Exact dynamics of two ultra-cold bosons confined in a one-dimensional double-well potential

TL;DR

This paper investigates the exact and approximate dynamics of two ultra-cold bosons in a 1D double-well, highlighting the limitations of the two-mode model at strong interactions.

Contribution

It provides a detailed comparison between exact two-body dynamics and two-mode approximation, emphasizing the need to include higher states for strong interactions.

Findings

Two-mode model fails at large interactions

Higher single-particle states are necessary for accurate dynamics

Exact solutions reveal limitations of simplified models

Abstract

The dynamics of two ultra-cold bosons confined in a one-dimensional double-well potential is studied. We compare the exact dynamics governed by a full two-body Hamiltonian with the dynamics obtained in a two-mode model approximation. We show that for sufficiently large interactions the two-mode model breaks down and higher single-particle states have to be taken into account to describe the dynamical properties of the system correctly.