Transport controlled by Poincaré orbit topology in a driven inhomogeneous lattice gas

In periodic quantum systems which are both homogeneously tilted and driven, the interplay between drive and Bloch oscillations controls transport dynamics. Using a quantum gas in a modulated optical lattice, we show experimentally that inhomogeneity of the applied force leads to a rich variety of dynamical behaviors controlled by the drive phase, from self-parametrically-modulated Bloch epicycles to adaptive driving of transport against a force gradient to modulation-enhanced monopole modes. By examining Poincaré portraits of the semiclassical transport equations, we demonstrate that the observed dynamics reflect the rich topological structure of stroboscopic orbits on a Brillouin phase-space cylinder.