State-Selective Signatures of Quantum and Classical Gravitational Environments

Abstract

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.

Figures (3)

• Figure 1: Inverse decoherence time $\tau_{\alpha}^{-1}$ as a function of the detector frequency $\omega_{c}$ for different spectral profiles $f(\omega_{c})\propto\omega_{c}^{s}$. The green, blue, and yellow curves correspond respectively to $s=-1, 1,$ and $-2$, illustrating the strong sensitivity of the decoherence rate to the gravitational spectral density.
• Figure 2: Comparison of gravitationally induced decoherence rates for the lowest Fock superpositions. In a quantum-vacuum gravitational environment the rate $\Gamma_{01}$ vanishes while $\Gamma_{02}$ remains finite, reflecting the $\Delta n=\pm2$ selection rule of the quadratic coupling. Thermal and classical phase-randomized gravitational backgrounds instead exhibit the universal scaling $\Gamma_{02}=2\Gamma_{01}$, indicating the absence of a protected subspace.
• Figure 3: Schematic illustration of the state-selective diagnostic. Classical stochastic, thermal, and phase-randomized coherent gravitational backgrounds yield the universal scaling $\Gamma_{02}=2\Gamma_{01}$ and therefore $R=1$. Vacuum fluctuations of a quantized gravitational field instead produce $R=1+g$, reflecting suppression of decoherence within the $\{|0\rangle,|1\rangle\}$ manifold. The horizontal axis is displayed schematically for clarity; realistic laboratory parameters correspond to $g\ll 1$.