Estimation of instability induced by probe laser frequency noise in cold-atom microwave clocks

The influence of laser frequency noise on the stability of a compact cold-atom microwave clock was investigated theoretically in this study. The phase-noisy laser was characterized by a phase-diffusion field. Given the laser linewidth, the analytical expressions of the atomic covariance function and the noise power spectral density of the relative intensity noise transferred from the frequency noise were derived based on stochastic differential equations. Our results provide an effective method to estimate the impact of laser frequency noise on the stability of an integrating sphere cold atomic clock. This method can be extended to other cold atom detection cases.