The unification of Einstein's general relativity and quantum mechanics remains a central challenge in modern physics. A crucial piece of evidence missing is direct experimental verification of quantum gravity. While cosmological observations offer potential indirect clues, recent advancements in quantum control of various systems have opened doors for laboratory-based low-energy investigations. This research is driven by the increasing ability to manipulate quantum phenomena at various mass scales, including large molecules, opto-mechanical systems, and macroscopic resonators. While many proposals focus on testing phenomenological quantum gravity models or effects stemming from quantum noise or large gravitational source masses, the direct detection of single spin-2 gravitons – the most direct evidence of quantum gravity – has been deemed nearly impossible. This paper challenges this assertion by proposing a novel method for detecting single gravitons using quantum sensing and a gravito-phonic analog of the photoelectric effect.

Existing literature extensively explores theoretical aspects of quantum gravity and proposes various experimental tests. Cosmological observations are considered, although the detection of single gravitons remains elusive. Several experimental approaches utilize quantum systems, including tests of modified quantum dynamics stemming from hypothetical quantum gravity phenomenology, and studies of entanglement potentially generated by gravitating masses in superposition. These latter methods often rely on the challenging creation of macroscopic quantum superpositions. Previous proposals to test entanglement generation using gravity focus on expected Newtonian interactions between static masses in superposition. Prior research also considers the effects of quantum noise from gravitons, but these remain beyond current experimental capabilities. The challenge highlighted in many papers is the exceedingly weak interaction strength between gravitational waves and matter, making graviton detection extremely difficult.

The authors propose a novel approach to detect single gravitons using massive quantum acoustic resonators, cooled to their ground state. The interaction between gravitational waves and these resonators is analyzed using the linearized Einstein equations in the weak field limit, quantized to describe gravitons analogous to photons. The Hamiltonian describing the interaction between the gravitational field (quantized as gravitons) and the matter (the resonator) is derived, considering both stimulated and spontaneous emission and absorption. Fermi's Golden Rule is applied to calculate the spontaneous and stimulated emission and absorption rates. The analysis reveals that the spontaneous emission rate remains extremely small for typical masses, while the stimulated emission and absorption rates open possibilities for experimental detection. The rate of stimulated transition between the ground and first excited states of the resonator is derived, demonstrating that for appropriately chosen parameters (large mass resonator, suitable gravitational wave amplitude), the rate can become appreciable, allowing for the resolution of single graviton absorption events. The full quantum mechanical treatment considers the dynamics of individual atoms in the resonator and derives the interaction Hamiltonian, considering both the leading contribution (macroscopic effective interaction from the gradient of the quadrupole moment) and a sub-leading contribution (direct quadrupole interaction). The authors solve the dynamics exactly for a single mode gravitational wave using a time-dependent Magnus expansion, finding that an initial vacuum state of the resonator evolves into a coherent state. The probability of detecting a single graviton absorption is derived and maximized by selecting the appropriate resonator mass. The methodology includes applying the derived results to various gravitational wave sources, including compact binary mergers (correlating with LIGO detections), continuous waves from neutron stars, and hypothetical high-frequency sources. The experimental feasibility is assessed by considering ground state cooling requirements, noise sources (thermal fluctuations, electronic noise), and the development of appropriate quantum sensing techniques capable of detecting single energy quanta changes in kilogram-scale resonators. Numerical simulations of time-continuous, weak, number-resolving quantum measurements of the resonator are presented, illustrating the detection of a single graviton absorption from a gravitational wave. The simulations incorporate various noise sources. The authors also explore optimizing the detector parameters (mass, frequency, material) to maximize single graviton detection probabilities for different types of gravitational wave sources. A detailed microscopic derivation of the collective interaction between the gravitational wave and the solid-bar resonator is provided, considering the dynamics of individual atoms.

