Driven Kerr resonators: new regimes of solvability and quantum bistability

The driven Kerr resonator is one of the most iconic solvable models in cavity QED [1]. When subject to two-photon (parametric) driving it can exhibit bistability, something that has been exploited in several recent experiments in circuit quantum electrodynamics and proposals for protected quantum memories [2, 3]. Here, we develop a more physically transparent method for finding analytic solutions to driven Kerr resonators. This allows us to solve for a wider class of systems than in previous work, and also allows us to derive closed-form expressions for steady-state Wigner functions. More intriguingly, our approach also uncovers a new class of previously-overlooked points of quantum bistability in the resonator's phase diagram. Our work could open up new avenues for using nonlinear driven superconducting quantum circuits as quantum processors.

[1] Drummond, P. D. et al. Quantum theory of optical bistability. J. Phys. A 13, 725 (1980)
[2] Mirrahimi, M. et al. Dynamically protected cat-qubits: a new paradigm for universal quantum computation. New J. Phys. 16, 045014 (2014).
[3] Leghtas, Z. et al. Confining the state of light to a quantum manifold by engineered two-photon loss. Science 347, 853–857 (2015).