Floquet engineering with spatially non-uniform driving fields

We generalize the scope of Floquet engineering to include spatially-dependent modulations of an optical system. As an application, we show that we can transform large classes of Hamiltonians into one another by driving them in a time-periodic but spatially non-uniform manner. We propose several experimental realizations in 1D optical lattices, including freeing disordered lattices from Anderson localization, as well as effectively disconnecting all their sites. These techniques straightforwardly extend to more complex classes of systems.