Physics and Applications of Cooperative Effects in Nonlinear and Quantum Optics

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A dense collection of atoms can display collective phenomena which are fundamentally different from those in dilute samples. An example is super-radiance, where an ensemble of atoms collectively interacts with a specific light field. While recognized long ago, this topic has gained importance over the last few years. Many areas of fundamental research, such as quantum information science, and of applications, such as the construction of accurate atomic clocks, now utilize collective properties of dense ensembles. Density effects can be detrimental. Increasing the interaction strength between atoms can destroy the coherent response of the atoms to external stimuli, which is necessary for quantum computers or precise clocks. The goal of this project is to (i) find and understand density-dependent collective effects and their consequences, (ii) to investigate methods to either mitigate or isolate the effects in a way to improve experimental control of the ensembles, and (iii) to research the various ways in which such effects can enable new technologies. Basic questions will be studied regarding collective effects in cooperative media, such as: Do super-radiant effects depend on density or optical depth? What exactly is the role of the exchange interaction? What makes driven cooperative systems special? Is super-radiance fully described by pairwise correlations, and for which systems are other approximations needed? In order to achieve these goals, new analytical and numerical methods will be developed. In addition, the particular effects that will be investigated in this project include induced and spontaneous collective line shifts, spin and light field "squeezing" and entanglement. In addition, statistics and nonlinearities of the dynamic Casimir effect will be compared to the collective effects of super-radiant systems. Most of these projects will include collaboration with experimental efforts.