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arXiv · 2311.00297

Emergent equilibrium and quantum criticality in a two-photon dissipative oscillator

V. Yu. Mylnikov·S. O. Potashin·G. S. Sokolovskii·N. S. Averkiev
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Abstract

We study the dissipative phase transition in a quantum oscillator with two-photon drive and two-photon dissipation. Using the semi-classical Langevin equation and the Fokker-Plank approach, we construct a theory of non-perturbative quantum fluctuations and go beyond the semi-classical approximation. We demonstrate the mapping of a two-photon quantum dissipative oscillator onto a classical equilibrium model of a nonlinear classical oscillator in a colored-noise environment. Then, we justify the applicability of the Landau theory for a given dissipative phase transition. To do that, we explicitly demonstrate the Boltzmann-like form of stationary distribution function depending on the effective temperature, which is determined by the frequency detuning and the rates of two-photon drive and dissipation. In addition, we provide a description of the quantum critical region and obtain critical exponents that appear to be in very good agreement with numerical simulations.

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V. Yu. Mylnikov, S. O. Potashin, G. S. Sokolovskii, N. S. Averkiev. 2023-11-01. Emergent equilibrium and quantum criticality in a two-photon dissipative oscillator. https://doi.org/10.1103/physrevresearch.7.013061

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