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

Quantum dots in semiconductor photonic reservoirs are important systems for studying and exploiting quantum optics on a chip, and it is essential to understand fundamental concepts such as spontaneous emission. According to Fermi's golden rule, the spontaneous emission rate of a quantum emitter weakly coupled to a structured photonic reservoir is proportional to the local density of photon states (LDOS) at the emitter's position and frequency. Coupling to lattice vibrations or phonons, however, significantly modifies the emission properties of a quantum dot (QD) compared to an isolated emitter (e.g., an atom). In the regime of phonon-dressed reservoir coupling, we demonstrate why and how the broadband frequency dependence of the LDOS determines the spontaneous emission rate of a QD, manifesting in a dramatic breakdown of Fermi's golden rule. We analyze this problem using a polaron transformed master equation and consider specific examples of a semiconductor microcavity and a coupled-cavity waveguide. For a leaky single cavity resonance, we generalize Purcell's formula to include the effects of electron - phonon coupling, and for a waveguide, we show a suppression and a 200-fold enhancement of the photon emission rate. These results have important consequences for modeling and understanding emerging QD experiments in a wide range of photonic reservoir systems. (C) 2015 Optical Society of America