Cavity quantum electrodynamics (cQED) has enjoyed 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 variation of system parameters, 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. This theoretical study aims at demonstrating how the marriage of these two theories can help not only to interpret nonlinear dynamics from the perspective of the first-principle physics, but also to 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. In this study we elucidated 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 suggested how we can make use of the system's sensitivity to this instability for small-signal amplification. For the cQED analog of absorptive bistability we explained how transitions between the two metastable states---the quantum counterparts of the absorptive bistable states---can result from spontaneous emission, and suggested how based on the understanding of this switching mechanism we can implement an optical flip-flop using the Purcell effect. 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. The investigation is extended to multi-atom cases in the current study, 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.
Jie Wu, Michael A. Armen, and Hideo Mabuchi, The Mechanism of Automatic Switching in the Quantum Analog of Absorptive Bistability, To Be Submitted
Jie Wu, Hideo Mabuchi, Self-Oscillation in the Maxwell-Bloch Equations, To Be Submitted
PhD Oral Defense Presentation Slides: JieWuOralDefenseSlidesFinal.pdf
PhD Disssertation: JieWuThesis.pdf