Relaxation-Rectified Anti-Jaynes-Cummings Cascades for Autonomous Fock-State Stabilization

We propose an autonomous scheme for stabilizing prescribed Fock states in a Kerr cavity by rectifying anti-Jaynes–Cummings interactions with auxiliary-qubit relaxation. Full Lindblad simulations demonstrate steady states dominated by the Fock states $\mathrm{\mid }1⟩$ through $\mathrm{\mid }4⟩$, accompanied by pronounced Wigner negativity. An analytical birth–death model captures the steady-state populations and identifies the operating regime for stabilization. These results establish auxiliary-qubit relaxation as a resource for autonomous reservoir engineering and provide a route to nonclassical bosonic-state preparation in a single Kerr cavity and, through a boundary reservoir, in a Kerr-cavity chain.