Influence of electron-acoustic phonon scattering on intensity power broadening in a coherently driven quantum-dot cavity system

We present a quantum optics formalism to study intensity power broadening of a semiconductor quantum dot interacting with an acoustic phonon bath and a high $Q$ microcavity. Power broadening is investigated using a time-convolutionless master equation in the polaron frame which allows for a nonperturbative treatment of the interaction of the quantum dot with the phonon reservoir. We calculate the full non-Lorentzian photoluminescence (PL) lineshapes and numerically extract the intensity linewidths of the quantum dot exciton and the cavity mode as a function of pump rate and temperature. For increasing field strengths, multiphonon and multiphoton effects are found to be important, even for phonon bath temperatures as low as 4 K. We show that the interaction of the quantum dot with the phonon reservoir introduces pronounced features in the power broadened PL lineshape, enabling one to observe clear signatures of electron-phonon scattering. The PL lineshapes from cavity pumping and exciton pumping are found to be distinctly different, primarily since the latter is excited through the exciton-phonon reservoir. To help explain the underlying physics of phonon scattering on the power broadened lineshape, an effective phonon Lindblad master equation derived from the full time-convolutionless master equation is introduced; we identify and calculate distinct Lindblad scattering contributions from electron-phonon interactions, including effects such as excitation-induced dephasing, incoherent exciton excitation and exciton-cavity feeding. Our effective phonon master equation is shown to reproduce the full intensity PL and the phonon-coupling effects very well, suggesting that its general Lindblad form may find widespread use in semiconductor cavity-QED.