Wave Interferences and Nonlinearities in Atomic Physics and Quantum Optics

波的相干性影响了广泛的物理现象，从海浪的传播或光通过星际云的传输，到纳米电路中单个电子的运动或光子通过光纤和其他波导的传输。它们产生丰富多样的干涉现象，例如增强的后向散射、弱和安德森局域化或高阶相干效应，例如量子噪声、粒子的聚束和反聚束。这些影响是很好理解的非相互作用领域，然而，治疗波在非线性介质中的干扰或在相互作用的存在是一项艰巨的任务。本研究的主要目标是开发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与无序或复杂环境中的相互作用电子类似，这是凝聚态物理学中的一个深入研究的问题。据预测，在研究中开发的方法将找到广泛的应用，并引发新的理论研究对非线性在广泛的一类复杂的量子系统，在凝聚态，分子和统计物理，以及在数学的动力系统，混沌理论和流体动力学，并构成了一个垫脚石，为发展新的理论方法，在广泛的一类非线性复杂的量子系统。该研究还具有帮助构建更强大的微激光器的潜力，这些微激光器具有增强的设计和性能，可应用于生物科学，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.