Regular spatial structures in arrays of Bose–Einstein condensates induced bymodulational instability

Abstract

We show that the phenomenon of modulational instability in arrays ofBose–Einstein condensates confined to optical lattices gives rise to coherentspatial structures of localized excitations. These excitations represent thin discs in1D, narrow tubes in 2D, and small hollows in 3D arrays, filled in with condensedatoms of much greater density compared to surrounding array sites. Aspects ofthe developed pattern depend on the initial distribution function of thecondensate over the optical lattice, corresponding to particular points of theBrillouin zone. The long-time behaviour of the spatial structures emerging dueto modulational instability is characterized by the periodic recurrenceto the initial low-density state in a finite optical lattice. We propose asimple way to retain the localized spatial structures with high atomicconcentration, which may be of interest for applications. A theoretical model,based on the multiple-scale expansion, describes the basic features of thephenomenon. Results of numerical simulations confirm the analytical predictions.