Non-uniform vortex lattices in inhomogeneous rotating Bose-Einstein condensates

TL;DR

This paper develops a comprehensive elastic theory framework to describe vortex lattice distortions in rotating Bose-Einstein condensates, accounting for inhomogeneity and higher Landau level excitations, with implications for understanding equilibrium configurations.

Contribution

It introduces a general elastic theory for vortex lattice distortions in inhomogeneous BECs, including effects of higher Landau levels and their impact on lattice equilibrium.

Findings

Distortion depends on density inhomogeneity and higher Landau level excitations.

Higher Landau levels effectively renormalize the trap frequency to the rotational frequency.

Elastic theory explains how lattice distortion emerges in inhomogeneous systems.

Abstract

We derive a general framework, in terms of elastic theory, for describing the distortion of the vortex lattice in a rotating Bose-Einstein condensate at arbitrary rotation speed and determining the dependence of the distortion on the density inhomogeneity of the system. In the rapidly rotating limit, we derive the energetics in terms of Landau levels, including excitation to higher levels; the distortion depends on the excitation of higher levels as well as on the density gradient. As we show, the dominant effect of higher Landau levels in a distorted lattice in equilibrium is simply to renormalize the frequency entering the lowest Landau level condensate wave function -- from the transverse trap frequency, $\omega$, to the rotational frequency, $\Omega$, of the system. Finally, we show how the equilibrium lattice distortion emerges from elastohydrodynamic theory for inhomogeneous systems.