Stacking atom-thin sheets of material like graphene creates new electronic landscapes—moiré patterns—that can trap and control electrons in ways impossible in natural crystals. This project builds a theoretical framework to understand and exploit those landscapes, combining ideas from condensed matter physics and quantum computing. The problem is that these moiré materials and noisy intermediate-scale quantum (NISQ) devices are developing rapidly, but no unified theory exists to describe the exotic quantum states they can produce—topological phases, non-ergodic dynamics, or "measurement-enriched" states of matter. Without that theory, researchers cannot reliably design or control these states for practical use. If successful, this fundamental science project will provide the mathematical tools to steer experiments toward useful quantum phenomena. That could eventually enable new types of quantum sensors, more stable qubits for quantum computers, or materials with tailored electronic properties. For now, the work is curiosity-driven—but similar theoretical advances in the past, such as the understanding of topological insulators, later enabled everything from more efficient thermoelectric devices to new approaches for fault-tolerant quantum computing.
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This project will build a theoretical foundation for the "tunability frontier" anticipated to emerge from the convergence of materials physics and quantum engineering. This convergence is driven by two key advances. The first is the ability to engineer "moiré superlattices" by stacking atomically-thin layers, leading to new tunable material platforms with unprecedented access to local probes, enhanced electron interactions, and rich topological structure. The second is the development of "noisy, intermediate-scale quantum" (NISQ) computing devices that are also exquisitely-controllable simulators of quantum many-body phenomena. Leveraging these developments to fully access macroscopic quantum phenomena and control entangled states of matter will require a holistic framework that combines concepts from condensed matter and techniques from quantum control: the goal of this project. The project will first develop new directions in moiré systems and NISQ devices, and then use these as scaffolding to explore the convergence of these themes. It will (i) build theories of topological phases of neutral bosons and the interplay of disorder and interactions in moiré systems, motivated by similar questions in NISQ and cold-atom systems; (ii) explore new uses for NISQ devices in studying random systems and noisy non-ergodic dynamics; (iii) develop theories of nonlinear response, inspired by precision atomic and optical spectroscopy, in the many-body, solid-state setting, impacting near-term experiments on quantum materials; and (iv) identify new phases and phenomena that emerge at the tunability frontier, including topological phases at the quantum optics-moiré interface, non-ergodic dynamics in moiré bands, and "measurement-enriched" states of matter. At its close, this project will have built a theoretical framework that will have informed one generation of experiments, and stand ready to steer the next generation to a new tunability frontier of quantum matter.
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