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Multiple-time-scale Landau-Zener transitions in many-body systems

Motivated by recent cold atom experiments in optical lattices, we consider a lattice version of the Landau-Zener problem. Every single site is described by a Landau-Zener problem, but due to particle tunnelling between neighboring lattice sites this onsite single particle Landau-Zener dynamics couples to the particle motion within the lattice. The lattice, apart from having a dephasing effect on single site Landau-Zener transitions, also implies, in the presence of a confining trap, an inter-site particle flow induced by the Landau-Zener sweeping. This gives rise to an interplay between intra- and inter-site dynamics. The adiabaticity constrain is therefor not simply given by the standard one; the Hamiltonian rate of change relative to the gap of the onsite problem. In experimentally realistic situations, the full system evolution is well described by Franck-Condon physics, e.g. non-adiabatic excitations are predominantly external ones characterized by large phononic vibrations in the atomic cloud, while internal excitations are very weak as close to perfect onsite transitions take place.