Semiclassical-quantum correspondence and the onset of chaos

This dissertation explores the connection between two models for a two-level atom interacting with a single mode electromagnetic field. The first is a semiclassical model in which the field is treated classically and the atom is treated quantum mechanically, while the second is a full quantum model in which both the atom and the field are treated quantum mechanically (sometimes known in quantum optics and other fields as the spin-boson model). A unique pair of states, which remain factorizable for long times and are termed quasiclassical states, are derived from the semiclassical model. The quasiclassical states are found to match the evolution of the quantum model well for fields with the average photon number sufficiently large. These quasiclassical states are also derived from the eigenvalues and eigenvectors of the full quantum mechanical model alone.; The semiclassical system has been shown to exhibit chaos. We identify the causes of the transition to chaotic behavior in the semiclassical system in the vicinity of the quasiclassical orbits and examine the quantum system for signatures of that transition. Several authors have claimed to have found such signatures, but by using the quasiclassical states we show these supposed signatures are not unambiguously related to the appearance of chaos in the semiclassical model. The quasiclassical states also establish a basis for comparing results for calculations which use the rotating-wave ayproximation (RWA) with results from those which do not.; Finally, we extend the work by considering the effects of up to three atoms interacting with the quantum field. The result is that the system behaves more classically than for a single atom and some possible signatures of chaos are identified but cannot be established unequivocally.