Floquet engineering of individual band gaps in an optical lattice using a two-tone drive

The dynamic engineering of band structures for ultracold atoms in optical lattices represents an innovative approach to understanding and exploring the fundamental principles topological matter. In particular, folded Floquet spectrum determines associated topology via inversion. We experimentally theoretically study two-frequency phase modulation asymmetrically hybridize lowest two bands a one-dimensional lattice. Using quasidegenerate perturbation theory extended space we derive effective two-band model that quantitatively describes our setting. energy gaps are probed Landau-Zener transitions between Floquet-Bloch using accelerated Bose-Einstein condensate. Separate simultaneous control over closing reopening these is demonstrated. find good agreement experiment theory, establishing analytic description resonant includes single- multiphoton couplings, as well interference effects several commensurate drives.