Emission spectra of atoms with non-Markovian interaction: Fluorescence in a photonic crystal

TL;DR

This paper derives a formula for the emission spectra of atoms in non-Markovian environments, specifically analyzing fluorescence in photonic crystals with spectral gaps, highlighting how emission is affected by environment and detector placement.

Contribution

It introduces a new formula for calculating non-Markovian emission spectra based on two-time correlations and environmental functions, applicable to complex quantum systems.

Findings

Emission occurs as evanescent waves in photonic crystals with spectral gaps.

Detection efficiency decreases with increasing distance from the atom.

The formula can be applied to various quantum open systems in linear regimes.

Abstract

We present a formula to evaluate the spontaneous emission spectra of an atom in contact with a radiation field with non-Markovian effects. This formula is written in terms of a two-time correlation of system observables and the environmental correlation function, and depends on the distance between the emitting atom and the detector. As an example, we use it to analyze the fluorescence spectra of a two level atom placed as an impurity in a photonic crystal. The radiation field within those materials has a gap or discontinuity where electromagnetic modes cannot propagate in the stationary limit. In that situation, the atomic emission occurs in the form of evanescent waves which are detected with less efficiency the farther we place the detector. The methodology presented in this paper may be useful to study the non-Markovian dynamics of any quantum open system in linear interaction with a harmonic oscillator reservoir and within the weak coupling approximation.