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We establish the phase diagram of the strongly-interacting Bose-Hubbard modeldefined on a two-leg ladder geometry in the presence of a homogeneous flux. Ourwork is motivated by a recent experiment [Atala et al., Nature Phys. 10, 588(2014)], which studied the same system, in the complementary regime of weakinteractions. Based on extensive density matrix renormalization groupsimulations and a bosonization analysis, we fully explore the parameter spacespanned by filling, inter-leg tunneling, and flux. As a main result, wedemonstrate the existence of gapless and gapped Meissner and vortex phases,with the gapped states emerging in Mott-insulating regimes. We calculateexperimentally accessible observables such as chiral currents and vortexpatterns.

Vortex and Meissner phases of strongly-interacting bosons on a two-leg ladder