Spontaneous emission from a quantum dot in a structured photonic reservoir: phonon-mediated breakdown of Fermi's golden rule

TL;DR

This paper investigates how electron-phonon interactions in structured photonic environments cause deviations from Fermi's golden rule in quantum dot spontaneous emission, revealing complex phonon effects on emission rates.

Contribution

It introduces a polaron transformed master equation to analyze phonon effects on quantum dot emission in photonic structures, extending Purcell's formula and demonstrating significant emission rate modifications.

Findings

Phonons cause non-trivial modifications to emission rates when photon and phonon bath relaxation times are comparable.

The local photon density of states critically influences emission, leading to Fermi's golden rule breakdown.

Emission can be suppressed or enhanced up to 200-fold depending on the photonic environment.

Abstract

We describe how a structured photonic medium controls the spontaneous emission rate from an excited quantum dot in the presence of electron-phonon coupling. We analyze this problem using a polaron transformed master equation and we consider specific examples of a photonic crystal cavity and a coupled cavity waveguide. We find that when the relaxation times of the photon and phonon baths are comparable, phonons influence spontaneous emission in a non-trivial way. We demonstrate why and how the broadband frequency dependence of the local photon density of states determines the photon emission rate, manifesting in a complete breakdown of Fermi's golden rule. For a single cavity resonance, we generalize Purcell's formula to include the effects of electron-phonon coupling. For a waveguide, we show a suppression and a 200-fold enhancement of the photon emission rate.