Bound states and expansion dynamics of interacting bosons on a one-dimensional lattice

TL;DR

This paper investigates the expansion dynamics of two interacting bosons in a one-dimensional lattice, revealing a link between expansion velocities and bound states, and examining the lattice's influence on this process.

Contribution

It introduces a numerical Bethe ansatz approach to connect asymptotic expansion velocities with bound state projections in lattice bosonic systems.

Findings

Expansion velocities correlate with bound state projections.

The lattice significantly influences the expansion dynamics.

Bound states play a crucial role in the evolution of interacting bosons.

Abstract

The expansion dynamics of bosonic gases in optical lattices has recently been the focus of increasing attention, both experimental and theoretical. We consider, by means of numerical Bethe ansatz, the expansion dynamics of initially confined wave packets of two interacting bosons on a lattice. We show that a correspondence between the asymptotic expansion velocities and the projection of the evolved wave function over the bound states of the system exists, clarifying the existing picture for such situations. Moreover, we investigate the role of the lattice in this kind of evolution.