Many-body cavity QED: The Dicke model, phase transitions, and engineering of multipartite entangled atomic states

Abstract

The interaction of matter with an electromagnetic field is an old problem. We performed theoretical modelling for experiments simulating a fundamental model of this interaction: the Dicke model. We then made use of this model, and the methods used to simulate it, to propose the production of a variety of entangled many-body states of an atomic ensemble.Our research focussed on engineering interactions between a gas of cold atoms and light, in particular laser fields and modes of an optical cavity. These interactions are engineered via cavity-assisted Raman transitions: two-photon transitions where one photon is provided by a laser field and the other is associated to a mode of an optical cavity. Two types of interactions were considered: between the cavity mode and the gas, and within the gas via the cavity mode. Results of our research included contributions to the experiments of our collaborators, who mapped out phase boundaries of the Dicke model, giving a fundamental insight into how atoms interact with a field. Using these methods in the context of a generalised Dicke model with an added non-linear coupling, we discovered the presence of strong entanglement for atoms in steady state and proposed how to access such entanglement. A key concept of the thesis is the introduction of spinor atoms - i.e. atoms with integer spin - to many-body cavity QED. We showed that the Dicke model, and more simply a Tavis-Cummings model, acting on a particular state of spin-1 atoms produces highly entangled states heralded by measurement of the cavity output. In the context of interactions within the gas, we proposed the emulation and extension of physics currently accessible only to spinor Bose-Einstein condensates. We then proposed the use of those engineered interactions to emulate a particular experiment performed in spinor Bose-Einstein condensates, creating a novel type of squeezing and entanglement in a spinor gas. Our research has not only helped explain how light and matter interact and given specific methods to produce interesting many-body states using those interactions, but it also implies a rich field of novel results for spinor atoms in many-body cavity QED systems.