It turns out to be advantageous to start with some entanglement rather than with a product state. Remarkably, we find that the optimal initial entanglement is independent of the Hamiltonian. 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.