  We investigate the effect of electron-phonon interactions on the coherence
properties of single photons emitted from a semiconductor cavity QED system,
i.e. a quantum dot embedded in an optical cavity. The degree of
indistinguishability, governing the quantum mechanical interference between two
single photons, is calculated as a function of important parameters describing
the cavity QED system and the phonon reservoir, e.g. cavity quality factor,
light-matter coupling strength, temperature and phonon lifetime. We show that
non-Markovian effects play an important role in determining the coherence
properties for typical parameter values and establish the conditions under
which a Markovian approximation may be applied. The calculations are performed
using a recently developed second order perturbation theory, the limits of
validity of which are established by comparing to an exact diagonalization
approach. We find that for large cavity decay rates the perturbation theory may
break down.
