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Cavity quantum electrodynamics with semiconductor quantum dots: The 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 coupling, 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. 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.