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We analyze a modified Bose-Hubbard model, where two cavities having on-siteKerr interactions are subject to two-photon driving and correlated dissipation.We derive an exact solution for the steady state of this interactingdriven-dissipative system, and use it show that the system permits thepreparation and stabilization of pure entangled non-Gaussian states, so-calledentangled cat states. Unlike previous proposals for dissipative stabilizationof such states, our approach requires only a linear coupling to a singleengineered reservoir (as opposed to nonlinear couplings to two or morereservoirs). Our scheme is within the reach of state-of-the-art experiments incircuit QED.

Dissipative stabilization of entangled cat states using a driven Bose-Hubbard dimer