A quantum resonance catastrophe for transport through an AC driven impurity

We consider the quantum transport in a tight-binding chain with a locally applied potential which is oscillating in time. The steady state for such a driven impurity can be calculated exactly for any energy and applied potential using the Floquet formalism. The resulting transmission has a non-trivial, non-monotonic behavior depending on incoming momentum, driving frequency, and the strength of the applied periodic potential. Hence there is an abundance of tuning possibilities, which allows to find resonances of total reflection for any choice of incoming momentum and periodic potential. Remarkably, this implies that even for an arbitrarily small infinitesimal impurity potential it is always possible to find a resonance frequency at which there is a catastrophic breakdown of the transmission T=0. The points of zero transmission are closely related to the phenomenon of Fano resonances at dynamically created bound states in the continuum. The results are relevant for a variety of one-dimensional systems where local AC driving is possible, such as quantum nanodot arrays, ultracold gases in optical lattices, photonic crystals, or molecular electronics.