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We study transport of interacting bosons through an Aharonov-Bohm cage - abuilding block of flat band networks - with coherent pump and sink leads. Inthe absence of interactions the cage is insulating due to destructiveinterference. We find that the cage stays insulating up to a critical value ofthe pump strength in the presence of mean field interactions, while the quantumregime induces particle pair transport and weak conductance below the criticalpump strength. A swift crossover from quantum into the classical regime uponfurther pump strength increase is observed. We solve the time dependent masterequations for the density matrix of the many body problem both in theclassical, pure quantum, and pseudoclassical regimes. We start with an emptycage and switch on driving. We characterize the transient dynamics, and thecomplexity of the resulting steady states and attractors. Our results can bereadily realized using experimental platforms involving interacting ultracoldatoms and photons on finetuned optical lattices.

Conductance transition with interacting bosons in an Aharonov-Bohm cage