Quantum theory of light emission from quantum dots coupled to structured photonic reservoirs and acoustic phonons

摘要

Electron-phonon coupling in semiconductor quantum dots plays a significantrole in determining the optical properties of excited excitons, especially thespectral nature of emitted photons. This paper presents a comprehensive theoryand analysis of emission spectra from artificial atoms or quantum dots coupledto structured photon reservoirs and acoustic phonons, when excited withincoherent pump fields. As specific examples of structured reservoirs, we chosea Lorentzian cavity and a coupled cavity waveguide, which are of currentexperimental interest. For the case of optical cavities, we directly compareand contrast the spectra from three distinct theoretical approaches to treatelectron-phonon coupling, including a Markovian polaron master equation, anon-Markovian phonon correlation expansion technique and a semiclassical linearsusceptibility approach, and we point out the limitations of these models. Forthe cavity-QED polaron master equation, we give closed form analyticalsolutions to the phonon-assisted scattering rates in the weak excitationapproximation, fully accounting for temperature, cavity-exciton detuning andcavity dot coupling. We show explicitly why the semiclassical linearsusceptibility approach fails to correctly account for phonon-mediated cavityfeeding. For weakly coupled cavities, we calculate the optical spectra using amore general reservoir approach and explain its differences from the aboveapproaches in the low Q limit of a Lorentzian cavity. We subsequently use thisgeneral reservoir to calculate the emission spectra from quantum dots coupledto slow-light photonic crystal waveguides, which demonstrate a number ofstriking photon-phonon coupling effects. Our quantum theory can be applied to awide range of photonic structures including photonic molecules andcoupled-cavity waveguide systems.