Kerr Nonlinearity-Induced Nonreciprocity in Dissipatively Coupled Resonators

Nonreciprocal light propagation is increasingly attracting attention for applications in integrated photonics and quantum information processing. Historically, this has been achieved with magneto-optical crystals requiring an external magnetic bias, which are incompatible with semiconductor chip integration. Here, we investigate an approach to inducing nonreciprocity using intrinsic Kerr nonlinearities in a system which otherwise is reciprocal. We consider two systems, which could be resonators or qubits, coupled to a waveguide. We use a semiclassical approach and temporal coupled-mode theory, and include dissipative coupling between the waveguide and resonators, along with the input-output relations. We consider a large number of cases in which nonreciprocity can arise. For the case when the linear system does not exhibit nonreciprocal behavior, we show how significant nonreciprocal behavior can result from Kerr nonlinearities. We find that the bistability enables sharp, directional-dependent transitions between stable transmission states, thus achieving large nonreciprocity. Additionally, we bring out nonreciprocity in the excitation of each resonator, which can be monitored independently. Nonlinearity-induced nonreciprocity would significantly affect quantum fluctuations when our system is treated quantum mechanically. We will present some examples of experimentally realizable systems.