Competition between two-photon driving, dissipation and interactions in bosonic lattice models: an exact solution

Abstract

We present an exact solution in arbitrary dimensions for the steady states of a class of quantum driven-dissipative bosonic models, where a set of modes is subject to arbitrary two-photon driving, single-photon loss and a global Hubbard (or Kerr)-like interaction. Our solutions reveal a wealth of striking phenomena, including the emergence of dissipative phase transitions, nontrivial mode competition physics and symmetry breaking, and the stabilization of many-body $SU(1,1)$ pair coherent states. Our exact solutions enable the description of spatial correlations, and are fully valid in regimes where traditional mean-field and semiclassical approaches break down.

6 pages + 24 page supplemental, 4 figures

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• Nonequilibrium Nonlinear Effects and Dynamical Boson Condensation in a Driven-Dissipative Wannier-Stark Lattice
• Non-perturbative switching rates in bistable open quantum systems: from driven Kerr oscillators to dissipative cat qubits
• A solvable model for strongly interacting nonequilibrium excitons