Dynamical generation of two-dimensional matter-wave discrete solitons

TL;DR

The paper proposes a method to generate two-dimensional matter-wave discrete solitons in a self-repulsive BEC within optical lattices, utilizing negative effective mass at the Brillouin zone edge to induce localization.

Contribution

It introduces a novel experimental approach for creating 2D matter-wave discrete solitons using negative effective mass in optical lattices with self-repulsive BECs.

Findings

Wave packets collapse into localized modes above a critical nonlinearity.

Discrete solitons form in the gap between energy bands.

Numerical simulations confirm the process in different lattice geometries.

Abstract

We suggest a method to experimentally obtain two-dimensional matter-wave discrete solitons with a {\it self-repulsive} BEC in optical lattices. At the edge of the Brillouin zone, a wave packet effective mass is negative which could be treated as inversion of the nonlinearity sign. Above critical nonlinearity this makes the wave packets collapse partially into localized modes with a chemical potential located in the gap between the first and the second bands. This critical nonlinearity is also associated with the smallest nonlinearity for which the discrete solitons are possible in the gap. Extensive numerical simulations for square and asymmetric honeycomb lattices in continuous model illustrate every stage of the process.