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arXiv:2110.10962 · Physica Scripta

Sensing quantum nature of primordial gravitational waves using electromagnetic probes

Fateme Shojaei Arani, M. Bagheri Harouni, Brahim Lamine, Alain Blanchard

Published Jan 31, 2023• 4 citations
arXivHTMLPDF

Abstract

Abstract Based on optical medium analogy, we establish a formalism to describe the interaction between an electromagnetic (EM) system with gravitational waves (GWs) background. After a full discussion on the classical treatment of the EM-GW interaction and finding the EM field mode-functions in the presence of the magneto-dielectric media caused by GWs, the governing quantum interaction Hamiltonian is obtained. Investigation of the optical quadrature variance as well as the visibility of a laser field interacting with the multi-mode squeezed primordial gravitational waves imply that the inflationary primordial gravitational waves (PGWs) act as a decoherence mechanism that destroy EM coherency after a characteristic time scale, τ c , which depends on the inflationary parameters (β, β s , r), or equivalently, the fractional energy density of PGWs, Ω gw,0. The decoherency mechanism overcomes the coherent effects, such as revivals of optical squeezing, thus leaving their confirmation out of reach. Influenced by the continuum of the squeezed PGWs, the laser field suffers a line-width broadening by γ = τ c − 1 . The most peculiar property of the EM spectrum is the apparition of side bands at ω ∼ ω 0 ± 1.39 τ c − 1 Hz, stemming from the squeezed nature of PGWs. The laser phase noise induced by the squeezed PGWs grows with time squarely, Δ ϕ = t / τ c 2 , that can most possibly be sensed within a finite flight time.

