Extended Data Fig. 3.
Calibration of quantum noise limited Faraday rotation probing of atomic spins. We plot the measured variance var(φ) as a function of the number of atoms N in an input coherent spins state with 〈F〉 = {0, N, 0}. Solid curve: a fit using the polynomial var(φ) = a0 + a1N + a2N2. The linear term a1 = αµ2N/2 corresponds to the atomic quantum noise from atoms in the input coherent spin state. We estimate a0 = (11.7 ± 0.7) × 10−10, a1 = (6.5 ± 0.8) × 10−15, and a2 = (2.8 ± 12) × 10−22, consistent with negligible technical noise in the atomic state preparation. Dashed line: var(φ) = a0 + a1N. Error bars indicate ±1 standard error in the variance for 206 repetitions.