Lattice mapping for many-body open quantum systems and its application to atoms in photonic crystals

Abstract

We present a derivation that maps the original problem of a many-body open quantum system (OQS) coupled to a harmonic oscillator reservoir into that of a many-body OQS coupled to a lattice of harmonic oscillators. The present method is particularly suitable to analyze the dynamics of atoms arranged in a periodic structure and coupled with the electromagnetic field within a photonic crystal. It allows to solve the dynamics of a many-body OQS with methods alternative to the commonly used master, stochastic Schr\"odinger, and Heisenberg equations, and thus to reach regimes well beyond the weak coupling and Born-Markov approximations.