Lattice solitons with quadrupolar intersite interactions

We study two-dimensional (2D) solitons in the mean-field models of ultracold gases with long-range quadrupole-quadrupole interaction (QQI) between particles. The condensate is loaded into a deep optical-lattice (OL) potential, therefore the model is based on the 2D discrete nonlinear Schrodinger equation with contact on site and long-range intersite interactions, which represent the QQI. The quadrupoles are built as pairs of electric dipoles and antidipoles orientated perpendicular to the 2D plane to which the gas is confined. Because the quadrupoles interact with the local gradient of the external field, they are polarized by an inhomogeneous dc electric field that may be supplied by a tapered capacitor. Shapes, stability, mobility, and collisions of fundamental discrete solitons are studied by means of systematic simulations. In particular, threshold values of the norm, which are necessary for the existence of the solitons, are found and anisotropy of their static and dynamical properties is explored. As concerns the mobility and collisions, we analyze such properties for discrete solitons on 2D lattices with long-range intersite interactions. Estimates demonstrate that the setting can be realized under experimentally available conditions, predicting solitons built of similar to 10 000 particles.