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Physical Review A

Critical optical-hysteresis regime and optical-bistability transformation

Jianning Li, Dianzhen Cui

Published Mar 31, 2023• 2 citations
Publisher

Abstract

In this paper, we study the optical-hysteresis regime in a driven-dissipative Bose-Hubbard dimer under a symmetric configuration and analyze the classical optical bistability with the Gross-Pitaevskii mean-field approach. We find that the critical point of the optical-hysteresis regime can be determined by the classical optical-bistability transformation predicted with a steady state equation, and the critical tunneling rate is given by analyzing the bistable threshold points. In addition, we apply the same approach to a single nonlinear microcavity coupled with an atom and the critical atom-cavity coupling strength of the optical-hysteresis regime is also obtained. Finally, in order to illustrate that the critical point could be determined by the classical optical-bistability transformation, we analyze the Liouvillian gap and find it opens at the critical point of the optical-hysteresis regime. This work clarifies the relation between optical hysteresis and classical optical bistability, which provides theoretical references for the modulation of optical hysteresis in experiment.

DOI
10.1103/physreva.107.033715

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In this paper, we study the optical-hysteresis regime in a driven-dissipative Bose-Hubbard dimer under a symmetric configuration and analyze the classical optical bistability with the Gross-Pitaevskii mean-field approach. We find that the critical point of the optical-hysteresis regime can be determined by the classical optical-bistability transformation predicted with a steady state equation, and the critical tunneling rate is given by analyzing the bistable threshold points. In addition, we apply the same approach to a single nonlinear microcavity coupled with an atom and the critical atom-cavity coupling strength of the optical-hysteresis regime is also obtained. Finally, in order to illustrate that the critical point could be determined by the classical optical-bistability transformation, we analyze the Liouvillian gap and find it opens at the critical point of the optical-hysteresis regime. This work clarifies the relation between optical hysteresis and classical optical bistability, which provides theoretical references for the modulation of optical hysteresis in experiment.
We introduce a two-level atom into a cavity as an ancilla to control the hysteresis of the system where the cavity is described by a driven-dissipative nonlinear Kerr model. We find that the dynamic optical hysteresis can be modulated by changing the atom-cavity coupling strength, and the nonlinearity induced by atom-cavity coupling weakens the Kerr nonlinearity in the weak coupling regime. This leads to the change in the critical point corresponding to the decrease in the hysteresis area. The physics behind the modulation is closely related to the effect of the atom-cavity coupling on the discontinuity of the first nonzero Liouvillian eigenvalue. A relative deviation of the metastable state and target steady state is defined to characterize the relation between the hysteresis and adiabaticity of the system. Taking only two Liouvillian eigenvectors into account in the composite system, we derive an expression for the dependence of the hysteresis area on the sweeping speed and discuss its feature in the slow sweeping limit.
We theoretically investigate the critical properties of a single driven-dissipative nonlinear photon mode. In a well-defined thermodynamical limit of large excitation numbers, the exact quantum solution describes a first-order phase transition in the regime where semiclassical theory predicts optical bistability. We study the behavior of the complex spectral gap associated with the Liouvillian superoperator of the corresponding master equation. We show that in this limit the Liouvillian gap vanishes exponentially and that the bimodality of the photon Wigner function disappears. The connection between the considered thermodynamical limit of large photon numbers for the single-mode cavity and the thermodynamical limit of many cavities for a driven-dissipative Bose-Hubbard system is discussed.
We present analytical solutions for the mean-field master equation of the driven-dissipative Bose-Hubbard model for cavity photons, in the limit of both weak pumping and weak dissipation. Instead of pure Mott-insulator states, we find statistical mixtures with the same second-order coherence g(2)(0){g}^{(2)}(0)g(2)(0) as a Fock state with nnn photons, but a mean photon number of n/2.n/2.n/2. These mixed states occur when nnn pump photons have the same energy as nnn interacting photons inside the nonlinear cavity and survive up to a critical tunneling coupling strength, above which a crossover to a classical coherent state takes place. We also explain the origin of both antibunching and superbunching predicted by P-representation mean-field theory at higher pumping and dissipation. In particular, we show that the strongly correlated region of the associated phase diagram cannot be described within the semiclassical Gross-Pitaevskii approach.
We study the dynamical properties of a driven-dissipative Bose-Hubbard model in the strongly interacting regime through a quantum trajectory approach with a cluster Gutzwiller Ansatz for the wave function. This allows us to take classical and quantum correlations into account. By studying the dynamical hysteresis surface that arises by sweeping through the coherent driving strength we show that the phase diagram for this system is in qualitative correspondence with the Gutzwiller mean-field result. However, quantitative differences are present and the inclusion of classical and quantum correlations causes a significant shift of the critical parameters. Additionally, we show that approximation techniques relying on a unimodal distribution such as the mean field and 1/z1/z1/z expansion drastically underestimate the particle number fluctuations. Finally, we show that a proposed mapping of the driven-dissipative many-body Bose-Hubbard model onto a single driven-dissipative Kerr model is not accurate for parameters in the hysteresis regime.