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

TL;DR

This study investigates the non-Markovian dynamics of a microcavity coupled to a waveguide in photonic crystals, revealing a critical coupling strength where the cavity becomes dissipationless and maintains coherence.

Contribution

The paper provides an analytical and numerical analysis of the non-Markovian behavior in microcavity-waveguide systems, highlighting a critical transition and coherence preservation at strong coupling.

Findings

Cavity becomes dissipationless beyond a critical coupling strength.

Strong coupling allows the cavity to maintain coherence with few photons.

Physical observables can be measured via photon current in experiments.

Abstract

In this paper, the non-Markovian dynamics of a microcavity coupled to a waveguide in photonic crystals is studied based on Fano-type tight binding model. Using the exact master equation, we solve analytically and numerically the temporal evolution of the cavity coherent state and the associated physical observables. A critical transition is revealed when the coupling increase 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.