Tkachenko oscillations and the compressibility of a rotating Bose gas

TL;DR

This paper investigates how Tkachenko oscillations in a rotating Bose gas influence its compressibility and structure factor, revealing their role in the system's collective excitations and agreement with experimental data.

Contribution

It demonstrates the impact of vortex lattice oscillations on the compressibility sum rule and provides calculations of Tkachenko frequencies in trapped Bose gases.

Findings

Vortex lattice causes a $q^2$ static structure factor at small $q$.

Tkachenko oscillations influence the saturation of the compressibility sum rule.

Results agree with experimental observations and previous theories.

Abstract

The elastic oscillations of the vortex lattice of a cold Bose gas (Tkachenko modes) are shown to play a crucial role in the saturation of the compressibility sum rule, as a consequence of the hybridization with the longitudinal degrees of freedom. The presence of the vortex lattice is responsible for a $q^2$ behavior of the static structure factor at small wavevectors $q$, which implies the absence of long range order in 2D configurations at zero temperature. Sum rules are used to calculate the Tkachenko frequency in the presence of harmonic trapping. Results are derived in the Thomas-Fermi regime and compared with experiments as well as with previous theoretical estimates.