Q.e.d. beyond rotating wave approximation

This thesis studies counter-rotating terms part of an Hamiltonian usually neglected in the so-called Rotating Wave Approximation. Generalising the usual description
of light-matter interactions and open quantum systems it is demonstrated that normally neglected counter-rotating terms have the potential to allocate energy among different system degrees of freedom. It is pointed out in examples that this aspect can affect the energy concentration in quantum systems.

Initially, a composite quantum system is considered, i.e. bipartite systems like atom-cavity systems and coupled optical resonators without decay. By resorting
to methods from quantum field theory it is shown that for such bosonic systems, the Rotating Wave Approximation cannot be applied far off resonance. In fact, the
counter-rotating terms are related to an entropy operator that is capable of generating an irreversible time evolution. The vacuum state of the system is shown to
evolve into a generalised coherent state exhibiting entanglement of the modes in which the counter-rotating terms are expressed.

Furthermore, it is demonstrated that a non-trivial behaviour of the photon emission rate of such composite quantum system can occur when the counter-rotating
terms are not dropped. In such a system, there is a coupling to infinitely many modes with most of them being far off resonance. An energy concentrating mechanism
is discussed which cannot be described by the Rotating Wave Approximation. Its result is the continuous leakage of photons from open quantum system, even in the absence of external driving.

Finally, a model is proposed to explain the origin of the sudden energy concentration in the intriguing phenomenon of sonoluminescence. The model is based on the quantum dynamics of trapped particles and assumes the presence of a weak but highly inhomogeneous electric field. It is shown that the counter-rotating terms can significantly contribute to the energy focussing mechanism in terms of quantum coherences.