Decoherence of the quantum superradiant cloud from graviton emission

arXiv:2610.30723 · gr-qc, astro-ph.CO, hep-ph · Submitted 2026-10-22 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: We're looking at the paper: "Decoherence of the quantum superradiant cloud from graviton emission".

Jocelyn: Here's the gist of the paper. Graviton emission suppresses interference between cloud configurations with different amplitudes, but leaves interference between configurations that differ only by an overall sign unchanged, and this suppression becomes significant when the expected number of emitted gravitons is of order unity Quantum Superradiant Cloud Description The paper studies the evolution of the quantum superradiant cloud under the effect of graviton emission The growing component of the cloud admits a classical statistical description even in the absence of decoherence However, the full state of the cloud remains coherent and entangled The quantum description involves quantizing a massive scalar field on Kerr spacetime, where the field operator is represented by linear combinations of mode functions v+ and v- The Hamiltonian of the superradiant mode shows that the instability can be regarded as two-mode squeezing Effect of Graviton Emission on Quantum Correlations The decoherence induced by graviton emission has been studied for superpositions of massive particles The master equation of the density matrix is derived by tracing out the graviton environment The interference between the cloud with different amplitude would be significantly suppressed For typical configurations of the cloud seeded by the vacuum fluctuation, this suppression becomes significant when the expected number of emitted gravitons exceeds order unity At a larger occupation number, all first and second moments can be reproduced by a classical mixture of coherent states Measurements of the first and second moments alone cannot distinguish the cloud from such a classical mixture Decoherence Time Scale The decoherence time in the regime where interference is suppressed is given by td = 1 / (4ωI log 8ωI γgw) The occupation number evaluated at t = td in the free evolution is Nd = sinh 2(ωI td) r ωI squared γgw >> 1 This indicates strong suppression of the off-diagonal elements of the density matrix for c squared - c'squared >> Nd/N The expected number of gravitons emitted by time t is ngrav(t) γgw / 8ωI e 4ωI t - 1 At time td, we find ngrav(td) 1 Evolution of Moments and Entanglement Certification The evolution of the covariance matrix is calculated to see how graviton emission changes the covariance matrix The master equation gives dM4 dt = 2ωIM4 - γgw M6 The evolution of G2 is the same as for free evolution G2(t) = e 2ωI t The particle number difference Q = ⟨n+ - n-⟩ evolves as dQ/dt = -γgw / 4ωI e 4ωI t - 1 When substituting M2, G2, and Q into the entanglement criterion Eq.

Vera: (40), the squeezing first decreases˜ν−, while graviton emission eventually makes it increase The covariance matrix still certifies entanglement when quantum interference starts to be suppressed When˜ν− reaches 1/2, the matrix V-I/2 is positive semidefinite, and all first and second moments can be reproduced by a classical statistical mixture of coherent states Comparison of Scales The scales are compared against the occupation numbers at which the classical growth of the cloud is significantly modified The suppression of interference occurs much before spin-down saturation N Nent The loss of entanglement certification by the covariance matrix occurs when N Nent These events happen when the effect of energy loss due to graviton on the growth of the cloud is small Graviton emission suppresses quantum interference between different growing mode amplitudes and erases the entanglement signature accessible by first and second moments The occupation numbers continue to grow approximately as in the free evolution The contribution of gravitons associated with horizon flux also remains to be evaluated Page 1 --- Decoherence of the quantum superradiant cloud from graviton emission Lingyun Fu∗ Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road,Cambridge, CB3 0WA, UK Hidetoshi Omiya† Department of Physics, Kyoto University, Kyoto 606-8502, Japan Takahiro Tanaka‡ Department of Physics, Kyoto University, Kyoto 606-8502.

Jocelyn: and Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University.

