Theoretical analysis of quantum dynamics in one-dimensional lattices: Wannier-Stark description

Abstract

This paper presents a formalism describing the dynamics of a quantum particle in a one-dimensional, tilted, time-dependent lattice. The description uses the Wannier-Stark states, which are localized in each site of the lattice, and provides a simple framework leading to fully analytical developments. Particular attention is devoted to the case of a time-dependent potential, which results in a rich variety of quantum coherent dynamics.