Analytical results on quantum correlations of few bosons in a double-well trap

TL;DR

This paper analytically investigates the ground state properties and quantum correlations of a few interacting bosons in a double-well trap using the Bose-Hubbard model, revealing differences based on particle number and interaction strength.

Contribution

It provides analytical solutions for the eigenstates of the two-site Bose-Hubbard model for N=2, 3, 4 bosons and characterizes ground state quantum correlations across interaction regimes.

Findings

Analytical formulas for Fisher information, coherence visibility, and entanglement entropy.

Distinct ground state structures for even and odd number of bosons in the deep repulsive regime.

Insights into how interaction strength affects quantum correlations in few-boson systems.

Abstract

We consider a finite number $N$ of interacting bosonic atoms at zero temperature confined in a one-dimensional double-well trap and study this system by using the two-site Bose-Hubbard (BH) Hamiltonian. For systems with $N=2$ and $N=3$, and $N=4$ bosons we analytically solve the eigenproblem associated to this Hamiltonian and find its lowest energetic state. We investigate the structure of the ground state by varying the strength of the boson-boson interaction from the strongly attractive regime to the deep repulsive one. We characterize the ground state of the two-site BH Hamiltonian by calculating the Fisher information $F$, the coherence visibility $\alpha$, and the entanglement entropy $S$. For these quantities we provide analytical formulas that we use to study $F$, $\alpha$, and $S$ as functions of the interaction between the particles. We discuss the difference existing, in the deep repulsive regime, between the case with an even number of bosons and that with an odd number of particles, both in the structure of the lowest energetic state and in the behavior of the three above ground-state characterizing parameters