Detecting single gravitons with quantum sensing

The study tackles the longstanding challenge of finding experimental evidence for quantum aspects of gravity. While linearized gravity is well understood theoretically and predicts gravitons as quantized excitations of gravitational waves, direct evidence is lacking. Prior laboratory proposals have either targeted phenomenological modifications to quantum mechanics or effects far beyond current experimental reach. This work proposes that single-graviton exchange with matter can leave observable signatures in massive quantum acoustic resonators operated in the quantum regime. The central hypothesis is that weak but coherent coupling of gravitational waves to internal modes of macroscopic resonators, combined with ground-state preparation and continuous, number-resolving energy measurements, can enable detection of single stimulated absorption events—quantum jumps—from gravitational waves, providing an experimental clue to gravity’s quantization. Correlation with classical detections (e.g., LIGO) can validate the origin of such events.

The paper situates itself among laboratory-scale searches for quantum gravity signatures, including matter-wave interferometry with large molecules, opto- and electromechanical systems, and proposals for macroscopic superpositions of massive objects. Previous efforts often tested phenomenological models (e.g., collapse models, nonlocality) or aimed to observe entanglement induced by Newtonian interactions, which require challenging macroscopic superpositions. Direct detection of gravitons has traditionally been deemed infeasible due to extremely weak coupling and vanishing spontaneous emission rates for small masses. Bar resonators (Weber bars and successors) have developed high-Q, cryogenic operation but focused on classical position readout near the standard quantum limit. This work leverages advances in ground-state cooling, quantum-limited measurements of phonon number in mechanical and acoustic systems, and the ability to correlate with LIGO events to propose energy-resolving detection of single graviton exchanges. Theoretical background includes linearized quantum gravity where gravitons arise from quantizing the metric perturbations and coupling to the stress-energy tensor, with precedents in quantized weak-field gravity analyses and quadrupole interactions.

Theory: Start from linearized gravity with metric g_{μν} = η_{μν} + h_{μν} and interaction Hamiltonian H_int = -(1/2) h_{μν} T^{μν}. Quantize both matter and gravitational perturbations (gravitons) to analyze emission/absorption. Spontaneous emission rates from small systems are negligible, but stimulated processes with classical-strength gravitational waves can enhance transition rates. Macroscopic resonator model: Model a solid-bar resonator as a chain of N+1 identical atoms (mass m) with nearest-neighbor couplings, extracting normal modes in 1D. In the large-N limit, each normal mode behaves as a harmonic oscillator with an effective mass scaling ~ M/2 (M total bar mass) and discrete mode spectrum determined by boundary conditions. A microscopic derivation of the gravitational coupling shows two contributions: (i) a dominant macroscopic coupling for odd acoustic modes arising from the gradient of the bar’s quadrupole moment, integrating coherently along the bar length; and (ii) a subleading direct quadrupole interaction with individual atoms, primarily affecting even modes. Stimulated absorption and exact dynamics: Treat the incoming gravitational wave as a coherent drive near a mechanical resonance. Under the rotating-wave and semi-classical approximations, the resonator evolves via a displacement operator into a coherent state with amplitude β that depends on detector parameters (length L, mass M, frequency ω) and on the GW waveform through χ(h, ω) = ∫ h(t) e^{iω t} dt. The exact unitary dynamics are solved using Lie-algebra/Magnus methods for a single resonator mode driven by a single-mode GW, yielding closed-form expressions for β and transition probabilities from |0⟩ to |1⟩. Transition rates: Using Fermi’s golden rule, derive stimulated transition rates between number states due to the GW drive. For realistic parameters (e.g., large mass bars and astrophysical strains), the stimulated absorption rate for |0⟩→|1⟩ can reach resolvable scales. An illustrative estimate shows that for an aluminum bar of mass ~1800 kg and strain h ~ 5×10^{-22}, the stimulated single-quantum exchange rate can be ~1 Hz, allowing resolution of individual graviton exchange events. Optimization and sources: Derive the single-event excitation probability as a function of β and identify detector regimes that maximize the probability of single-quantum absorption without populating higher levels. Provide an expression for the optimal detector mass that maximizes single-phonon excitation probability for a given GW waveform. Analyze transient (chirping) sources (e.g., compact binary inspirals like GW170817) using stationary-phase approximations for χ(h, ω) near resonance crossing, and evaluate continuous narrowband sources (e.g., millisecond pulsars). Present example parameter sets for materials (beryllium, niobium, sapphire, quartz, superfluid He) and source frequencies. Measurement protocol: Prepare the resonator’s fundamental acoustic mode in the ground state and perform continuous, weak, non-destructive, number-resolving energy measurements to detect quantum jumps to |1⟩. Runs are repeated with re-preparation if no event is recorded. For transient LIGO events, schedule windows around predicted resonance passages and correlate detections with LIGO data to confirm GW origin. Simulations model stochastic continuous measurements (e.g., homodyne-like readout), tracking populations ρ_{00}, ρ_{11}, ρ_{22}. Noise and feasibility: Estimate thermal excitation rates and set benchmark requirements such that thermal events over the measurement window are less likely than stimulated absorption. Discuss requirements on cryogenic temperature T and mechanical quality factor Q, ground-state cooling of bulk modes, and the challenge of number-resolving readout at kg scales (energy resolution at few μeV). Suggest optomechanical and electromechanical transducers (membrane-in-the-middle, Brillouin-like coupling, superconducting He resonators) and arrays of detectors to improve sensitivity and event confidence.

