  We investigate the influence of the electron-phonon interaction on the decay
dynamics of a quantum dot coupled to an optical microcavity. We show that the
electron-phonon interaction has important consequences on the dynamics,
especially when the quantum dot and cavity are tuned out of resonance, in which
case the phonons may add or remove energy leading to an effective non-resonant
coupling between quantum dot and cavity. The system is investigated using two
different theoretical approaches: (i) a second-order expansion in the bare
phonon coupling constant, and (ii) an expansion in a polaron-photon coupling
constant, arising from the polaron transformation which allows an accurate
description at high temperatures. In the low temperature regime we find
excellent agreement between the two approaches. An extensive study of the
quantum dot decay dynamics is performed, where important parameter dependencies
are covered. We find that in general the electron-phonon interaction gives rise
to a greatly increased bandwidth of the coupling between quantum dot and
cavity. At low temperature an asymmetry in the quantum dot decay rate is
observed, leading to a faster decay when the quantum dot has a larger energy
than to the cavity. We explain this as due to the absence of phonon absorption
processes. Furthermore, we derive approximate analytical expressions for the
quantum dot decay rate, applicable when the cavity can be adiabatically
eliminated. The expressions lead to a clear interpretation of the physics and
emphasizes the important role played by the effective phonon density,
describing the availability of phonons for scattering, in quantum dot decay
dynamics. Based on the analytical expressions we present the parameter regimes
where phonon effects are expected to be important. Also, we include all
technical developments in appendices.
