  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.
