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arXiv:2606.24613

The ωωω-Effect from a Multimode Squeezed Graviton State

Nick E. Mavromatos, Sarben Sarkar

gr-qchep-phhep-thquant-phSubmitted Jun 23, 2026• Announced Jun 24, 2026
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Abstract

The $ω$-effect in entangled neutral-meson systems provides a sensitive probe of CPT violation induced by quantum-gravitational environments. In open quantum systems, interactions with inaccessible gravitational degrees of freedom can render the reduced meson dynamics non-unitary, causing the CPT operator to become ill-defined, even when the underlying microscopic Hamiltonian is CPT invariant. We present a microscopic derivation of the $ω$-effect arising from a multimode squeezed gravitational environment generated by an axion cloud around a Kerr black hole. Using the Takagi decomposition of the associated complex symmetric squeezing kernel, the graviton field is expressed in terms of independent squeezed supermodes possessing anomalous correlators. These correlators provide a microscopic quantum counterpart of the stochastic fluctuations that appear in earlier D-particle foam descriptions of the $ω$-effect, replacing phenomenological variances of flavour-changing D-particle recoil by calculable graviton correlation functions. After tracing over the graviton bath, the anomalous correlators and the weak-interactions-induced mixing combine to generate transitions between the antisymmetric and symmetric two-meson sectors. This results in a small exchange-symmetric admixture, parametrised by $ω$, in the otherwise antisymmetric EPR state. We obtain an explicit expression for $ω$ in terms of a sum over Takagi supermodes weighted by their squeezing amplitudes and phases together with the weak-interaction flavour-mixing matrix element. The resulting framework suggests that the $ω$-effect may be a generic signature of non-classical states of gravitational environments, extending beyond the specific axion-cloud scenario considered here. The observability of the $ω$-effect from other astrophysical and microscopic black-hole sources is discussed.

