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arXiv:2511.09169

Boosting Gravity-Induced Entanglement through Parametric Resonance

Yuka Shiomatsu, Youka Kaku, Akira Matsumura, Tomohiro Fujita

gr-qcquant-phSubmitted Nov 12, 2025• Announced Nov 13, 2025
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Abstract

Establishing quantum gravity theory remains one of the major challenges in modern physics, as the lack of experimental evidence makes it difficult to explore. In response to this challenge, proposals to test quantum entanglement induced by Newtonian gravity in table-top experiments have attracted significant attention as a potentially feasible approach far below the Planck energy scale. In this work, we propose a scheme to amplify gravity-induced entanglement between two masses using parametric resonance. Specifically, we consider two parametrically resonant oscillators interacting through Newtonian gravity, each governed by the Mathieu equation. We analyzed the logarithmic negativity between two oscillators and investigate the effects of random force noise and linear damping. As a result, we find an exponential growth of gravity-induced entanglement between the oscillators, which reflects the dynamical instability of parametric resonant systems.

Comments
11 pages, 6 figures

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Establishing quantum gravity theory remains one of the major challenges in modern physics, as the lack of experimental evidence makes it difficult to explore. In response to this challenge, proposals to test quantum entanglement induced by Newtonian gravity in table-top experiments have attracted significant attention as a potentially feasible approach far below the Planck energy scale. In this work, we propose a scheme to amplify gravity-induced entanglement between two masses using parametric resonance. Specifically, we consider two parametrically resonant oscillators interacting through Newtonian gravity, each governed by the Mathieu equation. We analyzed the logarithmic negativity between two oscillators and investigate the effects of random force noise and linear damping. As a result, we find an exponential growth of gravity-induced entanglement between the oscillators, which reflects the dynamical instability of parametric resonant systems.
We propose a novel method to probe gravity-induced entanglement. We consider the gravitational interaction between a particle trapped in a shallow potential and a harmonic oscillator. The harmonic oscillator is in a quantum superposition of two frequencies and only one of these states can excite the trapped particle via resonance. Once the excited particle is detected, the quantum state of the oscillator is collapsed, which can be observed as the sudden disappearance of the superposition of oscillator frequencies. Thus, the sudden decoherence, which is only triggered by particle detection, can be a smoking gun evidence of gravity-induced entanglement. Since the probability of particle excitation increases linearly with time, the total probability is multiplied by repeating experiments. We will also discuss experimental implementations using optomechanics.
Gravity-induced entanglement has been proposed as a method for testing the non-classical nature of gravity via tabletop experiments. While most existing proposals are restricted to the Newtonian limit, the frame dragging effect offers access to genuinely post-Newtonian features of the gravitational interaction and remains comparatively less explored. Here, we study gravity-induced entanglement generated by frame dragging in an interferometric setting and compute the entanglement phase between the rotational degrees of freedom of a source mass and the paths of a particle in two complementary ways: (i) via Schrödinger evolution with a quantized Lense-Thirring Hamiltonian in the large angular momentum limit, and (ii) via the on-shell action of linearized quantum gravity within the stationary phase approximation. Both approaches yield the same entanglement phase, consistent with the proper time difference between the interferometer arms. The path integral derivation further reveals how gravitational retardation modifies the entanglement phase, thereby making the local, relativistically causal linearized-gravity description explicit. Under the standard locality/mediator assumptions used in existing arguments, the resulting entanglement would witness non-classicality of the gravitational interaction.
We propose an experiment to test the non-classicality of the gravitational interaction. We consider two optomechanical systems that are perfectly isolated, except for a weak gravitational coupling. If a suitable resonance condition is satisfied, an optical signal can be transmitted from one system to the other over a narrow frequency band, a phenomenon that we call gravitationally induced transparency. In this framework, the challenging problem of testing the quantum nature of gravity is mapped to the easier task of determining the non-classicality of the gravitationally-induced optical channel: If the optical channel is not entanglement-breaking, then gravity must have a quantum nature. This approach is applicable without making any assumption on the, currently unknown, correct model of gravity in the quantum regime. In the second part of this work, we model gravity as a quadratic Hamiltonian interaction (e.g. a weak Newtonian force), resulting in a Gaussian thermal attenuator channel between the two systems. Depending on the strength of thermal noise, the system presents a sharp transition from an entanglement-breaking to a non-classical channel capable not only of entanglement preservation but also of asymptotically perfect quantum communication.
The quest for a quantum theory of gravity remains a central challenge in modern physics, driven by the goal of unifying general relativity and quantum mechanics. Direct experimental access to quantum gravitational effects is notoriously difficult due to the inaccessibility of the Planck scale. Recent proposals, however, suggest that gravitationally induced quantum entanglement between two massive particles, realized through advanced quantum interferometric techniques, could provide empirical evidence for the quantum nature of gravity. We demonstrate that the geometrical configuration of an interferometer plays a decisive role in entanglement generation. Our analysis reveals that geometric optimization can substantially enhance the gravitationally induced phase shift, thereby improving the prospects for experimental detection of gravity-mediated entanglement. Moreover, we show that standard approximations employed in prior proposals may severely limit predictive accuracy and compromise experimental feasibility.
Abstract One of the outstanding questions in modern physics is how to test whether gravity is classical or quantum in a laboratory. Recently there has been a proposal to test the quantum nature of gravity by creating quantum superpositions of two nearby neutral masses, close enough that the quantum nature of gravity can entangle the two quantum systems, but still sufficiently far away that all other known Standard Model interactions remain negligible. However, preparing superposition states of a neutral mass (the light system) requires the vicinity of laboratory apparatus (the heavy system). We will suppose that such a heavy system can be modelled as another quantum system; since gravity is universal, the lighter system can get entangled with the heavier system, providing an inherent source of gravitational decoherence. In this paper, we will consider a toy model composed of two light and two heavy quantum oscillators prepared in the motional ground state, forming pairs of probe-detector systems, and study under what conditions the entanglement between two light systems evades the decoherence induced by the heavy systems. We conclude by estimating the decoherence in the proposed experiment for testing the quantum nature of gravity.
One of the major challenges of modern foundational physics is the combination of quantum physics and general relativity into a theory of quantum gravity. A severe obstacle are the required extremely high energy scales for direct tests of quantum gravity effects. In recent years, attention has shifted towards near-future experimental predictions of effective or phenomenological models, such as gravitationally induced entanglement or interactions of linearized gravity with non-relativistic measurement devices. These developments motivate us to study the coupling between the quantized metric perturbation and an anisotropic quantum rigid rotor. The intuitive motivation for our study is that a sufficiently heavy rotor consists of a very large number of component systems. Although quantum gravitational effects are completely negligible at the scale of a single atom or molecule, the effects can get amplified by the sheer number of constituents. The resulting effective model describes the gravitational analogue of the angulon quasiparticle excitations discussed in condensed matter physics, suggesting a pathway for future analogue experiments. As a first concrete test of our model, we derive the gravitational Lamb shift for the energy eigenstates of the rotor, which become dressed by a cloud of virtual gravitons. Although the effect is very small, it could provide a concrete test for whether gravity is truly quantum.