Magnetic fields and chaos in coupled atom-cavity systems

© 2016 Dr. Andrew Lewis Copplestone HaywardThis thesis explores the manifestation of many-body quantum physics in coupled atom- cavity systems, through the lens of the Jaynes-Cummings-Hubbard model. This model captures the behaviour of a strongly interacting photon system, with the entailing complex many-body quantum states. In particular, this work explores two distinct, but related, topics in many-body quantum mechanics. The first part of the work is concerned with a number of phenomena arising from the introduction of (synthetic) magnetic fields to the Jaynes-Cummings-Hubbard model. In this context, the Mott-superfluid phase transition is suppressed by strong magnetic fields, and vortices are observed in the superfluids regime. Also studied is the regime of high synthetic magnetic field to particle density, where the fractional quantum Hall effect manifests. Laughlin-like states are indicated by a number of metrics. Pfaffian like states are also show to exist when a three-body interaction is induced by the inclusion of a three level atom in the photonic cavities. In the latter part of the thesis, the relationship between classical and quantum chaos is explored through the introduction of a periodically perturbing force to a pair of coupled cavities. Demonstrated in this system are such chaotic behaviours such as localization, partially chaotic phase space, dynamic localization and dynamic tunneling