Comments
35 pages revtex, no figures

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The ωωω-effect in entangled neutral-meson systems provides a sensitive probe of CPT violation induced by quantum-gravitational environments. In open quantum systems, interactions with inaccessible gravitational degrees of freedom can render the reduced meson dynamics non-unitary, causing the CPT operator to become ill-defined, even when the underlying microscopic Hamiltonian is CPT invariant. We present a microscopic derivation of the ωωω-effect arising from a multimode squeezed gravitational environment generated by an axion cloud around a Kerr black hole. Using the Takagi decomposition of the associated complex symmetric squeezing kernel, the graviton field is expressed in terms of independent squeezed supermodes possessing anomalous correlators. These correlators provide a microscopic quantum counterpart of the stochastic fluctuations that appear in earlier D-particle foam descriptions of the ωωω-effect, replacing phenomenological variances of flavour-changing D-particle recoil by calculable graviton correlation functions. After tracing over the graviton bath, the anomalous correlators and the weak-interactions-induced mixing combine to generate transitions between the antisymmetric and symmetric two-meson sectors. This results in a small exchange-symmetric admixture, parametrised by ωωω, in the otherwise antisymmetric EPR state. We obtain an explicit expression for ωωω in terms of a sum over Takagi supermodes weighted by their squeezing amplitudes and phases together with the weak-interaction flavour-mixing matrix element. The resulting framework suggests that the ωωω-effect may be a generic signature of non-classical states of gravitational environments, extending beyond the specific axion-cloud scenario considered here. The observability of the ωωω-effect from other astrophysical and microscopic black-hole sources is discussed.
We discuss two classes of semimicroscopic theoretical models of stochastic spacetime foam in quantum gravity and the associated effects on entangled states of neutral mesons, signalling an intrinsic breakdown of CPTCPTCPT invariance. One class of models deals with a specific model of foam, initially constructed in the context of noncritical (Liouville) string theory, but viewed here in the more general context of effective quantum-gravity models. The relevant Hamiltonian perturbation, describing the interaction of the meson with the foam medium, consists of off-diagonal stochastic metric fluctuations, connecting distinct mass eigenstates (or the appropriate generalization thereof in the case of KKK-mesons), and it is proportional to the relevant momentum transfer (along the direction of motion of the meson pair). There are two kinds of CPTCPTCPT-violating effects in this case, which can be experimentally disentangled: one (termed ``$\ensuremath{\omega}$-effect'') is associated with the failure of the indistinguishability between the neutral meson and its antiparticle, and affects certain symmetry properties of the initial state of the two-meson system; the second effect is generated by the time evolution of the system in the medium of the spacetime foam, and can result in time-dependent contributions of the $\ensuremath{\omega}$-effect type in the time profile of the two-meson state. Estimates of both effects are given, which show that, at least in certain models, such effects are not far from the sensitivity of experimental facilities available currently or in the near future. The other class of quantum-gravity models involves a medium of gravitational fluctuations which behaves like a ``thermal bath''. In this model both of the above-mentioned intrinsic CPTCPTCPT violation effects are not valid.
Quantum Gravity remains elusive, largely because its observable effects are suppressed by powers of the Planck scale. Direct detection of single gravitons is widely believed to be impossible. Here we propose a concrete astrophysical mechanism that may overcome this suppression. We show that superradiant axion-like-particle clouds surrounding rotating black holes can generate multimode squeezed states of gravitons containing up to 10610^6106 - 10710^7107 correlated quanta. Such states exhibit distinctive polarization correlations and quantum-noise signatures that could be detectable in future gravitational-wave interferometers. Observation of these signatures would constitute direct evidence for the quantum nature of gravitational radiation. Conversely, their absence can place constraints on axion-cloud lifetimes. Our approach also provides a test of General Relativity as an effective field theory.
The signal of ill-defined CPT weakening entanglement in the Bd{B_d}Bd​ B d system
In the presence of quantum-gravity fluctuations (space-time foam), the CPT operator may be ill-defined. Its perturbative treatment leads to a modification of the Einstein–Podolsky–Rosen correlation of the neutral meson system by adding an entanglement-weakening term of the wrong exchange symmetry, the ω\omega ω -effect. In the current paper we identify how to probe the complex ω\omega ω in the entangled BdB_dBd​ -system using the flavour (f)–CP(g) eigenstate decay channels: the connection between the intensities for the two time-ordered decays (f, g) and (g, f) is lost. Appropriate observables are constructed allowing independent experimental determinations of Re( ω\omega ω ) and Im( ω\omega ω ), disentangled from CPT violation in the evolution Hamiltonian Re( θ\theta θ ) and Im( θ\theta θ ). 2σ2\sigma 2σ tensions for both Re( θ\theta θ ) and Im( ω\omega ω ) are shown to be uncorrelated.
We establish the precise connection between the theoretical T, CP, CPT asymmetries, in terms of transition probabilities between the neutral meson B d states, and the experimental asymmetries, in terms of the double decay rate intensities for Flavour-CP eigenstate decay products in a B-Factory of entangled states. Genuine asymmetry parameters in the time distribution of the asymmetries are identified and their measurability analysed, disentangling genuine and possible fake terms. The nine asymmetry parameters – three different observables for each one of the three symmetries – are expressed in terms of the ingredients of the Weisskopf-Wigner dynamical description of the entangled B d -meson states and we obtain a global fit to their values from the BaBar Collaboration experimental results. The possible fake terms are all compatible with zero. The information content of the nine asymmetry parameters is indeed different. The non-vanishing and are impressive separate direct evidence of Time-Reversal-Violation and CP-Violation in these transitions (and compatible with Standard Model expectations). A 2σ effect for the Re(θ) parameter responsible of CPT-Violation appears; interpreted as an upper limit, it leads to eV at 95% C.L. for the diagonal flavour terms of the mass matrix. Finally, we consider scenarios where, in the presence of quantum gravity fluctuations (space-time foam), the CPT operator may be ill-defined. Its perturbative treatment leads to a modification of the Einstein-Podolsky-Rosen correlation of the neutral meson system by adding an Entanglement-weakening term of the wrong exchange symmetry, the ω -effect. The analysis is extended to identify how to probe the complex ω when the connection between the Intensities for the two time-ordered decays ( f, g ) and ( g, f ) is lost ( f flavour and g CP eigenstate decay channels), and how the ω -effect is disentangled from CPT violation in the evolution Hamiltonian.
Abstract. The possible role of decoherence due to space-time foam is discussed within the context of two models, one based on string/brane theory. and the other based on properties of black hole horizons in general relativity. It is argued that the density matrix satisfies a dissipative master equation, primarily from the study of renormalization group flows in non-critical string theory.This interpretation of the zero mode of the Liouville field as time leads necessarily to the CPT operator being ill defined. One striking consequence is that the quantum mechanical correlations of pair states of neutral mesons produced in meson factories are changed from the usual EPR state. The magnitude of this departure from EPR correlations is characterised by a parameter ω. The predicted value of ω is very small or zero. However it is shown explicitly that the the non-vanishing of ω is only a feature of the model based on string/brane theory. 1.
We derive and investigate the reduced dynamics of a nonrelativistic quantum matter system interacting with quantized gravitational waves. Because gravitational radiation couples tidally to the mass quadrupole moment, we emphasize that the leading interaction is quadratic in the mechanical displacement. Rather than treating it as a complication to be removed by linearization, we retain this full quadratic dependence, which gives rise to two-phonon rather single-phonon processes typical in dipolar interactions. We clarify its relation to the effective linear coupling that often appears in optomechanical literature, but which conceals the delicate quantum signatures of the full quadratic coupling. Using the Born-Markov and secular approximations, we microscopically derive Lindblad master equations for the matter dynamics induced by graviton baths in multi-mode vacuum, coherent, number, thermal, and squeezed states. We treat the ultraviolet-divergent Lamb-shift Hamiltonian by an explicit renormalization procedure, with the mechanical frequency identified as the physical frequency. Remarkably, owing to the nature of the interaction, the matter Hilbert space decomposes into even- and odd-parity sectors for all bath states considered. For a coherent graviton bath, the decoherence is identical to that of the vacuum, while the bath one-point function produces a coherent-shift Hamiltonian that exactly reproduces the tidal interaction with a classical gravitational wave. For a vacuum graviton bath, we recover the coherence protection between the two lowest mechanical number states, while number and thermal graviton baths remove this protection and enhance decoherence, although the effect remains small for realistic parameters. By contrast, a squeezed graviton bath enlarges the coupled coherence structure, and gives rise to a novel, coherence-protected sector spanned by dressed dark states.