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arXiv:2603.27180

Quantum gravitodiamagnetic interaction

Di Hao, Jiawei Hu, Hongwei Yu

gr-qchep-thquant-phSubmitted Mar 28, 2026• Announced Mar 31, 2026
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Abstract

In the framework of linearized quantum gravity, we investigate the quantum gravitational interaction induced by the gravitodiamagnetic coupling of two massive objects to vacuum fluctuations of the gravitational field. Starting from the Lagrangian of a particle in a gravitational field and employing the formalism of Weyl gravitoelectromagnetism, we derive the interaction Hamiltonian associated with gravitodiamagnetic coupling. Unlike the linear couplings that arise in gravitoelectric and gravitomagnetic interactions, the gravitodiamagnetic coupling depends quadratically on the gravitomagnetic field. Based on this Hamiltonian, we show that, for a spherically symmetric gravitational hydrogen-like system in its ground state, the induced quadrupole moment has the opposite sign to the applied gravitomagnetic field, which is the defining signature of gravitodiamagnetism. Using leading-order perturbation theory, we further obtain an explicit expression for the resulting interaction potential, which is attractive and scales as $r^{-11}$ at all separations, where $r$ denotes the distance between the two objects.

Comments
21 pages, 1 figure

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In the framework of linearized quantum gravity, we investigate the quantum gravitational interaction induced by the gravitodiamagnetic coupling of two massive objects to vacuum fluctuations of the gravitational field. Starting from the Lagrangian of a particle in a gravitational field and employing the formalism of Weyl gravitoelectromagnetism, we derive the interaction Hamiltonian associated with gravitodiamagnetic coupling. Unlike the linear couplings that arise in gravitoelectric and gravitomagnetic interactions, the gravitodiamagnetic coupling depends quadratically on the gravitomagnetic field. Based on this Hamiltonian, we show that, for a spherically symmetric gravitational hydrogen-like system in its ground state, the induced quadrupole moment has the opposite sign to the applied gravitomagnetic field, which is the defining signature of gravitodiamagnetism. Using leading-order perturbation theory, we further obtain an explicit expression for the resulting interaction potential, which is attractive and scales as r−11r^{-11}r−11 at all separations, where rrr denotes the distance between the two objects.
We investigate gravitationally generated entanglement in two quantum harmonic oscillators induced by quadratic (Stelle) gravity, including corrections up to 1.51.51.5 post-Newtonian order. Starting from the quadratic action, we derive the effective two-body Hamiltonian for two harmonically trapped masses, incorporating the contributions of the massive spin-222 ghost (m2m_2m2​) and massive spin-000 (m0m_0m0​) degrees of freedom of the gravitational field. For two quantised oscillators prepared in their ground state, we compute the von Neumann and Rényi entropies of the reduced state and identify a frequency at which the gravitationally-induced entanglement vanishes due to cancellation between relativistic momentum squeezing and quantum-delocalisation-induced position squeezing. We further analyze the cancellation frequency and derive the approximate constraint m0<43 m2m_0 < \sqrt[3]{4}\, m_2m0​<34​m2​ for the spin-222 and spin-000 modes. This relation follows from demanding a stable harmonic oscillator description. Finally, we study gravitationally-induced concurrence in a non-Gaussian setup and show how quadratic gravity modifies the entanglement generated between two spatial superpositions. The concurrence can approach O(1)\mathcal{O}(1)O(1) for certain choices of mass, spatial superposition, particle distance, and spin-222 and spin-000 modes. The concurrence will deviate from Newtonian gravity at certain particle separations, depending on the energy of the spin-222 and spin-000 modes. For example, spin modes as low as 0.01970.01970.0197 eV become distinguishable from Newtonian gravity at a distance d∼40μd \sim 40 μd∼40μm. This allows us to constrain the spin-222 and spin-000 masses in experiments.
We formulate the gravitationally induced quantum decoherence of a massive object prepared in a spatial superposition. Starting from linearized gravity coupled to a massive system particle and an environmental scalar field, we derive a closed-time-path influence functional governing the reduced system dynamics. In the nonrelativistic and quasi-static regime, the decoherence exponent can be written as a bilinear functional of the difference of the system stress-energy tensors and an effective noise kernel obtained by dressing the environmental stress-energy tensor correlator with graviton propagators. We then apply this framework to the Newtonian long-range gravitational interaction and evaluate the resulting decoherence function for a dilute nonrelativistic gas modeled by finite wave packets and coarse-grained in time and space. By performing controlled approximations, we obtain analytic expressions for the cumulative decoherence function and show that the dominant contribution is accumulated logarithmically over a broad range of distances, while remaining subdominant to conventional collisional decoherence under realistic conditions.
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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 introduce a general gravity-related collapse mechanism based on linearized gravity. Starting from the weak-field limit of general relativity, gravitoelectromagnetism suggests an effective coupling between the gravitoelectric potential and the mass density distribution. At the same time, it provides a similar relation for the gravitomagnetic vector potential and the mass current. Following a hybrid (classical-quantum) dynamics approach, these couplings lead to a master equation whose non-unitary part is determined by the underlying mass distribution and currents. When the gravitoelectric potential coupling is considered, the well-known Diósi-Penrose collapse model acting on positional degrees of freedom is recovered. However, upon including the gravitomagnetic vector potential, additional collapse mechanisms emerge for rotational degrees of freedom as well as for mixed mass-rotation contributions.
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