Bogoliubov theory of interacting bosons on a lattice in a synthetic magnetic field

TL;DR

This paper develops a Bogoliubov theoretical framework to analyze interacting bosons on a lattice under a synthetic magnetic field, predicting superfluid phases with spatial order and quasiparticle spectra, relevant for cold atom experiments.

Contribution

It introduces a Bogoliubov approach to study superfluid phases of interacting bosons in a magnetic field on a lattice, including spatial structure and excitation spectra analysis.

Findings

Superfluid phases exhibit spatial order influenced by magnetic field commensuration.

Quasiparticle spectra show Hofstadter butterfly features combined with superfluid characteristics.

The theory predicts experimental signatures for time-of-flight and Bragg spectroscopy.

Abstract

We consider theoretically the problem of an artificial gauge potential applied to a cold atomic system of interacting neutral bosons in a tight-binding optical lattice. Using the Bose-Hubbard model, we show that an effective magnetic field leads to superfluid phases with simultaneous spatial order, which we analyze using Bogoliubov theory. This gives a consistent expansion in terms of quantum and thermal fluctuations, in which the lowest order gives a Gross-Pitaevskii equation determining the condensate configuration. We apply an analysis based on the magnetic symmetry group to show how the spatial structure of this configuration depends on commensuration between the magnetic field and the lattice. Higher orders describe the quasiparticle excitations, whose spectrum combines the intricacy the Hofstadter butterfly with the characteristic features of the superfluid phase. We use the depletion of the condensate to determine the range of validity of our approximations and also to find an estimate for the onset of the Mott insulator phase. Our theory provides concrete experimental predictions, for both time-of-flight imagery and Bragg spectroscopy.