Fock-state stabilization and emission in superconducting circuits using dc-biased Josephson junctions

In this article we propose a protocol to autonomously stabilize a Fock state within a circuit QED architecture that doesn’t recourse to any ac-drive nor pulse. This protocol is realized with a microwave cavity driven by a Josephson junction and coupled to quantum engineered reservoir. It relies on two important ingredients. First, a high-impedance resonator to enable photon-dependent driving used as the cavity. Such device has recently been implemented in circuit QED platforms and removes the need for periodic driving. Second, on an auxiliary, low-quality factor cavity used as a engineered environment. Its damping rate must be scaled with respect to the Josephson energy and the main cavity quality factor in order to stabilize a quantum state. A second protocol, based on the same platform, is used to produce a flying qubit.