Experiments in periodic driving of Bose-condensed lithium

Driven quantum degenerate gases represent a versatile platform for exploring quantum dynamics. Our optical lattice experiments with Bose-condensed lithium lie at the two "extremes" of the spectrum of periodic driving: sharp delta-function-like pulses and sinusoidal amplitude modulation. Delta kicking can realize the quantum kicked rotor, a paradigmatic model of quantum chaos; we recently demonstrated that an interacting kicked rotor exhibits sub-diffusive many-body dynamical delocalization. In band synthesis experiments using sinusoidal amplitude modulation, both Floquet's and Bloch's theorems apply, creating a toroidal Brillouin zone periodic in both quasi-momentum and quasi-energy. Closed loops in the resulting Floquet-Bloch bands represent a novel platform for compact continuously-trapped atom interferometry and sensitive force measurement. In analogy to magic wavelengths used in optical lattice clocks, magic band structures can cancel the first-order trap amplitude noise sensitivity of such Floquet-Bloch atom interferometers.