Sensitivity of Rydberg microwave electrometry limited by laser frequency noise

Laser frequency or phase noise is a main factor that limits the sensitivity of Rydberg microwave (MW) electrometry. In this study, we proposed a theoretical approach to estimate the effect of laser frequency noise on the atomic coherence of Rydberg sensors based on an atomic superheterodyne receiver. The noisy lasers were characterized using a phase-diffusion model. In particular, explicit formulas were derived to evaluate the noise-limited sensitivity for a given laser linewidth. Furthermore, the effect of Doppler broadening on the sensitivity of the Rydberg sensor at different atomic temperatures was estimated. Our theoretical results provide guidance for the development of Rydberg MW sensors and the method discussed herein can be applied to many other quantum systems.