  We employ detuning-dependent decay-rate measurements of a quantum dot in a
photonic-crystal cavity to study the influence of phonon dephasing in a
solid-state quantum-electrodynamics experiment. The experimental data agree
with a microscopic non-Markovian model accounting for dephasing from
longitudinal acoustic phonons, and identifies the reason for the hitherto
unexplained difference between non-resonant cavity feeding in different
nanocavities. From the comparison between experiment and theory we extract the
effective phonon density of states experienced by the quantum dot. This
quantity determines all phonon dephasing properties of the system and is found
to be described well by a theory of bulk phonons.
