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We present a new approach for deriving exact, closed-form solutions for thesteady state of a wide class of driven-dissipative nonlinear resonators that isdistinct from more common positive-$P$ function methods. Our method generalizesthe coherent quantum absorber approach of Stannigel et al. to include nonlineardriving and dissipation, and relies crucially on exploiting the Segal-Bargmannrepresentation of Fock space. Our solutions and method reveal a wealth ofpreviously unexplored observable phenomena in these systems, including newgeneralized photon-blockade and anti-blockade effects, and an infinite numberof new parameter choices that yield quantum-bistability.

Driven-dissipative quantum Kerr resonators: new exact solutions, photon blockade and quantum bistability