The time scale of the cooling process can be optimized by suitably tailoring the pump field amplitude and frequency or using controlled nonlinear feedback of the transmitted cavity field to the pump. The key properties of the cooling mechanism are discussed using a linearized model, which is then compared with N-particle dynamical simulations of the full equations. For spherical mirrors with a finite Gaussian aperture we find a discrete complete set of normalizeable 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.
Numerical simulations support our theory.
We discuss some experimental approaches. According to statistical physics, a set of probabilistically behaving individual systems can exhibit critical behaviour when connected. In this paper we show that transition phenomena exist also in networks which behave probabilistically not because of finite temperature but due to their quantum nature. We give physical meaning to the transitions found. In the case of active components, such as amplifiers, the transition point coincides with the fundamental cloning limit given by quantum mechanics.