Quantum dynamics in driven and disordered systems: Floquet topological control and flow methods for many body localization

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NONTECHNICAL SUMMARYThis award supports theoretical research and education towards understanding and controlling the behavior of quantum materials, and on using their unique quantum behavior for possible technological applications. The PI will combine insights obtained from the recent discovery of new materials and the idea of simulating extra dimensions, whereby a periodically driven system appears to have an extra spatial dimension for each periodic drive it is subject to. For example, using these two ideas, one can take a microscopic magnet, illuminate it with two modulated light beams, and turn it into an energy pump which draws energy from one beam and gives it in full to another. The PI aims to show how this principle could be implemented into solid-state devices based on newly discovered semiconductors. In addition, the PI will develop a microscopic theory for a new type of phase transition, the many-body localization transition, which occurs when a system of quantum particles, such as electrons, stops obeying the common rules of thermodynamics due to the presence of sufficient disorder. Graduate students and postdocs will participate in the research and will receive training and education in a subject of high national priority. The PI will also conclude the writing of a textbook on how to model a variety of technologies and natural phenomena using fundamentals known to any physics undergraduate. This book will provide a unifying perspective, guiding budding physicists and engineering enthusiasts on how to apply core physics principles to obtain advanced understanding for a range of phenomena and devices, ranging from medical devices and energy production to space travel, cosmology, and living systems. TECHNICAL SUMMARYThis award supports theoretical research and education towards developing new topological quantum control principles and new analysis tools for the many-body localization transition. Quantum dynamics is among the most challenging fields in condensed matter. Experiments can now observe the dynamics of electrons, atoms, and light in a variety of environments. The theory of quantum control needs to harness these developments. Topological physics on the one hand, and disorder leading to many-body localization on the other, present parallel themes that enrich quantum many-body dynamics.The project will explore new tools for controlling electromagnetic radiation that are based on topological physics. The PI will study how these topological control tools behave when realized in interacting light-matter systems. This will require developing a comprehensive theory for multi-driven many-body quantum optics and solid-state electronic systems. The emerging theory will predict the electronic response of complex materials to strong external drives in the presence of electronic relaxation and many-body interactions. In the second part of the work, the PI will derive a new method for analyzing disordered and interacting many-body quantum systems through study of the many-body localization transition. The method envisioned combines unitary flow methods with strong-disorder renormalization group approaches and will not be restricted by the nature or the range of the interactions. It has the potential to lead to the discovery of fundamentally new universality classes.Beyond education and training of graduate students and postdocs, the work could pave the way to new photonic devices based on topological principles. Potential technological impacts include new tools for controlling low THz electromagnetic radiation for which only few control tools are available. In addition, the PI will complete a book addressed to all physics enthusiasts describing an analysis of real-world physics problems, natural phenomena, and technological breakthroughs drawing on college physics curriculum.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.