[Paper Review] Bipartite and tripartite entanglement in a Bose-Einstein acoustic black hole

Mathieu Isoard, Nadia Milazzo+2 more|arXiv (Cornell University)|Feb 11, 2021

Quantum Electrodynamics and Casimir EffectPhysics and Astronomy111 references18 citations

TL;DR

This paper investigates bipartite and tripartite entanglement in a Bose-Einstein condensate-based acoustic black hole, modeling the system as a three-mode Gaussian state with a temperature-dependent covariance matrix. It identifies the Gaussian contangle as a robust, experimentally accessible measure of entanglement that quantifies the quantum nature of Hawking radiation, while proposing an equivalent optical setup for measuring the analogue Hawking temperature and grey-body factor.

ABSTRACT

We investigate quantum entanglement in an analogue black hole realized in the flow of a Bose-Einstein condensate. The system is described by a three-mode Gaussian state and we construct the corresponding covariance matrix at zero and finite temperature. We study associated bipartite and tripartite entanglement measures and discuss their experimental observation. We identify a simple optical setup equivalent to the analogue Bose-Einstein black hole which suggests a new way of determining the Hawking temperature and grey-body factor of the system.

Motivation & Objective

• To quantify bipartite and tripartite entanglement in a Bose-Einstein condensate analogue black hole.
• To identify experimentally relevant and quantitatively reliable entanglement measures at finite temperature.
• To establish a connection between the acoustic black hole and an equivalent optical setup for probing Hawking radiation parameters.
• To demonstrate that genuine tripartite entanglement can exist even when two modes are not pairwise entangled.
• To provide a new definition of the analogue Hawking temperature and grey-body factor consistent with gravitational paradigms.

Proposed method

• Models the acoustic black hole as a three-mode Gaussian state derived from Bogoliubov theory.
• Constructs the covariance matrix for the system at zero and finite temperature.
• Applies the Gaussian contangle as a quantitative measure of bipartite entanglement, validated for finite-temperature states.
• Uses symplectic transformations and mode localization to reduce the three-mode system to an effective two-mode state.
• Derives a low-frequency approximation of scattering coefficients to describe wave propagation across the horizon.
• Proposes an equivalent optical setup that maps the acoustic system to a photonic system for experimental realization.

Experimental results

Research questions

• RQ1 Which entanglement measure provides a reliable, monotonic, and experimentally accessible quantification of bipartite entanglement in a finite-temperature BEC analogue black hole?
• RQ2 Can genuine tripartite entanglement emerge in a three-mode Gaussian state even when two modes are not pairwise entangled?
• RQ3 How can the analogue Hawking temperature and grey-body factor be redefined in a way consistent with the gravitational paradigm?
• RQ4 What is the role of dispersive effects and lack of Lorentz invariance in modifying the standard Hawking pair picture?
• RQ5 How can the entanglement structure be localized to enable a two-mode effective description for experimental probing?

Key findings

• The Gaussian contangle is identified as a robust, experimentally measurable quantity that quantitatively captures the degree of bipartite entanglement in the Hawking pair.
• Tripartite entanglement can be present in the system even when two of the three modes are not entangled, indicating non-trivial quantum correlations.
• The finite-temperature covariance matrix enables a quantitative analysis of entanglement robustness, showing that quantum effects persist despite thermal noise.
• A simple optical setup is proposed as a direct analogue of the acoustic black hole, enabling measurement of the Hawking temperature and grey-body factor.
• The study provides a new definition of the analogue Hawking temperature and grey-body factor that aligns more closely with the gravitational model than previous approaches.
• The paper proves the measurability of the Gaussian contangle in principle, establishing its relevance for future experimental validation of quantum Hawking radiation.