Regular spatial structures in arrays of Bose-Einstein condensates induced by modulational instability

TL;DR

This paper investigates how modulational instability in Bose-Einstein condensate arrays within optical lattices leads to the formation of stable, localized high-density structures, with potential applications in quantum technologies.

Contribution

It introduces a theoretical and numerical analysis of pattern formation due to modulational instability in BEC arrays, highlighting new stable localized structures and their dependence on initial conditions.

Findings

Localized structures are formed in 1D, 2D, and 3D arrays.

Long-term dynamics show periodic recurrence to initial states.

A method to sustain high-density localized structures is proposed.

Abstract

We show that the phenomenon of modulational instability in arrays of Bose-Einstein condensates confined to optical lattices gives rise to coherent spatial structures of localized excitations. These excitations represent thin disks in 1D, narrow tubes in 2D, and small hollows in 3D arrays, filled in with condensed atoms of much greater density compared to surrounding array sites. Aspects of the developed pattern depend on the initial distribution function of the condensate over the optical lattice, corresponding to particular points of the Brillouin zone. The long-time behavior of the spatial structures emerging due to modulational instability is characterized by the periodic recurrence to the initial low-density state in a finite optical lattice. We propose a simple way to retain the localized spatial structures with high atomic concentration, which may be of interest for applications. Theoretical model, based on the multiple scale expansion, describes the basic features of the phenomenon. Results of numerical simulations confirm the analytical predictions.