Chaos and bi-partite entanglement between Bose-Joephson junctions

TL;DR

This paper investigates the relationship between chaos, classical phase space structures, and quantum entanglement in coupled Bose-Josephson junctions, revealing how chaos influences entanglement spectra and the nature of eigenstates.

Contribution

It introduces a detailed analysis of symmetry-resolved entanglement spectra in Bose-Josephson junctions, linking classical chaos and quantum entanglement properties, including the identification of Schrödinger cat states.

Findings

Chaos correlates with higher bipartite entanglement entropy.

Eigenstates supported by regular islands are less entangled and resemble Schrödinger cat states.

Entanglement spectra of chaotic eigenstates match the Generalized Gibbs Ensemble structure.

Abstract

The entanglement between two weakly coupled bosonic Josephson junctions is studied in relation to the classical mixed phasespace structure of the system, containing symmetry-related regular islands separated by chaos. The symmetry-resolved entanglement spectrum and bi-partite entanglement entropy of the system's energy eigenstates are calculated and compared to their expected structure for random states that exhibit complete or partial ergodicity. The entanglement spectra of chaos-supported eigenstates match the microcanonical structure of a Generalized Gibbs Ensemble due to the existence of an adiabatic invariant that restricts ergodization on the energy shell. The symmetry-resolved entanglement entropy of these quasistochastic states consists of a mean-field maximum entanglement term and a fluctuation correction due to the finite size of the constituent subsystems. The total bi-partite entanglement entropy of the eigenstates correlates with their chaoticity. Island-supported eigenstates are macroscopic Schr\"odinger cat states for particles and excitations, with substantially lower entanglement.