The study's central finding is that detecting single gravitons via stimulated absorption is within reach of current and near-future experimental capabilities. The authors demonstrate that the weak coupling of gravitational waves to matter, which previously posed a significant obstacle, is advantageous in this context, facilitating the isolation of single graviton absorption events. The analysis shows that the stimulated absorption rate can become appreciable for massive quantum acoustic resonators, allowing single graviton transitions to be resolved through continuous sensing of quantum jumps. A crucial aspect is the capability to perform continuous, weak measurements of the resonator's energy, allowing for the detection of individual energy quanta transitions. The authors derive a formula for the optimal mass of the resonator to maximize the probability of a single graviton absorption. They apply this methodology to various gravitational wave sources, including compact binary mergers detectable by LIGO, continuous waves from neutron stars, and hypothetical high-frequency sources. The analysis identifies suitable resonator materials (beryllium, niobium, etc.) and specifies the required temperature and quality factor for the resonator. For compact binary mergers, the authors show that the optimal mass of the resonator is determined by the chirp mass of the binary system and the gravitational wave amplitude. The analysis of the gravitational wave from the NS-NS merger GW170817 demonstrates the feasibility of detecting a single graviton from such an event using a beryllium resonator with specific parameters. Simulations incorporating realistic noise levels confirm the potential to detect single graviton absorption. The key to the proposed detection method is the continuous monitoring of the resonator's energy levels, which is a significant experimental challenge but within the scope of ongoing advancements in quantum sensing. The study also highlights that the success of the proposed method relies heavily on correlating the detected single-graviton absorption events with independent classical LIGO detections of the same gravitational wave, providing further confirmation of the origin and nature of the detected event.

The successful implementation of the proposed experimental scheme would represent a landmark achievement, providing the first experimental evidence for the quantization of gravity. The analogy to the photoelectric effect—the historically significant experiment demonstrating the quantization of light—is highlighted. The authors emphasize that the focus is not on directly observing the quantum state of the graviton but rather on observing the exchange of a single quantum of energy between the gravitational wave and the resonator, analogous to the energy conservation in the photoelectric effect. The ability to continuously monitor and detect single energy quanta transitions is crucial, distinguishing this approach from previous attempts that focused on average energy transfer. The study's implications extend beyond the direct detection of gravitons, offering insights into fundamental aspects of quantum gravity and providing a novel experimental platform to explore the quantum behavior of gravity at macroscopic scales. The authors also note that while the linearized theory used in the analysis is well understood, there might be unexpected phenomena during the exchange of single quanta, underscoring the importance of experimental validation. The proposed method complements other tabletop tests of quantum gravity, offering a distinct approach that does not rely on macroscopic quantum superpositions.

This research presents a compelling theoretical framework and a feasible experimental pathway toward detecting single gravitons. The authors demonstrate that by leveraging advancements in quantum sensing and utilizing massive acoustic resonators, the detection of single gravitons, through stimulated absorption, becomes attainable. The proposed method relies on continuous monitoring of energy level changes, coupled with correlations to independent LIGO detections, to confirm graviton absorption from gravitational waves. Future research should focus on the experimental implementation of this protocol, building upon ongoing advancements in quantum sensing and ground state cooling of macroscopic mechanical resonators. The success of this endeavor would offer a groundbreaking confirmation of the quantization of gravity.

The proposed experimental scheme presents significant technological challenges. Achieving the necessary ground state cooling of kilogram-scale resonators and developing quantum sensing techniques with sufficient resolution to detect single energy quanta transitions require substantial advancements in experimental capabilities. The theoretical analysis uses the linearized theory of gravity in the weak field approximation, which might not be fully accurate in the regime where single graviton effects are observed. The accuracy of the simulations relies on the accuracy of the noise model used, and additional noise sources not explicitly considered in the simulations may affect the results. Correlating the single graviton detection events with independent LIGO detections assumes the presence of detectable gravitational waves from known sources within the resonator's frequency band. The absence of such correlating events will make it challenging to confirm the origin of the detected events.