Excitations of a Bose-Einstein condensate in a one-dimensional optical lattice

TL;DR

This paper analyzes the low-energy excitations of a stack of weakly-coupled two-dimensional Bose-Einstein condensates in a one-dimensional optical lattice, deriving analytical dispersion relations for various modes and vortex states.

Contribution

It provides an analytical variational method to calculate dispersion relations of excitations in layered BECs with vortices, applicable to arbitrary atom numbers and momenta.

Findings

Derived analytical dispersion relations for monopole and quadrupole modes.

Extended analysis to systems with vortices along the lattice direction.

Discussed experimental observability of the predicted excitations.

Abstract

We investigate the low-lying excitations of a stack of weakly-coupled two-dimensional Bose-Einstein condensates that is formed by a one-dimensional optical lattice. In particular, we calculate the dispersion relations of the monopole and quadrupole modes, both for the ground state as well as for the case in which the system contains a vortex along the direction of the lasers creating the optical lattice. Our variational approach enables us to determine analytically the dispersion relations for an arbitrary number of atoms in every two-dimensional condensate and for an arbitrary momentum. We also discuss the feasibility of experimentally observing our results.