Quantum state tomography of three-photon down conversion in a superconducting circuit

<!--StartFragment-->Circuit QED has proven to be a platform which offers possibilities for realizations beyond the scope of quantum optics. In particular, fast modulation of a boundary condition in the 1D field propagating through a transmission line has been employed for a realization of the dynamical Casimir effect. A remarkable advantage over quantum optics setups are effective photon-photon interactions engineered via a Josephson junction or a SQUID.

In this work we exploit both, tunability as well as non-linear interactions in order to explore the generation of three-photon processes in a tunable superconducting resonator. In particular we will study the degenerate three-photon down conversion. Theoretically, in the absence of losses the states generated via this type of interaction are non-classical [1], as characterized by a negative Wigner function.
Here we study if under realistic experimental conditions it is possible to observe signatures of this negativity for the field confined inside the resonator as well as for the external field propagating through an open transmission line.

[1] "Quantum interference in three-photon down-conversion", K. Banaszek and P. L. Knight. Phys. Rev. A 55, 2368 (1997).