Nonlinear dynamics of partially-coherent waves: experimental and theoretical studies in statistical light

自然界中的大多数波只是部分相干的，波动（热的、量子的或其他的）赋予它们的动力学统计特征。特别是在非线性情况下，由于有限关联的存在，输运变得复杂。波动产生扰动，可以产生或抑制不稳定性。在前一种情况下，噪声提供了一个自由能量和对称性破坏源，而在后一种情况下，统计去相可以抑制非线性模式耦合和能量转移。本工作的目的是利用统计光的非线性传播，从实验和理论上研究这些效应。出发点是观察到，完全凝聚的多体系统通常可以用一个单一的宏观波函数来描述，完全类似于激光的相干光场。在部分凝聚系统中，有限温度效应产生统计行为，这在非相干光的传播中具有对应关系。本研究利用了这些关系，用全新的场理论方法解释了非线性光束传播的许多方面。其结果是为各种不同的光学现象提供了一个统一的框架，从而导致了一系列新的实验方向。然而，这些新的观点甚至比新的解释更能说明一些从未在任何领域进行过的相关研究。研究这种行为对于理解统计动力学和非线性模态耦合是至关重要的，这既是基础科学的基础，也是具有重要技术意义的。光学成像的力量推动了这项工作的智力价值，因为与其他领域相关（但通常隐藏在）的复杂波动动力学可以直接可视化。实际上，光学系统有很大的潜力作为模拟复杂凝聚态行为的光学模拟器（类似于光信号处理用于高度并行计算）。从教学的角度来看，光的熟悉性和成像的便捷性使光学系统具有巨大的教学优势。实际上，这种通过光子学方法的物理可以通过相对简单的实验来证明，而这些系统中的波动动力学可以像场理论中的任何主题一样复杂。因此，强烈的教育成分是这项工作的主题，教学项目与研究计划紧密结合。这项工作的结果将直接纳入研究人员的课程中，既可以激发本科课程的活力，也可以说明领域理论研究生课程的基本原理。人们希望，这里提出的模型系统和研究计划将为普林斯顿大学内外一个更大的基于光学的科学项目提供支持。本项目由数学与物理科学理事会物理部光学物理项目和材料研究部凝聚态物理项目联合支持。

Most waves in nature are only partially coherent, with fluctuations (thermal, quantum, or other) imparting a statistical character to their dynamics. Particularly in the nonlinear case, transport is complicated by the presence of finite correlations. Fluctuations seed perturbations and can either generate or suppress instability. In the former case, noise provides a free-energy and symmetry-breaking source, while in the latter case statistical de-phasing can inhibit nonlinear mode coupling and energy transfer. The purpose of this work is to study these effects, both experimentally and theoretically, using the nonlinear propagation of statistical light.The starting point is the observation that fully-condensed, many-body systems can often be described by a single, macroscopic wavefunction, in complete analogy with the coherent light field from a laser. In partially-condensed systems, finite-temperature effects give rise to statistical behavior, which has correspondences in the propagation of incoherent light. This research takes advantage of these relations, interpreting many aspects of nonlinear beam propagation in fundamentally new, field-theoretic ways. The result is a unifying framework for a variety of disparate optical phenomena, leading to a series of new experimental directions. Even more than novel interpretations, though, the new perspectives suggest several types of correlation studies that have never been performed for any field. Studying such behavior is crucial to the understanding of statistical dynamics and nonlinear mode coupling, which is both fundamental to basic science and of great technological importance.The power of optical imaging drives the intellectual merit of this work, as complicated wave dynamics relevant to (but often hidden in) other fields can be directly visualized. Indeed, there is much potential in the ability of optical systems to serve as optical simulators for modeling complex condensed-matter behavior (similar to the use of optical signal processing for highly parallel computing). From a teaching perspective, the familiarity of light and the ease of imaging give optical systems an enormous pedagogical advantage. Practically, this physics through photonics approach can be demonstrated through experiments that are relatively simple to perform, while the wave dynamics in these systems can be as complex as any topic in field theory. A strong educational component is therefore a main theme of this work, with instructional projects coherently integrated with the research plan. Results from the work will be incorporated directly into the investigators courses, both to invigorate undergraduate classes and to illustrate basic principles in field-theoretic graduate courses. It is hoped that the model systems and research plans proposed here will feed into a larger optics-based science program, both within and beyond Princeton University.This project is jointly supported by the Optical Physics program in the Physics Division and the Condensed Matter Physics program in the Division of Materials Research of the Mathematical and Physical Sciences Directorate.