# Control of spontaneous emission of a single quantum emitter through a time-modulated photonic-band-gap environment

## TL;DR

This paper explores how a time-modulated photonic environment can control and modify the spontaneous emission spectrum and rate of a quantum emitter, revealing new spectral features and environmental insights.

## Contribution

It introduces a model of a dynamical photonic crystal environment and demonstrates how temporal modulation enables control over emission properties and spectral features.

## Key findings

- Appearance of two lateral peaks in emission spectrum due to modulation
- Asymmetry in side peak heights reveals environment's density of states
- Dynamical environments offer enhanced control over emission characteristics

## Abstract

We consider the spontaneous emission of a two-level quantum emitter, such as an atom or a quantum dot, in a modulated time-dependent environment with a photonic band gap. An example of such an environment is a dynamical photonic crystal or any other environment with a bandgap whose properties are modulated in time, in the effective mass approximation. After introducing our model of dynamical photonic crystal, we show that it allows new possibilities to control and tailor the physical features of the emitted radiation, specifically its frequency spectrum. In the weak coupling limit and in an adiabatic case, we obtain the emitted spectrum and we show the appearance of two lateral peaks due to the presence of the modulated environment, separated from the central peak by the modulation frequency. We show that the two side peaks are not symmetric in height, and that their height ratio can be exploited to investigate the density of states of the environment. Our results show that a dynamical environment can give further possibilities to modify the spontaneous emission features, such as its spectrum and emission rate, with respect to a static one. Observability of the phenomena we obtain is discussed, as well as relevance for tailoring and engineering radiative processes.