Cavity quantum electrodynamics with semiconductor quantum dots: Role of phonon-assisted cavity feeding

For a semiconductor quantum dot strongly coupled to a microcavity, we theoretically investigate phonon-assisted transitions from the exciton to a cavity photon, where the energy mismatch is compensated by phonon emission or absorption. By means of a Schrieffer-Wolff transformation we derive an effective Hamiltonian, which describes the combined effect of exciton-cavity and exciton-phonon couplings, and compute the scattering rates within a Fermi-golden-rule approach. The results of this approach are compared with those of a recently reported description scheme based on the independent boson model [U. Hohenester et al., Phys. Rev. B 80, 201311 (R) (2009)] and a numerical density-matrix approach. All description schemes are shown to give very similar results. This demonstrates that phonon-assisted cavity feeding can be described in terms of a simple scattering process and does not require a non-Markovian treatment as suggested elsewhere. We present results for the spontaneous emission lifetime of a quantum dot initially populated with a single exciton or biexciton and for the spectral properties of an optically driven dot-cavity system operating in the strong-coupling regime. Our results demonstrate that phonon-assisted feeding plays a dominant role for strongly coupled dot-cavity systems when the detuning is of the order of a few millielectron volts.