Observation of Wannier-Stark ladder beyond mobility edge in disorder-free mosaic lattices

Quantum transport and localization are fundamental concepts in condensed matter physics. It is commonly believed that in one-dimensional systems, the existence of mobility edges is highly dependent on disorder. Recent theoretical works have shown that a modulated mosaic model could manifest an exact mobility edge even without quenched disorder. Here, we experimentally implement such disorder-free mosaic photonic lattices using silicon photonics platform. By creating a synthetic electric field, we could observe energy-dependent coexistence of both extended and localized states in the system. The Wannier-Stark ladder emerges when the resulting potential is strong enough, and can be directly probed by exciting different spatial modes of the lattice. Our studies bridge the gap between mobility edge and Wannier-Stark localization. Our developed photonic devices hold the potential to encode high dimensional quantum resources with compact and robust structures