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Quantum Noise Fraction and the Thermal Frontier in High-Frequency Gravitational Wave Detection

Abstract

We introduce a diagnostic -- the quantum noise fraction β -- that determines the maximum sensitivity improvement achievable through quantum enhancement for any gravitational wave detector. Applied to the landscape of proposed high-frequency (kHz-GHz) detectors, this diagnostic reveals that resonant mass detectors operating through tidal coupling are thermally dominated (β ≈ 0) at all frequencies below ~230 MHz at dilution temperatures, rendering squeezing and entanglement limited in effectiveness. Only above this thermal frontier, defined by ℏ ω = k_B T ln 3, does the quantum regime become accessible. We identify a single concrete realization: a bulk acoustic wave resonator at 1 GHz and 10 mK (β = 0.98), and propose a gravitational wave detector employing squeezed phononic states via circuit QED readout. An array of 10⁴ such resonators with 10 dB mechanical squeezing reaches √S_h = 2.1 × 10⁻²²/√ Hz -- still a factor ~10¹² above the BBN bound on stochastic backgrounds at 1 GHz, indicating that the sensitivity gap remains predominantly classical in origin and that concurrent advances in classical detector parameters will be required.

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