenko and gapped sound modes. In contrast, in three dimensions the Tkachenko mode frequency at long wavelengths becomes linear in the wavevector for any propagation direction out of the transverse plane. We compute the correlation functions of the vortex displacements and the superfluid order parameter for a homogeneous Bose gas of bounded extent in the axial direction. At zero temperature the vortex displacement correlations are convergent at large separation, but at finite temperatures, they grow with separation. The growth of the vortex displacements should lead to observable melting of vortex lattices at higher temperatures and somewhat lower particle number and faster rotation than in current experiments. At zero temperature a system of large extent in the axial direction maintains long range order-parameter correlations for large separation, but at finite temperatures the correlations decay with separation.