State-Selective Signatures of Quantum and Classical Gravitational Environments

TL;DR

This paper proposes a unified framework to distinguish between classical and quantum gravitational-wave backgrounds by analyzing their effects on quantum systems, highlighting decoherence patterns as a key diagnostic tool.

Contribution

It introduces a common formalism for classical and quantum GWs and identifies decoherence structure as a novel criterion for testing gravitational quantumness.

Findings

Quantum graviton baths preserve coherence in low phonon states.

Classical stochastic GWs cause decoherence even in low phonon states.

Operational criteria for detecting quantum versus classical gravitational waves.

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.