Derivation of a Hamiltonian for photon decay in a cavity
S. M. Dutra, Gerard Nienhuis · Journal of Optics B Quantum and Semiclassical Optics · 2000
We present a rigorous first principles derivation of the heuristic approach behind most of cavity QED: the quantization of the field in a high-Q cavity as if the mirrors were perfect with losses modelled by a coupling with the outside. We derive the Hamiltonian describing this coupling, thereby allowing us to avoid the coarse-graining approximation implicit in the usual Langevin or master equation treatments of cavity damping. We obtain an explicit expression for the coupling constant that describes the non-Markovian nature of the reservoir in the regime beyond the validity of the coarse-graining approximation.