Quantum dot cavity-QED in the presence of strong electron-phonon interactions

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 analyzed without making a Born-Markov approximation. The analysis is based on a polaron operator technique that has been used to study the ``spin-boson'' Hamiltonian. For bulk acoustic phonons and for a large class of confined phonon models, we find that vacuum-Rabi splitting persists even in the presence of a large Stokes shift and at an appreciable temperature, but its magnitude is exponentially suppressed by the electron-phonon coupling strength.