Tkachenko modes of vortex lattices in rapidly rotating Bose-Einstein condensates

TL;DR

This paper investigates the behavior of Tkachenko modes in vortex lattices of rapidly rotating Bose-Einstein condensates, revealing how their frequencies depend on rotation speed and confirming experimental observations.

Contribution

It provides a theoretical analysis of Tkachenko modes across different regimes, connecting mode behavior with vortex lattice shear modulus at high rotation rates.

Findings

Tkachenko mode frequency transitions from linear to quadratic in wavevector with increasing rotation speed.

The system exhibits an inertial mode with frequency ≥ 2Ω.

Theoretical frequencies align with recent experimental observations at JILA.

Abstract

We calculate the in-plane modes of the vortex lattice in a rotating Bose condensate from the Thomas-Fermi to the mean-field quantum Hall regimes. The Tkachenko mode frequency goes from linear in the wavevector, $k$, for lattice rotational velocities, $\Omega$, much smaller than the lowest sound wave frequency in a finite system, to quadratic in $k$ in the opposite limit. The system also supports an inertial mode of frequency $\ge 2\Omega$. The calculated frequencies are in good agreement with recent observations of Tkachenko modes at JILA, and provide evidence for the decrease in the shear modulus of the vortex lattice at rapid rotation.