Semiclassical solitons in strongly correlated systems of ultracold bosonic atoms in optical lattices

TL;DR

This paper develops a theoretical framework for understanding soliton excitations and their dynamics in strongly correlated ultracold bosonic atoms in optical lattices, deriving nonlinear hydrodynamics equations applicable in various regimes.

Contribution

It introduces a novel derivation of nonlinear hydrodynamics equations for strongly interacting bosons in optical lattices, including KdV and modified KdV equations, and analyzes soliton stability and decay.

Findings

Derived KdV and modified KdV equations for different regimes

Analyzed decay of density steps in optical lattices

Assessed stability of 1D solutions to transverse fluctuations

Abstract

We investigate theoretically soliton excitations and dynamics of their formation in strongly correlated systems of ultracold bosonic atoms in two and three dimensional optical lattices. We derive equations of nonlinear hydrodynamics in the regime of strong interactions and incommensurate fillings, when atoms can be treated as hard core bosons. When parameters change in one direction only we obtain Korteweg-de Vries type equation away from half-filling and modified KdV equation at half-filling. We apply this general analysis to a problem of the decay of the density step. We consider stability of one dimensional solutions to transverse fluctuations. Our results are also relevant for understanding nonequilibrium dynamics of lattice spin models.