Bogoliubov theory of interacting bosons on a lattice in a synthetic magnetic field
arXiv:1009.1389 · doi:10.1103/PhysRevA.83.013612
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.
22 pages, 7 figures
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- Chiral Bosonic Phases on the Haldane Honeycomb Lattice
- A cavity-induced artificial gauge field in a Bose-Hubbard ladder
- Anyon Superconductivity from Topological Criticality in a Hofstadter-Hubbard Model
- Unconventional Self-Similar Hofstadter Superconductivity from Repulsive Interactions
- Time-of-flight patterns of ultra-cold bosons in optical lattices in various Abelian artificial magnetic field gauges
- Conductivity of strongly correlated bosons in optical lattices in an Abelian synthetic magnetic field
- Density wave propagation in a two-dimensional random dimer potential: from a single to a bipartite square lattice
- Theory of Hofstadter Superconductors