Vortex-lattice melting in a one-dimensional optical lattice

TL;DR

This paper studies quantum fluctuations and melting of vortex lattices in one-dimensional optical lattices, revealing inhomogeneous melting patterns and the effects of tunneling on vortex stability.

Contribution

It introduces a comprehensive method to analyze vortex lattice modes, including Bloch bands of Tkachenko modes, in a one-dimensional optical lattice with finite-size effects.

Findings

Vortex lattice fluctuations are inhomogeneous due to small particle numbers.

Melting occurs from outside inwards, influenced by finite-size effects.

Tunneling reduces inhomogeneity and vortex fluctuations.

Abstract

We investigate quantum fluctuations of a vortex lattice in a one-dimensional optical lattice. Our method gives full access to all the modes of the vortex lattice and we discuss in particular the Bloch bands of the Tkachenko modes. Because of the small number of particles in the pancake Bose-Einstein condensates at every site of the optical lattice, finite-size effects become very important. Therefore, the fluctuations in the vortex positions are inhomogeneous and the melting of the lattice occurs from the outside inwards. Tunneling between neighbouring pancakes substantially reduces the inhomogeneity as well as the size of the fluctuations.