Wave Interferences and Nonlinearities in Atomic Physics and Quantum Optics

波的相干性影响广泛的物理现象，从海浪的传播或光在星际云中的传输，到单个电子在纳米级电路中的运动或通过光纤和其他波导的光子传输。它们产生了各种各样的干涉现象，如增强的后向散射、弱的Anderson局域化或高阶相干的效应，如量子噪声、粒子的聚束和反聚束。对于非相互作用场，这些效应是很好理解的，然而，处理非线性介质中或存在相互作用时的波干扰是一项艰巨的任务。这项研究的主要目标是发展分析和计算工具来研究非线性量子和波相干系统的动力学。非线性以及局域化和波干扰的概念类似于无序或复杂环境中的电子相互作用，这是凝聚态物理中一个被广泛研究的问题。据预测，这一方法将在一大类复杂量子系统、凝聚态物理、分子和统计物理以及动力系统数学、混沌理论和流体力学中得到广泛的应用和引发新的理论研究，并为在一大类非线性复杂量子系统中发展新的理论方法奠定基础。此外，这项研究还有可能帮助建造更强大的微型激光器，改进设计和性能，应用于生物科学、通信或信息技术。该项目将具有强大的教育成分，本科生和研究生将接触到前沿科学研究。

Wave coherence influences a broad range of physical phenomena, ranging from the propagation of ocean waves or the transmission of light through interstellar clouds, down to the motion of individual electrons in nanoscale electrical circuits or the transmission of photons through optical fibers and other waveguides. They generate a rich variety of interference phenomena, such as enhanced backscattering, weak and Anderson localization or effects of higher-order coherence such as quantum noise, bunching and anti-bunching of particles. These effects are well understood for noninteracting fields, however treating wave interferences in nonlinear media or in presence of interactions is a formidable task. The main goal of this research is to develop analytical and computational tools to investigate the dynamics of nonlinear quantum and wave coherent systems. Nonlinearities as well as the notion of localization and wave interferences have analogies with interacting electrons in disordered or complex environments, an intensively investigated problem in condensed matter physics. It is forecast that the methodology developed in the research will find a broad range of applications and trigger novel theoretical investigations towards nonlinearities in a wide class of complex quantum systems, in condensed matter, molecular and statistical physics, as well as in the mathematics of dynamical systems, chaos theory and fluid dynamics, and constitute a stepping stone for the development of new theoretical approaches in a wide class of nonlinear complex quantum systems. The research furthermore has the potential to help construct more powerful microlasers with enhanced designs and performances, with applications in biosciences, communication or information technology.The project will have a strong educational component, where undergraduate and graduate students will be exposed to front edge scientific research.