Vera: Hui-Yu Zhu§ Cosmology, Gravity and Astroparticle Physics Group, Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS), Daejeon, 34126, Korea (Dated: October 23, 2026) Black hole superradiance amplifies vacuum fluctuations into a macroscopic cloud of a massive bosonic field around a rotating black hole Under free evolution, the quantum cloud is a two-mode squeezed state that remains entangled even at large occupation numbers, while its growing component admits a classical statistical description In this work, we study how graviton emission changes the quantum state of the cloud We find that graviton emission suppresses interference between cloud configurations with different amplitudes, but leaves interference between configurations that differ only by an overall sign unchanged For typical configurations realized under vacuum fluctuations, the suppression becomes significant when the expected number of emitted gravitons is of order unity We also show that, at larger occupation numbers, all first and second moments can be reproduced by a statistical mixture of coherent states For the astrophysical black holes, both changes occur much before the spin-down of the black hole becomes significant I.

Paper summary: Vera: So looking at "Decoherence of the quantum superradiant cloud from graviton emission," we see this paper investigates how graviton emission alters the quantum state of a bosonic field amplified around a rotating black hole.

Jocelyn: The title suggests they’re focusing on the decoherence part, and what they find is that gravitons suppress interference between different amplitude configurations while leaving sign-dependent interference intact.

Subrahmanyan: The implication for us is that this suppression becomes noticeable when we expect about one graviton to be emitted, which sets a concrete threshold for when the quantum nature of the cloud starts to wash out.

Vera: And they show that at higher occupation numbers, we can’t distinguish the quantum state from a classical statistical mixture based on just looking at first and second moments.

Jocelyn: It boils down to saying that while the full state is still coherent, it loses a measurable quantum signature when graviton emission is active and the occupation number is high enough.

Subrahmanyan: The authors compare this effect to what happens in astrophysical black holes, noting that these changes occur well before spin-down saturation begins.

Vera: It means we might be able to probe these quantum effects in systems that aren't fully settled into their final spin state yet.

Jocelyn: What this does for time-domain astronomy is telling us that the environmental interactions, like graviton emission, are active early on in the superradiant process.

Conclusion: Vera: So we’re wrapping up this look at "Decoherence of the quantum superradiant cloud from graviton emission." Basically, this paper is showing how emitting gravitons messes with the quantum state of that massive cloud around a black hole.

Jocelyn: Right. It’s about taking something that started out being entangled and seeing how it gets smeared out by the environment—the gravitational radiation—and what that means for what we can actually measure.

Subrahmanyan: The core finding is that graviton emission kills the interference between different versions of the cloud, but it leaves the interference between configurations that just have opposite signs unchanged. That’s a specific kind of suppression.

Vera: And they pinpoint exactly when this suppression becomes important: when you expect about one graviton to be emitted at any given time. It’s not a gradual decay; it happens once you hit that expected number of gravitons being roughly one.

Jocelyn: That’s a key point for us in radio astronomy because it gives us a timescale for when these quantum effects might fade away from the observable signal we see.

Subrahmanyan: The paper also shows that if the occupation number of particles gets really high, you can’t tell the cloud apart from just some random classical statistical mixture when you only look at the first and second moments. That means those specific moments won't give you any extra quantum info anymore in that regime.

Vera: So to sum it up, the paper argues that graviton emission erases a specific type of quantum entanglement signature accessible by just looking at the first two statistical moments. It’s a limitation on what those simple measurements can tell us about the cloud's true quantum nature.

Jocelyn: It suggests that for astrophysical black holes, these changes happen much earlier than you might think, well before the spin-down process itself becomes a big deal in terms of energy loss.

Subrahmanyan: That's interesting because it links the quantum description directly to the dynamics we expect from those systems over long timescales.

Vera: It’s definitely worth tracking how this affects our models for black hole evolution and what kind of gravitational wave signals we might be able to distinguish later on.

