Half a Quantum of Noise: Vacuum Fluctuations as the Floor of Microwave Measurement

Every microwave receiver fights two noises: the thermal noise of its own temperature and a floor that no cooling can remove, the half quantum of zero-point fluctuation in each mode. This paper tabulates the contest for a five-gigahertz mode from room temperature to ten millikelvin. The crossover, where thermal occupation falls to one photon, sits at 0.240 kelvin; far below it the total effective occupation approaches exactly one half, and the corresponding quantum noise temperature of 0.120 kelvin is the specification that the best amplifiers, built from Josephson junctions, now meet. The vacuum's half quantum is here not a cosmological inference but a datasheet quantity, the stated noise floor of commercial quantum hardware. All occupations are computed from the Planck factor in the script, not measured, and the paper closes the scale ladder of this study at its lowest rung: gigahertz modes at millikelvin temperatures are the coldest, cheapest vacuum fluctuations ever put to work.