Stability analysis in an optical lattice clock using the four-path measurement

In this paper, we propose a method for identifying the contribution of various sources of noise to the instability of an optical lattice clock. These sources include Dick noise, quantum projection noise, shot noise, and technical noise. By measuring the clock instability at four different sets of parameters, we can determine the frequency fluctuations due to each type of noise separately. Furthermore, we can accurately extract the absolute number of atoms, the photon number detected per atom by the photoelectric detector, and the root mean square fluctuations of the atom number. We demonstrate the effectiveness of our approach through numerical simulations, showcasing the ability to determine these parameters with an uncertainty of less than 10%. Specifically, a remarkable uncertainty of 1% can be achieved when determining the atom number.