  We analyze a modified Bose-Hubbard model, where two cavities having on-site
Kerr interactions are subject to two-photon driving and correlated dissipation.
We derive an exact solution for the steady state of this interacting
driven-dissipative system, and use it show that the system permits the
preparation and stabilization of pure entangled non-Gaussian states, so-called
entangled cat states. Unlike previous proposals for dissipative stabilization
of such states, our approach requires only a linear coupling to a single
engineered reservoir (as opposed to nonlinear couplings to two or more
reservoirs). Our scheme is within the reach of state-of-the-art experiments in
circuit QED.