Lingyun Fu, Hidetoshi Omiya, Takahiro Tanaka, Hui-Yu Zhu

University of Cambridge · Kyoto University · Yukawa Institute for Theoretical Physics, Kyoto University, Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS)

gr-qc, astro-ph.CO, hep-ph

Submitted: 2026-10-22

Updated: 2026-10-22

Comments: 13 pages, 1 figure

License: http://creativecommons.org/licenses/by/4.0/

The gist: The gist: Graviton emission suppresses interference between cloud configurations with different amplitudes, but leaves interference between configurations that differ only by an overall sign

Key concepts

Black Hole Superradiance: This process involves a rotating black hole amplifying vacuum fluctuations into a macroscopic cloud of a massive bosonic field. This amplification leads to an instability where the cloud grows spontaneously from quantum fluctuations.
Two-Mode Squeezed State: Under free evolution, the quantum superradiant cloud is described as a two-mode squeezed state. This means the quantum state is entangled, and it remains so even when the number of particles in each mode becomes very large.
Graviton Emission Suppression: When gravitons are emitted from the cloud, they cause decoherence that significantly suppresses interference between cloud configurations having different amplitudes. This effect is most pronounced when the expected number of emitted gravitons is approximately one.

Terminology

Decoherence — 1× in this paper · explained in 2 episodes

Summary

The gist: Graviton emission suppresses interference between cloud configurations with different amplitudes, but leaves interference between configurations that differ only by an overall sign unchanged, and this suppression becomes significant when the expected number of emitted gravitons is of order unity

Quantum Superradiant Cloud Description

The paper studies the evolution of the quantum superradiant cloud under the effect of graviton emission The growing component of the cloud admits a classical statistical description even in the absence of decoherence However, the full state of the cloud remains coherent and entangled The quantum description involves quantizing a massive scalar field on Kerr spacetime, where the field operator is represented by linear combinations of mode functions v+ and v- The Hamiltonian of the superradiant mode shows that the instability can be regarded as two-mode squeezing

Effect of Graviton Emission on Quantum Correlations

The decoherence induced by graviton emission has been studied for superpositions of massive particles The master equation of the density matrix is derived by tracing out the graviton environment The interference between the cloud with different amplitude would be significantly suppressed For typical configurations of the cloud seeded by the vacuum fluctuation, this suppression becomes significant when the expected number of emitted gravitons exceeds order unity At a larger occupation number, all first and second moments can be reproduced by a classical mixture of coherent states Measurements of the first and second moments alone cannot distinguish the cloud from such a classical mixture

Decoherence Time Scale

The decoherence time in the regime where interference is suppressed is given by td = 1 / (4ωI log 8ωI γgw) The occupation number evaluated at t = td in the free evolution is Nd = sinh 2(ωI td) r ωI squared γgw >> 1 This indicates strong suppression of the off-diagonal elements of the density matrix for c squared - c'squared >> Nd/N The expected number of gravitons emitted by time t is ngrav(t) γgw / 8ωI e 4ωI t - 1 At time td, we find ngrav(td) 1

Evolution of Moments and Entanglement Certification

The evolution of the covariance matrix is calculated to see how graviton emission changes the covariance matrix The master equation gives dM4 dt = 2ωIM4 - γgw M6 The evolution of G2 is the same as for free evolution G2(t) = e 2ωI t The particle number difference Q = ⟨n+ - n-⟩ evolves as dQ/dt = -γgw / 4ωI e 4ωI t - 1 When substituting M2, G2, and Q into the entanglement criterion Eq. (40), the squeezing first decreases˜ν−, while graviton emission eventually makes it increase The covariance matrix still certifies entanglement when quantum interference starts to be suppressed When˜ν− reaches 1/2, the matrix V-I/2 is positive semidefinite, and all first and second moments can be reproduced by a classical statistical mixture of coherent states

Comparison of Scales

The scales are compared against the occupation numbers at which the classical growth of the cloud is significantly modified The suppression of interference occurs much before spin-down saturation N ~ Nent The loss of entanglement certification by the covariance matrix occurs when N ~ Nent These events happen when the effect of energy loss due to graviton on the growth of the cloud is small

Conclusion

Graviton emission suppresses quantum interference between different growing mode amplitudes and erases the entanglement signature accessible by first and second moments The occupation numbers continue to grow approximately as in the free evolution The contribution of gravitons associated with horizon flux also remains to be evaluated

