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The Quantum Noise Fraction and the Addressable Fraction in High-Frequency Gravitational Wave Detection

Year: 2026
Type: article
Abstract: The quantum noise fraction β, the quantum-origin share of a detector's noise power, sets a ceiling E_max = 1/√(1−β) on the improvement obtainable by removing that noise. In the kHz–GHz band, where the readout degree of freedom is a bosonic mode, β = 1/(2n̄_th+1), with n̄_th the Bose–Einstein occupation. Quantum noise then dominates only on the cold side of the thermal frontier k_B T ln 3 = ħω, valid for mechanical resonators and electromagnetic cavities alike; a real readout, its added noise counted as quantum only up to the quantum limit of linear amplification, turns it into a joint condition on the occupation and the excess readout noise. On a multimode acoustic antenna the frontier is observable within one device: the logarithmic slope of √(S_h Q) along the odd-overtone comb increases by one half across it, whatever the overtone dependence of the quality factor. On this antenna, crossing the frontier costs more in classical sensitivity than quantum enhancement returns. For a GHz mode of an existing bulk acoustic wave device at 10 mK, β = 0.984 and E_max = 7.8. That ceiling cannot be reached with a linear readout: with intrinsic damping the zero-point term is the bath's force noise, fixed by the fluctuation–dissipation theorem and unaffected by any operation on the state of the mode. The addressable fraction β_a excludes it: at the standard quantum limit the same mode has β = 0.992 but β_a = 0.496, an available improvement of 1.41 against a ceiling of 11.0, and less through demonstrated GHz readout chains if their excess noise is technical. An array of 10^4 such devices cross-correlated for one year, integrating over the linewidth, reaches 3.6×10^−24 Hz^−1/2; even granting E_max in full, a factor 1.0×10^10 above the big-bang-nucleosynthesis bound remains, and it is classical.
DOI: 10.1088/1361-6382/aeb348
Language: English
Open Access status: hybrid
Estimated APC paid: $3,325
OpenAlex ID: W7160067672
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