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

Abstract

The quantum noise fraction $\beta$ -- the share of a detector's noise power that is quantum in origin -- bounds the sensitivity gain from any quantum technique at ${\mathcal{E}}_{\max }=1/\sqrt{1-\beta }$. In the kHz--GHz band the readout is a bosonic mode and $\beta =1/(2{\bar{n}}_{\mathrm{th}}+1+\nu )$, so quantum noise dominates only below a thermal frontier $k_{B}T\ln 3=\hslash \omega$ (229 MHz at 10 mK) that governs mechanical resonators and electromagnetic cavities alike. On a multimode acoustic antenna the frontier is directly observable: the logarithmic slope of $\sqrt{S_{h}Q}$ along the odd-overtone comb increases by exactly one half across it, for any dependence of the quality factor on overtone number. Crossing the frontier costs more in classical sensitivity than quantum enhancement returns. For a GHz bulk acoustic wave mode at 10 mK, $\beta =0.984$, but the ceiling is unattainable: with intrinsic damping the zero-point term is the bath's force noise, fixed by the fluctuation--dissipation theorem. The addressable fraction ${\beta }_a$ measures what a quantum technique can actually remove: at the standard quantum limit $\beta =0.992$ yet ${\beta }_a=0.496$, an available factor 1.41 against a ceiling of 11.0. The remaining gap to the big-bang-nucleosynthesis bound is classical.

30 pages, 3 figures. v2: retitled and substantially revised and extended; this version has been submitted for publication. Companion paper published in Class. Quantum Grav., doi:10.1088/1361-6382/ae9449. Data and code: doi:10.5281/zenodo.19862916