Multifrequency optical lattice for dynamic lattice-geometry control

Ultracold atoms in optical lattices are pristine model systems with a tunability and flexibility that goes beyond solid-state analogies, e.g., dynamical lattice-geometry changes allow tuning graphene lattice into boron-nitride lattice. However, fast modulation of the geometry remains intrinsically difficult. Here we introduce multi-frequency for flexible control demonstrate it three-beam lattice, realizing full between honeycomb triangular At same time, scheme ensures high stability geometry. We concept phase as parameter fully controls observe its signature staggered flux momentum space Tuning allows to dynamically sublattice offset use sweep transfer higher Bloch bands, perform new type band spectroscopy by modulating offset. Finally, generalize three-dimensional quasi-periodic potentials. This will further applications such novel Floquet quench protocols create probe, topological properties.