Non-Markovian Effects in a Simple Photonic Band Gap Cavity

Abstract

We propose a simple model for a cavity in a 1D photonic band gap material. It is shown that the exact dynamics contains three real functions of time, implicitly defined through an integrodifferential equation, all of them experimentally accessible. Several initial conditions are analyzed: (generalized) coherent states at finite temperature and Schr�dinger cat states at zero temperature. We use the simplest energy momentum relation which allows for a band gap and show that the perturbative solution of the integrodifferential equation presents non‐Markovian features.