- Single-graviton exchange signatures are, in principle, detectable in macroscopic quantum acoustic resonators via stimulated absorption from gravitational waves, monitored through quantum jumps between energy eigenstates. - Stimulated processes can occur at resolvable rates: for an aluminum bar of mass ~1800 kg and incident GW strain h ~ 5×10^{-22}, the stimulated single-quantum exchange rate is estimated at ~1 Hz, enabling time-resolved detection of individual events. - Exact solutions show that a coherent GW drive displaces the resonator into a coherent state; the single-excitation probability depends on |β|, which is determined by detector parameters (L, M, ω) and the GW waveform χ(h, ω). There exists an optimal detector mass that maximizes the single-quantum excitation probability; overly large masses push population into higher energy levels. - Feasibility analyses indicate that neutron-star mergers like GW170817 offer promising scenarios due to slow chirp through resonance and the ability to correlate events with LIGO detections, boosting confidence that an observed quantum jump corresponds to single graviton absorption. - The scheme extends to continuous-wave sources (kHz pulsars) and speculative high-frequency GW sources (MHz), where certain parameter regimes could allow single-graviton sensitivity with current or near-term technology. - Experimental requirements are stringent but approach the edge of current capabilities: ground-state cooling of massive resonators, very low temperatures (mK to sub-K), high mechanical Q, and quantum-limited number-resolving readout. Simulations of continuous measurement illustrate detection of isolated single-excitation events during a GW passage. - The approach focuses on energy-resolving measurements (quantum jumps) rather than average energy or position readout, providing a route to infer single-quantum exchanges analogous to the photoelectric effect for photons.

The proposed detection scheme addresses the central question of whether individual quanta of gravitational radiation can be observed exchanging discrete energy with matter. By leveraging weak coupling (which limits multi-quantum absorption) and quantum control of macroscopic resonators, the method makes single transitions distinguishable over relevant timescales. Correlating observed quantum jumps with independently measured LIGO events directly ties the excitation to a passing GW at the expected frequency, reinforcing the single-graviton interpretation within the rotating-wave and near-resonance approximations. The results indicate that single-graviton signatures could be within reach given near-future advances in cryogenics, mechanical Q, and quantum-limited phonon-number readout. This constitutes a gravitonic analog of the photoelectric effect: while not a full-state measurement of the gravitational field, resolving individual energy-conserving transitions provides compelling evidence of quantization. The work complements other quantum gravity tests (e.g., gravity-induced entanglement) by focusing on on-shell quanta exchange rather than virtual exchange or modified dynamics, offering a distinct and experimentally accessible pathway.

From first principles and microscopic modeling, the study derives stimulated single-graviton absorption/emission rates for macroscopic mechanical resonators in the quantum regime and shows that discrete graviton–phonon exchange events could be detected via continuous, number-resolving energy measurements. Example estimates (e.g., ~1 Hz stimulated rate for a ~1800 kg bar at h ~ 5×10^{-22}) and analyses of astrophysical sources (chirping binaries, continuous pulsars, speculative MHz sources) suggest feasible regimes, particularly when coupled with coincidence measurements from LIGO. The approach reframes GW detection from average classical response to resolving individual energy quanta, analogous to the photoelectric effect for photons. Future work should focus on advancing phonon-number-resolving readout at kilogram scales, improving cryogenic Q and T, engineering optimal transducer coupling, deploying detector arrays for coincidence, and integrating real-time correlation with GW observatories to validate events and reduce false positives.

- Experimental parameters are demanding: very low temperatures (mK to sub-μK in some scenarios), high mechanical Q factors, and ground-state preparation of bulk acoustic modes of massive resonators. - Number-resolving, continuous, quantum non-demolition energy measurements at kilogram scales require μeV-level energy resolution, beyond current capabilities but potentially achievable with advanced opto/electromechanical transduction. - Thermal and technical noise (e.g., electronic noise, environmental vibrations, transducer backaction) can mimic or obscure single-event signatures; stringent isolation and calibration are needed. - Some source classes (e.g., high-frequency GWs) are speculative with uncertain strain amplitudes; feasibility depends on actual source strengths and occurrence rates. - The analysis relies on semi-classical treatment of the GW field (coherent-state approximation) and rotating-wave/near-resonance conditions; while analogous to the photoelectric effect, observations would indicate quantization indirectly rather than constituting a full quantum-state tomography of the gravitational field. - Certain quantitative estimates (e.g., optimal masses for specific events) depend on waveform details and approximations (stationary phase, long-time resonance), and may require refinement with full numerical models and real data.