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

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