Ground State and Tkachenko Modes of a Rapidly Rotating Bose-Einstein Condensate in the Lowest Landau Level State

TL;DR

This paper investigates the ground state and Tkachenko modes of a rapidly rotating Bose-Einstein condensate in the lowest Landau level, highlighting differences in vortex lattice elasticity compared to superconductors and implications for experimental observations.

Contribution

It provides a precise calculation of the shear elastic modulus of the vortex lattice in a rotating BEC, contrasting with previous estimates and enhancing understanding of Tkachenko modes.

Findings

Shear elastic modulus exceeds previous BEC estimates

Vortex lattice properties resemble those in type II superconductors

Implications for observing Tkachenko modes in experiments

Abstract

The Letter considers the ground state and the Tkachenko modes for a rapidly rotating Bose-Einstein condensate (BEC), when its macroscopic wave function is a coherent superposition of states analogous to the lowest Landau levels of a charge in a magnetic field. As well as in type II superconductors close to the critical magnetic field $H_{c2}$, this corresponds to a periodic vortex lattice. The exact value of the shear elastic modulus of the vortex lattice, which was known from the old works on type II superconductors, essentially exceeds the values calculated recently for BEC. This is important for comparison with observation of the Tkachenko mode in the rapidly rotating BEC.