We develop a quantum description for the dynamics of a single atom inside an unstable optical resonator. For spherical mirrors with a finite Gaussian aperture we find a discrete complete set of normalizable eigenmodes, their biorthogonal adjoint modes, eigenfrequencies, decay rates, and overlap integrals. With these modes we formulate a quantum description for the coupled dynamics of the field and a single atom inside the resonator. We find a strongly geometry and position dependent nonexponential decay probability. Under certain special conditions one gets a modified single-mode description incorporating the Petermann excess noise factor K even on a single-atom level.
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Lamprecht et al. (1999) studied this question.