Coherence and entanglement in the ground-state of a bosonic Josephson junction:from macroscopic Schr\"odinger cats to separable Fock states

TL;DR

This paper investigates the ground-state properties of a bosonic Josephson junction, revealing a transition from macroscopic Schrödinger-cat states to separable Fock states as interaction strength varies, using analytical and numerical methods.

Contribution

It provides analytical formulas for Fisher information and coherence, characterizing the crossover in ground states of the Bose-Hubbard model with high accuracy.

Findings

Ground state transitions from Schrödinger-cat to Fock states.

Analytical expressions for Fisher information and coherence match numerical results.

Entanglement entropy peaks near coherence loss and self-trapping onset.

Abstract

We consider a bosonic Josephson junction made of $N$ ultracold and dilute atoms confined by a quasi one-dimensional double-well potential within the two-site Bose-Hubbard model framework. The behaviour of the system is investigated at zero temperature by varying the inter-atomic interaction from the strongly attractive regime to the repulsive one. We show that the ground-state exhibits a crossover from a macroscopic Schr\"odinger-cat state to a separable Fock state through an atomic coherent regime. By diagonalizing the Bose-Hubbard Hamiltonian we characterize the emergence of the mascroscopic cat states by calculating the Fisher information $F$, the coherence by means of the visibility $\alpha$ of the interference fringes in the momentum distribution, and the quantum correlations by using the entanglement entropy $S$. Both Fisher information and visibility are shown to be related to the ground state energy by employing the Hellmann-Feynman theorem. This result, together with a perturbative calculation of the ground-state energy, makes possible to obtain simple analytical formulas for $F$ and $\alpha$ over a range of interactions, in excellent agreement with the exact diagonalization of the Bose-Hubbard Hamiltonian. In the attractive regime the entanglement entropy attains values very close to its upper limit for a specific interaction strength lying in the region where coherence is lost and self trapping sets in.