Floquet engineering of tight-binding Hamiltonians in momentum space lattices

Quantum simulation with ultracold atoms provides a versatile platform to emulate condensedmattermodels. In particular, momentum-space lattices enable the realization of programmabletight-binding Hamiltonians. Here, we generalize this approach by exploiting quantum resonances ofa periodically driven (shaken) rotor within the Floquet framework. Using first-order time-dependentperturbation theory, we derive analytical relations between the lattice modulation and the effectivetight-binding parameters, and identify explicit solutions for several resonances. We further applyoptimal-control techniques to enhance the multi-period Floquet fidelity and extend the accessibleparameter regimes. Experimentally, we implement this scheme with a Bose–Einstein condensate ofrubidium-87 atoms in a dynamically modulated optical lattice. We demonstrate the simulation ofthe Rice–Mele model, including band-structure measurements and topological edge states, as wellas momentum Bloch oscillations, and superlattice configurations with controlled periodicity. Ourresults establish quantum resonances as a powerful resource for Floquet engineering of tight-bindingmodels in momentum space.