Input-output relations in resonators are studied on the basis of a recently developed field-theoretical approach to the action of passive systems in quantum optics [Knöll, Vogel, and Welsch, Phys. Rev. A 36, 3803 (1987)]. This method allows the rigorous proof of recently adopted quantum stochastic approaches, including the presence of sources that form the active medium in the cavity. Quantum Langevin equations are obtained in a coarse-graining approximation. Moreover, we derive all required commutation relations that have been postulated so far. Correlation functions of the field quantities measured outside the cavity are related to correlation functions of field operators of the intracavity field and the incoming field.

• Received 9 March 1990

DOI:https://doi.org/10.1103/PhysRevA.43.543