Abstract

Nowadays, dissipative phase transition (DPT) attracts a great deal of interest from the physics and quantum optics community. It is characterized by abrupt changes of the physical observables on the parameters of the system, such as a dissipation and drive rates as well as coupling constants. The increased attention to the DPT roots in significant development of a new research area of quantum optics, known as reservoir engineering, which allows to obtain a wide range of controllable nonequilibrium quantum systems. A prime example of such a system, which we will study here, is an optical oscillator with two-photon drive and two-photon dissipation (Fig 1(a)). The immediate practical application of such a model is the qubit platform based on the quantum Schrödinger cat states which is applicable for universal quantum computation [1]. However, the quantum and dissipative nature of such a system significantly complicates its consideration beyond the mean-field description. In statistical physics, one can apply the well-developed Landau theory, which is used for a wide range of equilibrium phenomena. Here, we rigorously demonstrate that the nonequilibrium DPT that arises in an optical oscillator with two-photon drive and two-photon dissipation can be mapped onto a nonlinear classical oscillator in a colored-noise environment in regions distant from the critical point. Furthermore, using Fokker-Plank approach, we develop a description of the quantum critical region near the critical point, where strong quantum fluctuations destroy mean-field treatment.

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