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We investigate the ground state properties of ultracold atoms with long rangeinteractions trapped in a two leg ladder configuration in the presence of anartificial magnetic field. Using a Gross-Pitaevskii approach and a mean fieldGutzwiller variational method, we explore both the weakly interacting andstrongly interacting regime, respectively. We calculate the boundaries betweenthe density-wave/supersolid and the Mott-insulator/superfluid phases as afunction of magnetic flux and uncover regions of supersolidity. The mean-fieldresults are confirmed by numerical simulations using a cluster mean fieldapproach.

Extended Bose Hubbard model for two leg ladder systems in artificial magnetic fields