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We calculate the time-of-flight patterns of strongly interacting bosonsconfined in two-dimensional square lattice in the presence of an artificialmagnetic field using quantum rotor model that is inherently combined with theBogolyubov approach. We consider various geometries of the magnetic flux, whichare expected to be realizable, or have already been implemented in experimentalsettings. The flexibility of the method let us to study cases of the artificialmagnetic field being uniform, staggered or forming a checkerboardconfiguration. Effects of additional temporal modulation of the opticalpotential that results from application of Raman lasers driving particletransitions between lattice sites are also included. The presentedtime-of-flight patterns may serve as a verification of chosen gauge inexperiments, but also provide important hints on unconventional, non-zeromomentum condensates, or possibility of observing graphene-like physicsresulting from occurrence of Dirac cones in artificial magnetic fields insystems of ultra-cold bosons in optical lattices. Also, we elucidate ondifferences between effects of magnetic field in solids and the artificialmagnetic field in optical lattices, which can be controlled on much higherlevel leading to effects not possible in condensed matter physics.

Time-of-flight patterns of ultra-cold bosons in optical lattices in various Abelian artificial magnetic field gauges