QED OF RESONATORS IN QUANTUM OPTICS

The main features of quantum electrodynamics (QED) of a light matter system embedded in a dielectric with space-dependent refractive index are developed, and the QED formalism is applied to the description of the quantum-optical action of a resonator-like cavity with in/output coupling and filled with an active medium. In the case of a proper resonator with sufficiently large Q-value the rigorous QED approach naturally leads to the quantum-noise formalisms widely used in a quantum-optical resonator theory. In coarse-graining approximation intracavity-multi-mode photon creation and destruction operators can be introduced, which fulfil quantum Langevin equations with light-matter coupling. Both the time-dependent commutation relations needed to practically handle the Langevin equations and the input-output relations needed to relate the radiation field outside the cavity to the internal field can be established from QED-first principles.