Theory of interactions between cavity photons induced by a mesoscopic circuit

Audrey Cottet, Zaki Leghtas

Published 2019-10-17Version 1

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 conditions in which the cavity dynamics can be considered as Markovian. In this case, one can use a Lindblad equation to describe the cavity quantum dynamics, with effective parameters set by electronic correlation functions. This equation 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.