  We use a quantum path integral approach to describe the behavior of a
microwave cavity coupled to a dissipative mesoscopic circuit. We integrate out
the mesoscopic electronic degrees of freedom to obtain a cavity effective
action at fourth order in the light/matter coupling. By studying the structure
of this action, we establish sufficient conditions in which the cavity dynamics
can be described with a Lindblad equation. This equation depends on effective
parameters set by electronic correlation functions. It reveals that the
mesoscopic circuit induces an effective Kerr interaction and two-photon
dissipative processes. We use our method to study the effective dynamics of a
cavity coupled to a double quantum dot with normal metal reservoirs. If the
cavity is driven at twice its frequency, the double dot circuit generates
photonic squeezing and non-classicalities visible in the cavity Wigner
function. In particular, we find a counterintuitive situation where mesoscopic
dissipation enables the production of photonic Schr\"odinger cats. These
effects can occur for realistic circuit parameters. Our method can be
generalized straightforwardly to more complex circuit geometries with, for
instance, multiple quantum dots, and other types of fermionic reservoirs such
as superconductors and ferromagnets.
