Tkachenko modes and quantum melting of Josephson junction type of vortex array in rotating Bose-Einstein condensate

TL;DR

This paper models the vortex lattice in rotating Bose-Einstein condensates as Josephson junctions, analyzing Tkachenko modes and quantum melting, with results aligning well with experimental data.

Contribution

It introduces a novel interpretation of the vortex lattice as Josephson junctions and links Tkachenko modes to low energy excitations, explaining quantum melting.

Findings

Calculated Tkachenko mode frequencies match experimental data.

Quantum vortex melting occurs at a specific energy ratio.

Vortex fluctuations lead to quantum melting of the lattice.

Abstract

Using path integral formalism, we show that the Abrikosov-Tkachenko vortex lattice may equivalently be understood as an array of Josephson junctions. The Tkachenko modes are found to be basically equivalent to the low energy excitations (Goldstone modes) of an ordered state. The calculated frequencies are in very good agreement with recent experimental data. Calculations of the fluctuations of the relative displacements of the vortices show that vortex melting is a result of quantum fluctuations around the ordered state due to the low energy excitations (Tkachenko modes)and occurs when the ratio of the kinectic energy to the potential energy of the vortex lattice is 0.001.