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

This paper addresses the challenge of autonomously stabilizing non-classical bosonic Fock states in a Kerr-nonlinear cavity. Unlike transient preparation methods that require precise timing or active feedback, the authors propose an autonomous reservoir engineering scheme. They couple a Kerr cavity to an array of auxiliary qubits, each driven by a blue-sideband interaction. By engineering the qubit relaxation to be faster than the coherent cavity-qubit exchange, the authors rectify the reversible anti-Jaynes-Cummings (AJC) interaction into an irreversible, directed photon-raising process. The Kerr nonlinearity provides the necessary photon-number selectivity, allowing each qubit to resonantly address a specific transition in the Fock ladder.

• Dissipation-Rectified Cascades: The authors demonstrate that auxiliary-qubit relaxation acts as a rectification mechanism, converting reversible AJC exchanges into a directed ladder of photon-raising transitions. This cascade terminates at a prescribed Fock state because no auxiliary qubit resonantly addresses the subsequent transition.
• Autonomous Stabilization: Full Lindblad simulations confirm that the cavity steady state is dominated by the target Fock state (demonstrated for states |1⟩ through |4⟩). These states exhibit pronounced Wigner negativity, a hallmark of non-classicality.
• Analytical Modeling: An analytical birth-death model accurately captures the steady-state populations, identifying the competition between resonant pumping, cavity loss, and off-resonant leakage as the primary factors governing stabilization.
• Scalability: The authors extend the scheme to a Kerr-cavity chain, showing that the primary cavity acts as a boundary reservoir that can stabilize Fock states in indirectly coupled cavities through nearest-neighbor photon exchange.

This work provides a robust, autonomous route for preparing and maintaining non-classical bosonic states, which are essential resources for quantum metrology and bosonic quantum error correction. By using engineered dissipation rather than active feedback, the scheme simplifies the experimental requirements for state stabilization. Furthermore, the extension to cavity chains suggests a path toward creating and repairing integer-filled bosonic lattice states, offering a new tool for driven-dissipative quantum simulation.