Noise Differentiation and Atom Number Measurement in Optical Lattice Clocks by Analyzing Clock Stabilities with Various Parameters

We propose a method that enables the precise determination of the number of atoms in a Dick-noise-free optical lattice clock, by effectively addressing quantum projection noise. Our approach relies on conducting stability measurements at three distinct parameter sets, allowing us to differentiate between quantum projection noise, photon shot noise, and technical noise. Importantly, it enables accurate extraction of the atom number, even in the presence of photon shot noise and technical noise. We utilize numerical simulations to validate our approach, optimize the modulation parameters for minimal uncertainty, and investigate the impact of atom number fluctuations on the determinacy of our results. The numerical results show the validity of our method and demonstrate an estimated uncertainty in the atom number that is below 4% with 6.7 h measurement, provided that the standard deviation of atom number fluctuation is kept below 0.14 times the average atom number.