Mobility edges in long-range hopping models

The experimental platform of one-dimensional momentum state lattices (MSLs) offering individual control over lattice Hamiltonian terms has proven to be a versatile platform for studying various lattice models. In this talk, I will discuss our progress toward implementing the long-range hopping model with quasi-periodic site energy disorder. In the 1D quasi-periodic energy case, the model becomes the celebrated Aubry–André (AA) model, which is self-dual, and hence has no mobility edge. In the presence of long-range hopping terms, the AA model loses its self-duality and has a mobility edge. The control over the lattice parameters paves the way for engineering transport in this one-dimensional quasi-periodic lattice.