Transport controlled by Poincar\'e orbit topology in a driven inhomogeneous lattice gas

TL;DR

This paper demonstrates how inhomogeneity-induced phase space structures, classified by Poincaré orbit topology, govern transport phenomena in driven inhomogeneous lattice gases, with experimental validation using quantum gases in optical lattices.

Contribution

It reveals the topological classification of Poincaré orbits as a key factor controlling transport in driven inhomogeneous quantum systems, supported by experimental and numerical analysis.

Findings

Transport behaviors depend on drive phase and inhomogeneity.

Experimental results match numerical predictions without fitting parameters.

Topological classification explains diverse dynamical phenomena.

Abstract

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 new 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. Matching experimental observations to fit-parameter-free numerical predictions of time-dependent band theory, we show that these phenomena can be quantitatively understood as manifestations of an underlying inhomogeneity-induced phase space structure, in which topological classification of stroboscopic Poincar\'e orbits controls the transport dynamics.