Quantum fluctuations of a vortex in an optical lattice

TL;DR

This paper develops a quantum theory for vortices in a Bose-Einstein condensate within an optical lattice, revealing mode couplings and the potential for vortex squeezing, with numerical solutions showing novel properties beyond linear response.

Contribution

It introduces a variational quantum framework for vortex and quadrupole modes in optical lattices, highlighting mode coupling and vortex squeezing phenomena.

Findings

Coupling between quadrupole and Kelvin modes analogous to quantum optics processes

Numerical solutions reveal properties beyond linear-response theory

Potential for vortex squeezing in optical lattice systems

Abstract

Using a variational ansatz for the wave function of the Bose-Einstein condensate, we develop a quantum theory of vortices and quadrupole modes in a one-dimensional optical lattice. We study the coupling between the quadrupole modes and Kelvin modes, which turns out to be formally analogous to the theory of parametric processes in quantum optics. This leads to the possibility of squeezing vortices. We solve the quantum multimode problem for the Kelvin modes and quadrupole modes numerically and find properties that cannot be explained with a simple linear-response theory.