Conductance transition with interacting bosons in an Aharonov-Bohm cage

We study transport of interacting bosons through an Aharonov-Bohm cage - a building block of flat band networks - with coherent pump and sink leads. In the absence of interactions the cage is insulating due to destructive interference. In the presence of mean field interactions the cage stays insulating up to a critical value of the pump strength. Above the critical pump strength the insulating state turns unstable, and the cage reshuffles with a finite probability into a conducting state, and with a complementary probability into a new insulating state. The precise state choice is depending on tiny noise beyond any experimental or computational control. In the quantum regime, particle pair transport induces weak conductance below the critical pump strength. Above the critical pump strength more particles accumulate on the cage. A swift crossover into a classical regime upon further pump strength increase is observed, which agrees well with the pseudoclassical results.