Reentrant phase transition in quasiperiodic photonic waveguides

Anderson transition in quasiperiodic potentials and the associated mobility edges have been a central focus in quantum simulation across multidisciplinary physical platforms. While these transitions have been experimentally observed in ultracold atoms, acoustic systems, optical waveguides, and superconducting junctions, their interplay between quasiperiodic potential and long-range hopping remains unexplored experimentally. In this work, we report the observation of localization-delocalization transition induced by the hopping between the next-nearest neighboring sites using quasiperiodic photonic waveguides. Our findings demonstrate that increasing the next-nearest hopping strength induces a reentrant phase transition, where the system transitions from an initially extended phase into a localized phase before eventually returning to an extended phase. This remarkable interplay between hopping and quasiperiodic potential in the lattice models provides crucial insights into the mechanism of Anderson transition. Furthermore, our numerical simulation reveals that this phase transition exhibits a critical exponent of $\nu \simeq 1/3$, which is experimentally observable for system sizes $L\sim10^3$ - $10^4$. These results establish a framework for direct observation of the Anderson transition and precise determination of its critical exponents, which can significantly advance our understanding of localization physics in quasiperiodic systems.