Nonclassical photon-assisted transport in superconducting tunnel junctions

Advances in circuit quantum electrodynamics have enabled the generation of arbitrary nonclassical microwave states, enabling progress in physics. Here, we present a theoretical study of the electrical current in a Josephson tunnel junction interacting with a nonclassical electromagnetic environment. This allows us to generalize classical transport phenomena like photon-assisted tunneling and Shapiro steps to the quantum regime. We predict that the analysis of the supercurrent in such a setup enables the complete reconstruction of quantum states of the electromagnetic environment, something that is not possible with normal tunnel junctions.