Matter wave dynamics in an optical lattice: decoherence of Josephson-type oscillations from the Gross–Pitaevskii equation

Abstract

We consider an atomic Bose–Einstein condensate described by the nonlinear Gross–Pitaevskii equation (GPE), which is driven by a harmonic force to move through a spatially periodic potential representing a quasi-one-dimensional (1D) optical lattice. For moderate values of the centre-of-mass displacement and of the potential barrier height, the condensate executes undamped oscillations and the alternating matter current can be mapped into the superfluid current passing through a Josephson junction in an AC field. By solving numerically a quasi-1D reduction of the GPE, we study how this coherent transport behaviour breaks down as (i) the strength of the harmonic force is increased, and (ii) the barrier height of the lattice potential is raised towards an extreme tight-binding limit where phase coherence between atomic clouds in neighbouring potential wells is lost. The emergence of decoherence is followed in both coordinate and momentum space, to trace the region of experimentally accessible parameters in which localization from nonlinearity may be observable in a measurement of the momentum distribution.