Vortex lattices in Bose-Einstein condensates: from the Thomas-Fermi to the lowest Landau level regime

TL;DR

This paper investigates the properties of vortex lattices in rotating Bose-Einstein condensates, exploring the transition from the Thomas-Fermi regime to the lowest Landau level, and provides detailed numerical analysis of their ground states.

Contribution

It introduces a gauge transformation to solve the 2D Gross-Pitaevskii equation, enabling analysis across different interaction regimes in vortex lattices.

Findings

Derived the equation of state for vortex lattices.

Quantified vortex core size across regimes.

Calculated the elastic shear modulus relevant for Tkachenko modes.

Abstract

We consider a periodic vortex lattice in a rotating Bose-Einstein condensed gas, where the centrifugal potential is exactly compensated by the external harmonic trap. By introducing a gauge transformation which makes the Hamiltonian periodic, we solve numerically the 2D Gross-Pitaevskii equation finding the exact mean field ground state. In particular, we explore the crossover between the Thomas-Fermi regime, holding for large values of the coupling constant, and the lowest Landau level limit, corresponding to the weakly interacting case. Explicit results are given for the equation of state, the vortex core size, as well as the elastic shear modulus, which is crucial for the calculation of the Tkachenko frequencies.