Can propagating gravitational waves serve as operational probes of the quantum nature of gravity? We address this question by developing a unified theoretical framework that combines spacetime geometry, quantum information, and gravitational-wave physics. Starting from the geodesic deviation equation in linearized General Relativity, we derive the effective detector Hamiltonian directly from spacetime geometry and construct the complete quantum dynamics for detector subsystems interacting with both classical and quantized propagating gravitational-wave fields. This unified formulation enables a direct comparison between classical and quantum descriptions of gravitational radiation within the same physical framework. We demonstrate that classical gravitational-wave backgrounds can induce mixedness in the detector state but cannot generate genuine quantum correlations between the detector subsystems. In contrast, quantized gravitational waves coherently mediate gravity-induced entanglement, quantum coherence, quantum memory, and nonclassical correlations, providing clear operational signatures of the quantum nature of propagating gravitational radiation. We further discuss how mesoscopic quantum mechanical oscillators offer a promising route towards experimentally probing these effects. Our results establish a geometric and quantum-information-based framework for exploring quantum gravity through propagating gravitational waves.
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Proceedings of Quantum Universe 2025 (QU2025), Avellino, Italy, 27-31 October 2025. Submitted to the International Journal of Geometric Methods in Modern Physics (IJGMMP) for publication in the QU2025 Special Issue
Can propagating gravitational waves serve as operational probes of the quantum nature of gravity? We address this question by developing a unified theoretical framework that combines spacetime geometry, quantum information, and gravitational-wave physics. Starting from the geodesic deviation equation in linearized General Relativity, we derive the effective detector Hamiltonian directly from spacetime geometry and construct the complete quantum dynamics for detector subsystems interacting with both classical and quantized propagating gravitational-wave fields. This unified formulation enables a direct comparison between classical and quantum descriptions of gravitational radiation within the same physical framework. We demonstrate that classical gravitational-wave backgrounds can induce mixedness in the detector state but cannot generate genuine quantum correlations between the detector subsystems. In contrast, quantized gravitational waves coherently mediate gravity-induced entanglement, quantum coherence, quantum memory, and nonclassical correlations, providing clear operational signatures of the quantum nature of propagating gravitational radiation. We further discuss how mesoscopic quantum mechanical oscillators offer a promising route towards experimentally probing these effects. Our results establish a geometric and quantum-information-based framework for exploring quantum gravity through propagating gravitational waves.
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.
This thesis investigates the role of gravitational waves in quantum systems, motivated by advances in our understanding of the quantum–gravity interface and efforts to identify experimental signatures of quantum gravity. It focuses on gravitational decoherence and the interplay between internal energy and centre-of-mass dynamics in composite quantum systems, complemented by a study of internal-energy effects in gravitationally mediated entanglement. First, we develop relativistic Hamiltonian formulations showing that changes in a composite system’s internal energy increase its gravitational mass rather than alter its momentum. This removes earlier ad hoc arguments for eliminating “anomalous friction forces”. We show that gravitational waves act as a dynamical background, inducing curvature-dependent forces that modify total momentum. Second, we revisit a thought experiment in which tensions between causality and complementarity arise. We identify a scenario in which these tensions follow from energy–mass equivalence, making the effect specific to gravitational interactions. In a gravitationally mediated entanglement experiment using Newtonian gravity as mediator, we investigate whether decohering gravitational radiation can resolve the apparent conflict. Finally, we build upon a model of gravitational decoherence consistent with general relativity. This requires deriving a higher-derivative quantum Langevin equation and master equation. The resulting dynamics show that gravitational interactions induce decoherence in the canonical momentum basis of the quadrupole and generate acceleration- and jerk-dependent corrections absent in electrodynamics. Together, these results show that weak-field gravitational interactions leave distinct relativistic imprints on quantum systems, including effects unique to gravitational waves, providing potential signatures that distinguish gravity from other interactions.
