Quantum Matter in Curved Geometries: Cooperative Optics and Matrix-Model Gauge Fields

Quantum systems are shaped not only by their constituent particles but also by the geometric and symmetry structures that organize their interactions. This project will develop a unified agenda in which geometry, expressed through chirality, curvature, synthetic fluxes, and topological constraints, acts as a generative principle for quantum dynamics across cooperative quantum optics systems and quantum information science. The project will broaden how geometry and symmetry are used to design quantum systems, offering new strategies for robust devices, for simulating gauge and gravitational phenomena, and for connecting AMO platforms with high-energy and condensed-matter physics. By developing general methodologies for geometry-driven control, the work form new architectures in sensing, materials, and quantum technologies. Quantum science naturally attracts students, and this project will leverage that appeal to sustain a mentorship-centered research environment with a strong undergraduate presence. Graduate students and postdocs will mentor undergraduates engaged in research, benefiting both groups and reinforcing a collaborative culture. The PI will pursue two complementary thrusts: (1) cooperative quantum optical platforms such as chiral atom arrays and quantum-emitter ring lattices, where geometry is embedded directly into the hardware and leads to phenomena including emergent spin–orbit coupling, sub-radiance, and topology in open systems; and (2) a lattice-free, quantum-native simulation framework in which large-N matrix models encode gauge fields and curved spacetimes through operator commutators implemented via Floquet engineering. These directions address core questions: how geometric features reshape cooperative many-body dynamics; how gauge and geometric structure can emerge purely algebraically; and how these perspectives can be connected to build a coherent framework for geometry-driven quantum behavior. The project will establish geometry as a unifying design principle for both cooperative quantum optics and quantum simulation. On the AMO side, the work will elucidate how chiral and curved architectures, together with collective emission and dipolar exchange, generate new forms of spin–orbit coupling, non-Hermitian topology, and robust sub-radiant and topological modes. On the quantum-simulation side, the project introduces a fundamentally different approach to field theory on curved spacetimes by using matrix models and Floquet-engineered nested commutators to encode gauge structure and geometry directly in operator algebras, without spatial lattices. This paradigm preserves continuous symmetries natively and creates new opportunities for simulating gauge and gravitational dynamics. 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.