Multifractal-enriched mobility edges and emergent quantum phases in Rydberg atomic arrays

Anderson localization describes disorder-induced phase transitions, distinguishing between localized and extended states. In quasiperiodic systems, a third multifractal state emerges, characterized by unique energy and wave functions. However, the corresponding multifractal-enriched mobility edges and three-state-coexisting quantum phases have yet to be experimentally detected. In this work, we propose exactly solvable one-dimensional quasiperiodic lattice models that simultaneously host three-state-coexisting quantum phases, with their phase boundaries analytically derived via Avila??s global theorem. Furthermore, we propose experimental protocols via Rydberg atom arrays to realize these states. Notably, we demonstrate a spectroscopic technique capable of measuring inverse participation ratios across real-space and dual-space domains, enabling simultaneous characterization of localized, extended, and multifractal quantum phases in systems with up to tens of qubits. Our work opens new avenues for the experimental exploration of Anderson localization and multifractal states in artificial quantum systems.