Disorder-Free Localization: From Toy Models to Experimental Realizations

Localization is a fundamental phenomenon in quantum physics, conventionally associated with the disorder-induced scattering and the suppression of wave propagation. However, quantum particles can also become localized in perfectly ordered systems, where the lattice geometry, band structure, and quantum interference give rise to the suppression of particle propagation. Such disorder-free localization provides a fascinating platform known as the “flat-bands” for exploring the interplay between geometry, interference, and the dynamics of quantum matter. Flat bands are interesting as they offer highly degenerate manifold of single-particle states, which can act as an ideal platform to study various intriguing strongly correlated phenomena. In this talk, I will present a variety of interesting artificial engineered lattice geometries which show the appearance of multiple flat-band states in their band structure. I will demonstrate how one can tune the parameters of the underlying tight-binding Hamiltonian of the system to engineer these flat-band states with interesting properties. With the application of an external magnetic field or an intrinsic spin-orbit interaction, such flat bands often show interesting topological properties and provide an ideal setup to study the quantum Hall physics in a lattice model. Finally, I will demonstrate how these theoretical flatband toy models are realized in real-life experiments in the field of photonics using single-mode photonic waveguide networks.