Bifurcation in cavity quantum electrodynamics and its applications [electronic resource]
Keywords: Applied Physics.

Cavity quantum electrodynamics (cQED) has received much attention as an ideal platform for theoretical modeling and proof-of-concept experiments on ultra-low energy all-optical information processing. Cavities provide an effective means of reducing the energy scale of nonlinear-optical effects down to the level of ten or fewer energy quanta, deep into the quantum-mechanical regime. On the other hand, bifurcation theory, which analyzes changes in the number and properties of equilibrium states upon some system parameter crossing a critical value, has been used in practice not only to ensure safe operation in a stable parameter range but also to realize robust devices with signal processing functionalities. In this dissertation I present theoretical results and numerical simulations that demonstrate how these two theories can combine to help not only interpret nonlinear dynamics from the perspective of the first-principle physics, but also suggest designs of useful devices for optical signal processing networks. Under appropriate conditions the collective interaction of two-level atoms with a cavity field can give rise to interesting dynamical behaviors such as bistability and self-oscillation. Both of these phenomena can provide a physical basis for designing useful devices with signal processing functionalities. After introducing the necessary theoretical background I first discuss the cQED analog of absorptive bistability. I explain how transitions between the two metastable states---the quantum counterparts of the absorptive bistable states---can result from spontaneous emission and based on the understanding of this switching mechanism how we can implement an optical flip-flop using the Purcell effect. This is followed by the discussion of how the interaction between a two-level atom and a quantized cavity field in the semi-classical limit can give rise to self-oscillation in the cavity field intensity and how we can make use of the system's sensitivity to this instability for small-signal amplification. In addition to the potential applications, the present study of bifurcation-like phenomena in the context of cavity quantum electrodynamics is also motivated by the theoretical interest in investigating quantum-classical correspondence. The equations in the semi-classical limit have been found to be surprisingly accurate in predicting bifurcation-like phenomena for the full quantum model even in the strong coupling regime in which the semi-classical approximation necessarily breaks down. Therefore bifurcation has become a new subject for studying the correspondence. Nonetheless traits of quantum mechanical nature are omnipresent in these bifurcation-like phenomena such as the automatic switching in the quantum analog of classical absorptive bistability, which can be considered as the quantum-classical discrepancy in the context of absorptive bistability. In this dissertation I present the quantum-classical discrepancy in the context of Hopf bifurcation, which is demonstrated by the breakdown of the pre-Hopf small-signal amplification scheme. Moreover, previous study on the quantum-classical correspondence manifested in the prediction of bifurcation-like phenomena has focused on the single-atom cavity quantum electrodynamics. In the last part of this dissertation I extend the study to multi-atom cases, asking questions such as: would there be any new bifurcation-like phenomenon in a multi-atom cavity quantum electrodynamic system; if yes could it lead to new device application; in addition how would it depend on the number of atoms. This latter question in fact suggests a new perspective towards studying the quantum-classical transition.