  A quantum dot strongly coupled to a single high finesse optical microcavity
mode constitutes a new fundamental system for quantum optics. Here, the effect
of exciton-phonon interactions on reversible quantum-dot cavity coupling is
analysed without making Born-Markov approximation. The analysis is based on
techniques that have been used to study the ``spin boson'' Hamiltonian.
Observability of vacuum-Rabi splitting depends on the strength and the
frequency dependence of the spectral density function characterizing the
interactions with phonons, both of which can be influenced by phonon
confinement.
