Topological order and Anyons in and out of Equilibrium

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NONTECHNICAL SUMMARYThis award supports theoretical research into the quantum physics of many interacting particles, often referred to as quantum matter. These systems are the gateway to a rich and promising scientific arena, given the extraordinary ability of quantum particles to remain tied to one another even when separated, a property termed quantum entanglement. Realizations of quantum matter are everywhere, ranging from electrons in crystals to engineered platforms consisting of arrays of atoms. In this project, the PI and his team will explore strategies to create highly entangled quantum matter and to identify the features that characterize them. A particularly interesting subclass is topological matter, in which new excitations called "anyons" arise that are entirely distinct from the individual components that go into building them. Such excitations are speculated to lead to novel material properties and capabilities in quantum information. The PI will explore new arenas to realize topological states, including in artificial materials created by stacking atomically thin sheets and by driving matter with external fields far from thermal equilibrium. The education of the next generation of junior scientists is a key part of this project. Undergraduate and graduate students will be exposed to modern ideas of quantum condensed matter physics through coursework as well as research collaborations. This will contribute to the US workforce in fundamental science and quantum technologies. The research outcomes and course materials developed throughout the course of this project will be widely disseminated via non-technical summaries, pedagogical lecture notes, as well as seminars, colloquia and lecture series at scientific schools for young researchers.TECHNICAL SUMMARYThis award supports theoretical research on quantum states of matter with novel excitations stabilized by topology, to identify their experimental signatures and to enable their realizations in solids and ultracold quantum gases. While a glimpse of topological order and the associated anyon excitations have previously appeared in the fractional quantum Hall effect, this award will focus on realizing these and other topological states in a wider set of systems and in the absence of strong magnetic fields. The topological character of these states make their detection a challenge. The PI will study models of electronic and cold atom systems that are both promising platforms for topological orders and allow for measurements that can unequivocally point to their realization. Moving beyond ground states, driven systems harboring anyon excitations exhibit an extra layer of complexity and richness, and furnish an alternate route to stabilizing topological orders. The PI will explore topological orders driven far from equilibrium, due to external drives and/or measurements as well as out-of-equilibrium routes to realizing new states, including ones with non-Abelian anyon excitations.This award also supports the training of the next generation of researchers in modern theoretical physics, via research and coursework. New course material at the graduate level will be developed, which will incorporate insights gleaned from research. The research outcomes and course materials developed throughout the course of this project will be widely disseminated via non-technical summaries, pedagogical lecture notes, as well as seminars, colloquia and lecture series at scientific schools for young researchers.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.