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Among the most exciting recent advances in the field of superconducting quantum circuits is the ability to coherently couple microwave photons in low-loss cavities to quantum electronic conductors. These hybrid quantum systems hold great promise for quantum information-processing applications; even more strikingly, they enable exploration of new physical regimes. Here we study theoretically the new physics emerging when a quantum electronic conductor is exposed to nonclassical microwaves (for example, squeezed states, Fock states). We study this interplay in the experimentally relevant situation where a superconducting microwave cavity is coupled to a conductor in the tunnelling regime. We find that the conductor acts as a nontrivial probe of the microwave state: the emission and absorption of photons by the conductor is characterized by a nonpositive definite quasi-probability distribution, which is related to the Glauber–Sudarshan
P
-function of quantum optics. These negative quasi-probabilities have a direct influence on the conductance of the conductor.
Coherently coupling microwave photons to quantum electronic conductors could provide a useful platform for quantum information processing. Souquet
et al
. now theoretically demonstrate that such systems can also act as sensitive probes of the quantum properties of non-classical microwave radiation.