Non-Markovian dynamics of a microcavity coupled to a waveguide in photonic crystals

In this paper, the non-Markovian dynamics of a microcavity coupled to a waveguide in photonic crystals is studied based on a semi-finite tight binding model. Using the exact master equation, we solve analytically and numerically the general and exact solution of the non-Markovain dynamics for the cavity coupled to the waveguide in different coupling regime. A critical transition is revealed when the coupling increases between the cavity and the waveguide. In particular, the cavity field becomes dissipationless when the coupling strength goes beyond a critical value, as a manifestation of strong non-Markovian memory effect. The result also indicates that the cavity can maintain in a coherent state with arbitrary small number of photons when it strongly couples to the waveguide at very low temperature. These properties can be measured experimentally through the photon current flowing over the waveguide in photonic crystals.