Floquet engineering of tight-binding Hamiltonians in momentum space lattices

TL;DR

This paper demonstrates how quantum resonances in a periodically driven rotor can be used to engineer and simulate complex tight-binding Hamiltonians in momentum-space lattices, with experimental validation using ultracold rubidium atoms.

Contribution

It introduces a Floquet engineering approach leveraging quantum resonances for programmable tight-binding models in momentum space, including analytical derivations and experimental demonstrations.

Findings

Successfully simulated the Rice-Mele model with topological edge states.

Achieved high-fidelity multi-period Floquet control using optimal techniques.

Observed momentum Bloch oscillations and superlattice configurations.

Abstract

Quantum simulation with ultracold atoms provides a versatile platform to emulate condensed-matter models. In particular, momentum-space lattices enable the realization of programmable tight-binding Hamiltonians. Here, we generalize this approach by exploiting quantum resonances of a periodically driven (shaken) rotor within the Floquet framework. Using first-order time-dependent perturbation theory, we derive analytical relations between the lattice modulation and the effective tight-binding parameters, and identify explicit solutions for several resonances. We further apply optimal-control techniques to enhance the multi-period Floquet fidelity and extend the accessible parameter regimes. Experimentally, we implement this scheme with a Bose-Einstein condensate of rubidium-87 atoms in a dynamically modulated optical lattice. We demonstrate the simulation of the Rice-Mele model, including band-structure measurements and topological edge states, as well as momentum Bloch oscillations, and superlattice configurations with controlled periodicity. Our results establish quantum resonances as a powerful resource for Floquet engineering of tight-binding models in momentum space.