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arXiv:2608.07257

The small effect of graviton-induced decoherence

Guri K. Buza, Marko Toroš

quant-phgr-qcSubmitted Aug 7, 2026• Announced Aug 10, 2026• 0 citations

Abstract

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.

Comments: 56 pages, 2 figures

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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.

We consider a quantum harmonic oscillator coupled with a graviton bath. We discuss the loss of coherence in the matter sector due to the matter-graviton vertex interaction, which leads to a loss of coherence provided that the matter-wave system is allowed to gravitons by the kinematics. Working in the quantum-field-theory framework, we obtain a master equation by tracing away the gravitational field at the leading order ∼O(G) and ∼O(c−2) . We find that the decoherence rate is proportional to the cube of the harmonic trapping frequency and vanishes for a free particle, as expected for a system without a mass quadrupole. Furthermore, our quantum model of graviton emission recovers the known classical formula for gravitational radiation from a classical harmonic oscillator for coherent states with a large occupation number. In addition, we find that the quantum harmonic oscillator eventually settles in a steady state with of the ground and first excited states. While classical emission of gravitational waves would make the harmonic system loose all of its energy, our quantum field theory model does not allow the number states |1⟩ and |0⟩ to decay via graviton emission. In particular, the superposition of number states 12[|0⟩+|1⟩] is a steady state and never decoheres. Published by the American Physical Society 2024

We revisit gravitational decoherence of matter superpositions using the leading soft sector of the graviton

S

-matrix. Starting from Weinberg's soft theorem and the overlap of coherent radiation states, we derive, for branch configurations with the same total four-momentum, a gauge-invariant, nonnegative leading-soft decoherence exponent and evaluate the polarization sum and angular integrals exactly at this order. In the vacuum, coherence between branches with distinguishable soft radiation vanishes as the infrared cutoff is removed. The leading nonrelativistic term is purely quadrupolar as a consequence of energy--momentum conservation. We extend the analysis to single- and two-mode squeezed graviton states, including the two-mode case motivated by inflation. Squeezing can enhance or suppress decoherence depending on the relative phase, while phase averaging gives an enhancement governed by the graviton occupation. For a phase-averaged relic background with an approximately flat energy-density spectrum over the relevant soft frequency band, the sharp-cutoff identification of the infrared scale with the inverse observation time gives a contribution that grows with the gravitational-wave energy density and with the fourth power of the observation time. These results connect soft-graviton scattering, infrared quantum information, and decoherence in nonvacuum gravitational backgrounds.

A unified framework is developed for determining whether a gravitational-wave (GW) background behaves as a classical field or as a genuinely quantum environment. Unified here means that both descriptions originate from the same tidal coupling derived from geodesic deviation, which yields an identical quadratic interaction Hamiltonian for the detector; the only distinction lies in whether the GW degrees of freedom are modeled as classical phase-randomized coherent states or as quantized graviton modes. Within this common framework, the reduced dynamics of a quantum harmonic oscillator exhibit a sharp structural contrast: a quantized graviton bath preserves coherence within the lowest phonon-number manifold, forming a protected sector at leading order, whereas a classical stochastic GW field inevitably induces decoherence even inside this subspace. This difference provides an operational criterion for diagnosing the classical or quantum nature of gravitational waves using mesoscopic optomechanical systems. Our results establish decoherence structure - not merely its magnitude - as a sensitive probe of gravitational quantumness and delineate the experimental regimes under which such tests may become feasible.

The intersection between quantum mechanics and gravitational physics has been providing challenging puzzles for decades. In this thesis, we study the dynamics of an open quantum system coupled with a bath of gravitons, the quanta of the gravitational field in the linear limit of general relativity. We focus on two main aspects. First, we analyze the decoherence induced by gravitons when we consider the open system to be described by both external and internal degrees of freedom. Since gravity is universal, the internal variables also interact with the gravitons, and here we show that this interaction leads to the decoherence of spatial superpositions of microscopic systems in the long-time regime, even when the graviton bath alone does not. We then proceed to the second main aspect, which is the entropy production that arises when an external agent drives a quantum system through the graviton bath. This irreversibility comes from quantum fluctuations of spacetime itself and, as such, has a fundamentally universal aspect.

We derive which-path decoherence for matter-wave interferometry that arises from tracing out the gravitons of linearized quantum gravity. Because the gravitons are driven linearly by the matter source, the branch-dependent evolution can be solved exactly, and the reduced coherence is given by the characteristic function of the initial graviton state, evaluated at the difference of the branch-induced field displacements. In vacuum, the decoherence exponent equals half the mean number of gravitons radiated by the difference source. For a smooth Gaussian trajectory, it reduces to

Γ_{\rm vac}=(8/15)\,Gm^2d^4/(\hbar c^5τ^4)

, ranging from

10^{-89}

to

10^{-61}

across representative matter-wave platforms. For a general squeezed graviton vacuum, we obtain an exact expression in which squeezing either suppresses or enhances the vacuum response, depending on the squeezing phase. For the strongly squeezed state produced by inflation, this expression reduces to

Γ_{\rm inf}=(π/20)\,Ω_{\rm inf}(md^2H_0/\hbar)^2

and reaches at most

\sim10^{-27}

for optimistic parameters. Hence, the which-path decoherence induced by radiative gravitons is therefore negligible in current matter-wave interferometers.

We identify the phase of a Bargmann invariant of two matter-wave interferometers as a quantum gravity signature that cannot be reproduced by any branchwise-definite classical gravitational field. For matter coupled linearly to linearized gravity, the interferometric coherence factorizes exactly into a conservative Newtonian phase, the characteristic functional of the graviton state, and a commutator phase. For Wigner-positive graviton states, the first two are classically reproducible; therefore, decoherence alone cannot certify that gravity is quantized. The Bargmann phase isolates the commutator, which is independent of the graviton state and of all Newtonian interactions and is bounded by which-path decoherence. For gravity, this radiation-reaction effect is sixty orders of magnitude below experimental reach, but trapped-ion analogs can test it at order unity.