OP: Collaborative Research: Non-Hamiltonian Wave Dynamics in Atomic & Optical Models

本项目主要研究波在非线性介质中传播时的能量增益和/或能量损耗的影响。最简单的波动表现出一种被称为等时的性质，这是伽利略最先观察到的：波的振荡频率与其幅度(或大小)无关。在其中观察到这一简单行为的波介质被称为“线性”。非线性介质也是已知的，其中波的频率随其幅度而变化。如果介质也是色散的(如棱镜)，那么不同频率的波将以不同的速度传播。非线性和色散的组合效应可能非常显著，就像形成孤子稳定的波型一样，这些波型在不改变形状的情况下通过介质传播。这项工作的一个中心焦点是探索在非线性介质中形成的孤子和其他相干结构，如涡旋，如何负责能量和信息的局域化和传输。如果波传播的介质是耗散的，那么能量就会因摩擦或辐射而损失，因此稳定能量和信息流需要能量输入(增益)。这项工作将特别集中在当前对由超冷原子蒸气形成的非线性介质的行为的实验、理论和计算研究中增益和损耗的相互作用。这个项目涉及对这类系统中一些选定的关键方面的全面检查。这项研究是基于非线性波演化最典型和最相关的模型之一的变体：非线性薛定谔(NLS)方程。NLS方程是各种物理现象的核心，包括但不限于光纤、凝聚态物理、等离子体波和流体力学中的深水怪波/无赖波。特别是，该小组将在以下领域内研究增益和损耗的影响：(A)具有所谓的宇称-时间反转(PT)对称性的光学系统，并且在外部增益和内部损耗之间具有微妙的平衡，可以有力地维持相干结构的存在和传播；(B)有限温度玻色-爱因斯坦凝聚体，它被建议作为维持/处理量子信息的候选者，可能实现下一代计算结构；以及(C)激子-极化凝聚体，它为操纵宏观量子力学提供了另一个原始的和非常容易获得的实验环境。在这些系统中，该小组将探索由非线性和色散引起的内在尺度与由增益和损耗引起的外部尺度之间的相互作用，以及这种相互作用如何影响作为信息存储和处理的基石的不同相干结构的存在、稳定性和动力学。在这个计划中，该小组希望产生数学模型和方法，以及计算技术，不仅将揭示这些特殊的原子和光学应用及其实验观测，而且可能对其他非保守系统的研究也有更广泛的用途。

This project focusses on the effects of energy gain and/or loss when waves propagate through non-linear media. The simplest kinds of wave motion exhibit a property called isochronism which was first observed by Galileo: The frequency of oscillation of the wave is independent of its amplitude (or size). Wave media in which this simple behavior is observed are called "linear". Non-linear media are also known, in which the frequency of the wave varies with its amplitude. If the medium is also dispersive (like a prism), then waves with different frequency will travel with different speed. The combined effects of non-linearity and dispersion can be quite striking, as with the formation of solitons - stable wave patterns that propagate through the medium without changing shape. A central focus of this work is to explore how solitons and other coherent structures that form in non-linear media, such as vortices, are responsible for the localization and transport of energy and information. If the medium through which the wave propagates is dissipative, then energy is lost to friction or radiation, and so stabilizing the flow of energy and information requires energy input (gain). The work will focus especially on the interplay of gain and loss in current experimental, theoretical, and computational investigations into the behavior of non-linear media formed from ultra-cold atomic vapors. This project involves the comprehensive examination of some selected key aspects within this class of systems. The study is based on variants of one of the most prototypical and most relevant models for the evolution of nonlinear waves: the nonlinear Schroedinger (NLS) equation. The NLS equation is at the heart of a wide variety of physical phenomena including, but not limited to, optical fibers, condensed matter physics, plasma waves, and deep water freak/rogue waves in fluid mechanics. In particular, the group will study the effects of gain and loss within the realm of (A) optical systems that have the so-called Parity-Time reversal (PT) symmetry, and possess a delicate balance between external gain and intrinsic loss that can robustly sustain the existence and propagation of coherent structures, (B) finite temperature Bose-Einstein condensates which have been proposed as candidates for sustaining/processing quantum information that could potentially realize the next generation of computational architectures, and finally, (C) exciton-polariton condensates, which provide another pristine and very accessible experimental setting for the manipulation of macroscopic quantum mechanics. Within these systems, the group will explore the interplay of the intrinsic scales induced by nonlinearity and dispersion and the extrinsic ones, stemming from gain and loss, and how this interplay affects the existence, stability and dynamics of different coherent structures that are the building blocks of information storage and processing. Within this program, the group expects to generate mathematical models and methods, as well as computational techniques, that will not only shed light to these particular atomic and optical applications and their experimental observations, but which may also be of broader use for the study of other non-conservative systems.