We present a fully quantum field-theoretic framework for gravitational wave (GW) detection, describing the interaction as inelastic photon-graviton scattering. We demonstrate that for \textit{a coherent graviton state}, this microscopic model explicitly reproduces the standard classical geometric-optics time delay, providing a rigorous consistency test of the correspondence limit. We propose a detection scheme based on Hong-Ou-Mandel interference, where the GW-induced spectral shifts render entangled photon pairs distinguishable. This encodes the gravitational signal into the modulation of photon coincidence rates --- a quantum observable robust against laser intensity noise. Furthermore, we show that non-classical graviton states, such as squeezed states, induce unique decoherence signatures, establishing theoretical bounds on gravitational decoherence and defining the operational limits for probing the quantum nature of gravity.
This thesis examines how atomic quantum systems can be utilized to probe spacetime effects in regimes where quantum mechanics and general relativity intersect, and how gravitational phenomena imprint on experimentally accessible observables. The work is based on two complementary studies. In Article I, we propose an experimental scheme that combines trapped-atom interferometry with Ramsey interrogation to realize a clock held in a spatial superposition at two heights in Earth’s gravitational field. Using a path-integral treatment of interferometric phases and incorporating the internal-energy contribution to mass, we derive leading relativistic corrections and identify two signatures of proper-time superposition: (i) oscillations of interferometric visibility and (ii) an effective shift of the clock transition frequency. We argue that this frequency-shift signature may be within reach of current or near-term technology, even when visibility changes are too small to resolve. In Article II, we develop a general framework for spontaneous emission in curved spacetime and apply it to a gravitational-wave background. We demonstrate that gravitational waves can induce spectral sidebands and directional modulations in the emitted radiation, and formulate parameter estimation via Fisher-information-based sensitivity bounds, yielding order-of-magnitude requirements for detectability under idealized measurement conditions.
A consistent theory including gravitational effects in quantum mechanics has not been found. Although many different approaches have been proposed for theory of quantum gravity, several authors have suggested that gravity may be fundamentally classical. As there is no experimental evidence for a fundamentally quantum vs. fundamentally classical theory of gravity, it is hoped that investigating the consequences of semiclassical gravity, one may propose an experiment to distinguish between the quantum or classical nature of gravity. As opto- and electromechanical devices allow quantum limited measurement and control over massive, mechanical degrees of freedom, they are ideal systems to test violations of standard quantum mechanics arising from gravitational effects. After a brief introduction to the background theory and literature review, we begin by introducing a semiclassical model of gravity based on quantum measurement and control. We show under which conditions the theory behaves like a collapse model, and how a Newtonian potential is recovered in the multi particle case.We then go on to analyse our semiclassical model in two scenarios: firstly in a cosmological setting, and secondly by considering quantum clocks on the surface of the earth. In the cosmological description, we show that a violation of energy conservation, resulting from our model, can be reinterpreted as a dark energy fluid in the spacetime, suggesting that perhaps local violations of conservations of energy may be resolved in a cosmological framework. Secondly, we derive a minimum, gravitational dephasing rate for quantum clocks under the semiclassical model, which unsurprisingly, is is well below the resolution of current state of the art clocks. The next chapters diverge from analysing the gravitational model, and instead focus on novel methods of manipulating and measuring micromechanical devices, that may be used to experimentally probe the results of the semi-classical theory. Firstly we show that a sequence of coherently controlled pulses in an optomechanical system can be used to directly probe the momentum of an oscillator - opening up the possibility for direct detection of momentum diffusion, which is a consequence of the semiclassical gravity model. Secondly, we introduce an electro-mechanical device, and sequence of control operations, that may be understood as an interferometer for the wave function of a mechanical oscillator coupled to a qubit. We show how the resulting interference pattern can distinguish between unitary evolution, thermalisation/decoherence, and a purely classical description of the mechanical oscillator. We also show how the qubit-oscillator interaction can be used generate arbitrary wave functions of the mechanical oscillator, using only classical qubit driving.
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.