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

We present a theoretical study of the effect of a magnetic field on a bosonic superfluid in a tight-binding lattice, motivated by advances in the synthesis of gauge potentials for ultracold atoms. An analysis based on the magnetic symmetry group shows that the superfluid has simultaneous spatial order, and that this depends on commensuration between the magnetic field and lattice. We predict clear signatures of many-body effects in time-of-flight images, and use a Bogoliubov expansion to calculate quasiparticle spectra that may be measured using Bragg spectroscopy. This work has been supported by JQI-NSF-PFC, ARO-DARPA-OLE, and Atomtronics-ARO-MURI.