Continuum Theory of Tkachenko Modes in Rotating Bose-Einstein Condensate

TL;DR

This paper develops a continuum hydrodynamic theory for Tkachenko modes in rotating Bose-Einstein condensates, accounting for density inhomogeneity and compressibility, and aligns well with experimental data.

Contribution

It introduces a new continuum model that incorporates inhomogeneity and compressibility effects in Tkachenko mode analysis.

Findings

The theory agrees with experimental observations.

Compressibility is crucial at high rotation speeds.

Provides coupled hydrodynamic equations for vortex-liquid dynamics.

Abstract

The present paper suggests the continuum theory of Tkachenko modes in a rotating 2D Bose-Einstein condensate taking into account density inhomogeneity and compressibility of the condensate. The problem requires solution of coupled hydrodynamic equations for vortex and liquid motion with proper boundary conditions, which were derived for the condensate described by the Thomas-Fermi approximation. Compressibility becomes essential at rapid rotation with angular velocity close to the trap frequency. The theory is in a reasonable agreement with experimental observation of Tkachenko modes.