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

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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.