Thermal dissipation effects of the entangled photon generated by four-wave mixing process in a nonlinear ring resonator

We firstly analyze the thermal dissipation effects of the entangled photons generated by a nonlinear optical ring resonator. To obtain the corresponding equation of motion of the entangled photons generated by a four-wave mixing process within the system, we propose the Markov approximation to repel the reservoir operators. The system master equation in the interaction picture for both degenerate and non-degenerate cases is analyzed and obtained. The established system can be used to characterize the optimum entangled photons in some cases where the thermal dissipation effects may be introduced noise into the system. In this work, the entangled photons can be generated into two forms, firstly, the two entangled photon states is generated, the other, the four entangled photon states can be easily obtained. Results obtained have shown that the optimum entangled photon in term of entangled photon visibility can be compensated (i.e. unchanged) under thermal dissipation effects.