Photonic analogue of boson Josephson junction in two coupled nonlinear cavities with pumping and dissipation

Abstract

In this paper, we propose a photonic Josephson junction in two coupled, Kerr-type, nonlinear cavities. In the coherent state representation, saddle point analysis of the system action yields a mean-field description of the coherent photon current. The photonic analogs of the Rabi oscillation, the AC effect as well as the Shapiro resonance are found. The tunneling dynamics dramatically change at a critical point that is determined by the relative value of on-site nonlinear strength versus intercavity tunneling rate. We discuss this critical behavior for various parameters in detail. Furthermore, the influences of the initial conditions and the environment-induced pumping–dissipation process on the system dynamics are also studied.