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Decoherence of the quantum superradiant cloud from graviton emission Lingyun Fu∗ Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road,Cambridge, CB3 0WA, UK Hidetoshi Omiya† Department of Physics, Kyoto University, Kyoto 606-8502, Japan Takahiro Tanaka‡ Department of Physics, Kyoto University, Kyoto 606-8502. and Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University. Hui-Yu Zhu§ Cosmology, Gravity and Astroparticle Physics Group, Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS), Daejeon, 34126, Korea (Dated: October 23, 2026) Black hole superradiance amplifies vacuum fluctuations into a macroscopic cloud of a massive bosonic field around a rotating black hole Under free evolution, the quantum cloud is a two-mode squeezed state that remains entangled even at large occupation numbers, while its growing component admits a classical statistical description In this work, we study how graviton emission changes the quantum state of the cloud We find that graviton emission suppresses interference between cloud configurations with different amplitudes, but leaves interference between configurations that differ only by an overall sign unchanged For typical configurations realized under vacuum fluctuations, the suppression becomes significant when the expected number of emitted gravitons is of order unity We also show that, at larger occupation numbers, all first and second moments can be reproduced by a statistical mixture of coherent states For the astrophysical black holes, both changes occur much before the spin-down of the black hole becomes significant I. INTRODUCTION Black hole superradiance, a process in which bosonic waves extract energy from a rotating black hole [1], provides a promising way to search for ultralight bosonic fields [2–4] For a massive bosonic field, the amplified modes can remain gravitationally bound to the black hole, repeatedly undergoing superradiant amplification, leading to an instability [5–8] The instability results in the spontaneous formation of a macroscopic cloud that can potentially produce various observational signatures Such observable signatures are the characteristic black hole spin distributions [9–12], gravitational waves emitted from the cloud with frequencies can fall within the sensitivity bands of current and future gravitational wave detectors [13–21], modifications to binary dynamics and stellar orbits [22–40], and imprints on photon ring observations [41, 42] The cloud is generally assumed to grow from quantum fluctuations and then amplified by the superradiant instability However, large occupation alone does not justify the classical description Interactions with the environment have been suggested as a possible mechanism [44], but no explicit description of this process was given in that work In Ref.

Improvements for AI systems

System capable of predicting decoherence times for quantum superradiant clouds based on expected graviton emission numbers. This allows for a quantitative assessment of when quantum interference between cloud configurations with different amplitudes becomes significantly suppressed, specifically when the expected number of emitted gravitons exceeds order unity.
AI system that can distinguish between classical statistical mixtures and true quantum states using only the first and second moments of the cloud observables. This capability stems from finding that all first and second moments can be reproduced by a classical mixture of coherent states, meaning measurements alone cannot distinguish the cloud from such a classical mixture.
AI system capable of predicting entanglement loss in two-mode squeezed states under environmental coupling by analyzing the evolution of the covariance matrix. The system can identify that the uncertainty relation (23) reduces to the condition νtilde minus 1/2 and when this bound is violated, the two modes therefore remain entangled even when a large occupation number is realized.
AI system that can estimate critical occupation numbers for entanglement loss based on the ratio of different physical scales. This allows it to predict that "the suppression of the interference between the different growing mode amplitude basis (N Nd) and the loss of the entanglement certification by the covariance matrix (N Nent) occur much before spin-down saturation (N Nstar)."
AI system that can model non-classicality in evolving quantum states under dissipation using higher moments or full density matrices. Since the cloud becomes non-Gaussian under the non-linear dissipation D[c2g], the system can determine if "the non-classicality remains after N >= Nent" by analyzing moments beyond the first and second.

Abstract

Black hole superradiance amplifies vacuum fluctuations into a macroscopic cloud of a massive bosonic field around a rotating black hole. Under free evolution, the quantum cloud is a two-mode squeezed state that remains entangled even at large occupation numbers, while its growing component admits a classical statistical description. In this work, we study how graviton emission changes the quantum state of the cloud. We find that graviton emission suppresses interference between cloud configurations with different amplitudes, but leaves interference between configurations that differ only by an overall sign unchanged. For typical configurations realized under vacuum fluctuations, the suppression becomes significant when the expected number of emitted gravitons is of order unity.We also show that, at larger occupation numbers, all first and second moments can be reproduced by a statistical mixture of coherent states. For the astrophysical black holes, both changes occur much before the spin-down of the black hole becomes significant.