Quantum theory of a vortex line in an optical lattice

TL;DR

This paper develops a quantum theoretical framework for vortex lines in Bose-Einstein condensates within optical lattices, deriving their dispersion relations and exploring quantum state manipulation through mode coupling.

Contribution

It introduces a quantum model for vortex lines in optical lattice BECs, including mode coupling and the potential for generating squeezed vortex states.

Findings

Derived the dispersion relation of Kelvin modes.

Analyzed the coupling between Kelvin and quadrupole modes.

Showed the possibility of creating squeezed vortex states.

Abstract

We investigate the quantum theory of a vortex line in a stack of weakly-coupled two-dimensional Bose-Einstein condensates, that is created by a one-dimensional optical lattice. We derive the dispersion relation of the Kelvin modes of the vortex line and also study the coupling between the Kelvin modes and the quadrupole modes. We solve the coupled dynamics of the vortex line and the quadrupole modes, both classically as well as quantum mechanically. The quantum mechanical solution reveals the possibility of generating nonequilibrium squeezed vortex states by strongly driving the quadrupole modes.