Exploration of localization physics with atomic, molecular, and optical platforms

Anderson localization (AL)-a fundamental wave phenomenon resulting from coherent interference in disordered potentials-has attracted substantial attention in quantum optics and ultracold atomic physics due to its universal nature and controllable experimental realizations. In this review, we survey recent advances in the study of localization physics, focusing primarily on AL, quasi-periodic modulation, and the emergence of mobility edges in optical and atomic systems. After briefly introducing the theoretical origins and historical context, we discuss the theoretical frameworks underlying localization phenomena, highlighting key models such as the Anderson tight-binding model and the Aubry-André quasiperiodic lattice. The core emphasis of this review lies in experimental developments: we comprehensively describe how ultracold atomic gases and optical platforms-including disordered waveguides and fiber loop systems-have enabled precise observation and characterization of localization transitions and mobility edges. Experimental methodologies, diagnostics, and challenges unique to each system are thoroughly addressed. Finally, we conclude by outlining promising future directions, such as many-body localization, non-Hermitian Anderson physics, and synthetic-dimension systems, emphasizing how the interplay between theory and experimental innovation continues to drive the field forward.