Population Monitoring and the Quantum Input-Output Formalism

The quantum Input-Output formalism of Gardiner and Collett is used to derive the rate equation describing the photoelectron counting statistics of an electromagnetic field output from a high-Q optical cavity. The evolution of the cavity field is assumed to be governed by an arbitrary Hamiltonian for a single mode of the field. The resulting equation is shown to conform with one previously derived on intuitive grounds, using purely population statistical arguments. As an explicit example, the solution for a freely-evolving cavity field is computed.