Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions

Abstract

We present exact results for the steady-state density matrix of a general class of driven-dissipative systems consisting of a nonlinear Kerr resonator in the presence of both coherent (one-photon) and parametric (two-photon) driving and dissipation. Thanks to the analytical solution, obtained via the complex P-representation formalism, we are able to explore any regime, including photon blockade, multiphoton resonant effects, and a mesoscopic regime with large photon density and quantum correlations. We show how the interplay between one- and two-photon driving provides a way to control the multimodality of the Wigner function in regimes where the semiclassical theory exhibits multistability. We also study the emergence of dissipative phase transitions in the thermodynamic limit of large photon numbers.

12 pages, 10 figures. Highlighted as Editors' Suggestion on Physical Review A

References in corpus (6)

• Quantum fluids of light
• Confining the state of light to a quantum manifold by engineered two-photon loss
• Dynamical Phase Transitions and Instabilities in Open Atomic Many-Body Systems
• The quantum optical Josephson interferometer
• Polaritonic Feshbach Resonance
• Steady-state phase diagram of a driven QED-cavity array with cross-Kerr nonlinearities

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• Fisher information approach to non-equilibrium phase transitions in quantum XXZ spin chain with boundary noise
• Simulating frustrated antiferromagnets with quadratically driven QED cavities
• Quantum features of entropy production in driven-dissipative transitions
• Dissipation-induced antiferromagnetic-like frustration in coupled photonic resonators
• Time- and frequency-domain two-particle correlations of a driven dissipative Bose-Hubbard model
• Correspondence between dissipative phase transitions of light and time crystals
• Single-photon nonlinearities and blockade from a strongly driven photonic molecule
• Josephson Photonics with Simultaneous Resonances