Interferometric modulation of quantum cascade interactions

We consider many-body quantum systems dissipatively coupled by a cascade network, i.e., a setup in which interactions are mediated by unidirectional environmental modes propagating through a linear optical interferometer. In particular we are interested in the possibility of inducing different effective interactions by properly engineering an external dissipative network of beam splitters and phase shifters. In this work we first derive the general structure of the master equation for a symmetric class of translation-invariant cascade networks. Then we show how, by tuning the parameters of the interferometer, one can exploit interference effects to tailor a large variety of many-body interactions.