DOI
10.1088/1402-4896/acb7ac

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Abstract Based on optical medium analogy, we establish a formalism to describe the interaction between an electromagnetic (EM) system with gravitational waves (GWs) background. After a full discussion on the classical treatment of the EM-GW interaction and finding the EM field mode-functions in the presence of the magneto-dielectric media caused by GWs, the governing quantum interaction Hamiltonian is obtained. Investigation of the optical quadrature variance as well as the visibility of a laser field interacting with the multi-mode squeezed primordial gravitational waves imply that the inflationary primordial gravitational waves (PGWs) act as a decoherence mechanism that destroy EM coherency after a characteristic time scale, τ c , which depends on the inflationary parameters (β, β s , r), or equivalently, the fractional energy density of PGWs, Ω gw,0. The decoherency mechanism overcomes the coherent effects, such as revivals of optical squeezing, thus leaving their confirmation out of reach. Influenced by the continuum of the squeezed PGWs, the laser field suffers a line-width broadening by γ = τ c − 1 . The most peculiar property of the EM spectrum is the apparition of side bands at ω ∼ ω 0 ± 1.39 τ c − 1 Hz, stemming from the squeezed nature of PGWs. The laser phase noise induced by the squeezed PGWs grows with time squarely, Δ ϕ = t / τ c 2 , that can most possibly be sensed within a finite flight time.
We develop a quantum description of the resonant interaction between electromagnetic (EM) and gravitational waves (GW). We first show that Lorentz invariance together with polarization selection rules forbids any photon-graviton mixing in free space. We demonstrate that confining the EM field within a cavity quantum electrodynamics (cavity-QED) environment breaks translational symmetry and isotropy, leading to non-vanishing mode coupling between EM and gravitational degrees of freedom. Within this framework, we identify multiple photon-graviton scattering channels, including photon up- and down-conversion and photon creation. In the semiclassical limit of the trilinear interaction where GW acts as a classical pump and the EM field is in a vacuum, spontaneous parametric photon amplification and two-mode squeezing occur. When the gravitational field is quantized, however, the back-action and energy exchange between photons and gravitons result in saturation of amplification, in contrast to exponential growth, and the loss of purity in the photonic subsystem. The characteristic timescale scales as tsp∼(gng)−1t_{\text{sp}}\sim (g\sqrt{n_g})^{-1}tsp​∼(gng​​)−1, where ggg and ngn_gng​ refer to the coupling strength and the mean graviton number, demonstrating collective enhancement of the interaction with the graviton occupation number. In the stimulated regime, where one EM mode is initially populated, the effective coupling is further enhanced, analogous to Dicke-type superradiant emission. This work introduces a cavity-based graviton transducer for probing quantum aspects of GWs.
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.
Primordial black holes (PBHs) form when large primordial curvature perturbations re-enter the Hubble radius and exceed the classical collapse threshold. These perturbations originate as quantum fluctuations of the inflationary vacuum, motivating a quantum-information description of the PBH-producing scalar sector. We develop a conservative extension of the standard PBH and scalar-induced gravitational-wave (SIGW) framework in which Gaussian quantum discord is used as a diagnostic of residual quantum correlations, not as a new PBH-formation criterion. We describe each (k,−k)(\bm k,-\bm k)(k,−k) pair as a two-mode Gaussian state and show that, in the pure squeezed limit, discord grows rapidly with the squeezing parameter, so low discord thresholds are automatically satisfied for strongly squeezed modes. The nontrivial regime is the mixed state produced by decoherence. Using a Lindblad open-system description, we motivate a Gaussian loss channel for the scalar covariance matrix and distinguish the discord from a covariance-survival factor Qdec(k)Q_{\rm dec}(k)Qdec​(k). If the decoherence channel suppresses the scalar two-point covariance, PBH abundance can be affected through the classical collapse variance, while the SIGW spectrum is modified more directly by the factors Qdec(ku)Qdec(kv)Q_{\rm dec}(ku)Q_{\rm dec}(kv)Qdec​(ku)Qdec​(kv) inside the radiation-era convolution. For a narrow scalar peak and slowly varying QdecQ_{\rm dec}Qdec​, this gives the benchmark scaling ΩGWeff≃Qdec2ΩGWclassΩ_{\rm GW}^{\rm eff}\simeq Q_{\rm dec}^2Ω_{\rm GW}^{\rm class}ΩGWeff​≃Qdec2​ΩGWclass​. Thus quantum discord and decoherence provide a controlled way to characterize the quantum-to-classical transition of PBH-producing perturbations, with the clearest imprint appearing in scalar-induced gravitational waves.
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.
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.
Abstract Recent advances in quantum sensing—optical clocks at 5.5 × 10 − 19 systematic uncertainty, frequency-dependent squeezing below the standard quantum limit, quantum magnetometers approaching fundamental sensitivity limits—raise a natural question: can these technologies detect gravitational waves directly, or enhance existing detectors beyond current capabilities? We show that the answer is primarily determined by the coupling mechanism between the gravitational wave and the sensor. Starting from the tidal Hamiltonian in Fermi normal coordinates, we identify three physically distinct mechanisms by which a gravitational wave couples directly to a quantum system, and derive their transducer gains within linearized general relativity and non-relativistic quantum mechanics. Internal atomic coupling (tidal distortion of electronic wavefunctions) yields a transducer gain G A = 2.4 × 10 − 20 , with vanishing first-order energy shifts for all J = 0 clock states—a ∼ 10 35 deficit relative to laser interferometry that exceeds any projected quantum enhancement. Center-of-mass coupling (Doppler shifts from geodesic motion) reaches strain sensitivities of ∼ 10 − 18 , still 10 4 above LISA requirements. Light propagation coupling (phase accumulation over macroscopic baselines) provides the enormous transducer gain that makes laser interferometry—and atom interferometry—viable. For detectors exploiting this third mechanism, we quantify how much improvement quantum sensors can provide through the detector’s noise architecture: LISA’s noise budget is predominantly classical, limiting combined quantum enhancement to E ≈ 1.04 , while ground-based detectors in the shot-noise-dominated regime achieve E = 1.6 – 2.1 . Atom interferometers exploit the same light-propagation mechanism to target the 0.01–10 Hz band between the LISA and LIGO ranges.