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arXiv:2508.00423 · Physical review. D/Physical review. D.

Quantum entanglement of Hawking-partner modes in expanding cavities

José Manuel Montes-Armenteros, Javier Olmedo

Published Nov 21, 2025• 1 citation
arXivHTMLPDF

Abstract

This article investigates quantum entanglement generated within a one-dimensional cavity where one boundary undergoes prescribed acceleration, a setup designed to mimic aspects of Hawking radiation. We quantify quantum correlations using logarithmic negativity for bipartitions, where subsystem $A$ is a given mode and subsystem $B$ is the rest of the system. For initial pure states, we also consider a given mode and reconstruct its partner using the Hotta-Sch\"utzhold-Unruh formula, obtaining identical results. Interestingly, this last method offers notable computational efficiency. However, partner modes do not commute, due to the nontrivial multimode entanglement structure. Hence, a pairwise description will not be suitable for describing the full system. Besides, our findings reveal that the expanding cavity effectively acts as a squeezing device, with Hawking-partner pairs largely behaving as two-mode squeezed states. We checked that, in our setting, purification of Hawking modes is predominantly a low-energy process, with high-energetic particles contributing negligibly to the partner modes. Indeed, in both small and large acceleration regimes of the boundaries, quantum entanglement decreases toward the ultraviolet modes, indicating that higher-energy particles are more challenging to entangle and hence less probable to contribute in the purification process. Besides the initial vacuum state, we also consider one-mode squeezed and two-mode squeezed states, in order to confirm if quantum entanglement can be stimulated. Moreover, we analyze its robustness against initial thermal noise. Our analysis is based on numerical simulations and does not assume any approximation beyond the validity of our numerical algorithms. We conclude with a discussion about the possible implementation and observation of our results in the laboratory.

DOI
10.1103/szzj-pq9z

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This article investigates quantum entanglement generated within a one-dimensional cavity where one boundary undergoes prescribed acceleration, a setup designed to mimic aspects of Hawking radiation. We quantify quantum correlations using logarithmic negativity for bipartitions, where subsystem AAA is a given mode and subsystem BBB is the rest of the system. For initial pure states, we also consider a given mode and reconstruct its partner using the Hotta-Sch"utzhold-Unruh formula, obtaining identical results. Interestingly, this last method offers notable computational efficiency. However, partner modes do not commute, due to the nontrivial multimode entanglement structure. Hence, a pairwise description will not be suitable for describing the full system. Besides, our findings reveal that the expanding cavity effectively acts as a squeezing device, with Hawking-partner pairs largely behaving as two-mode squeezed states. We checked that, in our setting, purification of Hawking modes is predominantly a low-energy process, with high-energetic particles contributing negligibly to the partner modes. Indeed, in both small and large acceleration regimes of the boundaries, quantum entanglement decreases toward the ultraviolet modes, indicating that higher-energy particles are more challenging to entangle and hence less probable to contribute in the purification process. Besides the initial vacuum state, we also consider one-mode squeezed and two-mode squeezed states, in order to confirm if quantum entanglement can be stimulated. Moreover, we analyze its robustness against initial thermal noise. Our analysis is based on numerical simulations and does not assume any approximation beyond the validity of our numerical algorithms. We conclude with a discussion about the possible implementation and observation of our results in the laboratory.
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This Letter introduces a synergistic combination of analytical and numerical methods to study the Hawking effect in optical systems containing the analog of a white-black hole pair. Our analytical treatment, based on techniques from Gaussian quantum information, provides a simple and efficient model to describe all aspects of the out-state, including the entanglement between any bipartition. We complement the study with a numerical analysis and apply our tools to investigate the influence that ambient thermal noise and detector inefficiencies have on the out-state. We find that aspects of the Hawking effect that are of quantum origin, i.e., quantum entanglement, are extremely fragile to the influence of inefficiencies and noise. We propose a protocol to amplify and observe these quantum aspects, based on seeding the process with a single-mode squeezed input, opening the door to new possibilities for experimental verification of the Hawking effect.
The influence of Hawking radiation on quantum entanglement for bimodal Gaussian states near a Schwarzschild black hole is investigated. It is shown that for a thermal squeezed state of a bimodal bosonic system the Hawking radiation reduces and even can destroy the entanglement between the mode of a Kruskal observer Alice and the mode of Bob, who is an accelerated observer hovering outside the event horizon of black hole. By contrary, the Hawking radiation increases and even can generate quantum entanglement between Bob and anti-Bob, who is a hypothetical observer inside event horizon. We show that in both these scenarios the competition between the contrary influences produced by Hawking temperature, squeezing and field frequency, may favour the preservation of the quantum entanglement. We investigate also the influence of the thermal environment on the behaviour in time of the entanglement between the considered observers and show that the entanglement is destroyed in a finite time for both considered bipartite scenarios of observers Alice and Bob, and respectively Bob and anti-Bob, for non-zero values of the temperature of the thermal environment, i.e. the phenomenon of entanglement sudden death takes place. For a zero temperature of the thermal bath the initial existing entanglement is decreasing over time, but it keeps for all finite times a non-zero value and the logarithmic negativity tends to zero only in the limit of infinite time.
We analyze entanglement generated by the Schwinger effect using a mode-by-mode formalism for scalar and spinor QED in constant backgrounds. Starting from thermal initial states, we derive compact, closed-form results for bipartite entanglement between particle-antiparticle partners in terms of the Bogoliubov coefficients. For bosons, thermal fluctuations enhance production but suppress quantum correlations: the logarithmic negativity is nonzero only below a (mode-dependent) critical temperature TcT_cTc​. At fixed TTT, entanglement appears only above a critical field EentangE_{\text{entang}}Eentang​. For fermions, we observe a qualitatively different pattern: the fermionic logarithmic negativity is non-vanishing at finite temperature, and is monotonically suppressed by thermal noise. As a function of the electric field, it is non-monotonic, featuring a temperature-independent optimal field strength E∗E_*E∗​ and decreasing on both sides of the maximum. We give quantitative estimates for analog experiments, where our entanglement criteria convert directly into concrete temperature and electric field constraints. These findings identify realistic regimes where the quantum character of Schwinger physics may be tested in the laboratory.
We examine the condition necessary for extracting entanglement from a quantum field through the use of two local modes A and B (detector modes). We show that Simon's entanglement criterion for the bipartite Gaussian state can be reformulated in terms of commutators between the canonical operators of the detector mode B and the partner mode P of the detector mode A. Using the profile representation of detector modes, we identify that harvesting is prohibited under certain specific conditions. According to analyses based on moving mirror models, Hawking radiation originates from the Milne modes at past null infinity, that reflect off at the mirror and ultimately transform into real particle modes. Drawing parallels between the Unruh effect and Hawking radiation, our findings indicate an absence of quantum correlations between ``real particles" emitted as Hawking radiation.
We present a general, analytic recipe to compute the entanglement that is generated between arbitrary, discrete modes of bosonic quantum fields by Bogoliubov transformations. Our setup allows the complete characterization of the quantum correlations in all Gaussian field states. Additionally, it holds for all Bogoliubov transformations. These are commonly applied in quantum optics for the description of squeezing operations, relate the mode decompositions of observers in different regions of curved spacetimes, and describe observers moving along non-stationary trajectories. We focus on a quantum optical example in a cavity quantum electrodynamics setting: an uncharged scalar field within a cavity provides a model for an optical resonator, in which entanglement is created by non-uniform acceleration. We show that the amount of generated entanglement can be magnified by initial single-mode squeezing, for which we provide an explicit formula. Applications to quantum fields in curved spacetimes, such as an expanding universe, are discussed.