Critical optical-hysteresis regime and optical-bistability transformation

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.