Theory of phonon-modified spontaneous emission and photoluminescence intensity from quantum dots coupled to structured photonic reservoirs

Abstract

We present a general theory for calculating the spontaneous emission (SE) rate and the photoluminescence intensity of a quantum dot (QD) exciton coupled to an arbitrary structured photonic reservoir and a bath of acoustic phonons. We describe a polaron master equation (ME) approach which includes phonon interaction nonperturbatively and assume a weak coupling with the photon reservoir which is valid in the Purcell coupling regime. As examples of structured photonic reservoirs, we choose the cases of a Lorentzian cavity and a slow-light coupled-cavity waveguide. In analogy with a simple atom, the SE rate of a QD is expected to be proportional to the local density of photon states (LDOS) of the structured reservoir at the resonant frequency of a QD exciton. However, using a polaron ME theory, we show how the phonon-dressed SE rate of a QD is determined by a broad bandwidth of the photonic LDOS, in violation of the well known Fermi’s golden rule. This broadband frequency dependence results in rich spontaneous emission enhancement and suppression, manifesting in significant changes in the Purcell factor and photoluminescence intensity as a function of frequency.