Study of the optimal duty cycle and pumping rate for square-wave amplitude-modulated Bell-Bloom magnetometers

We theoretically and experimentally study the optimal duty cycle and pumping rate for square-wave amplitude-modulated Bell-Bloom magnetometers. The theoretical and the experimental results are in good agreement for duty cycles and corresponding pumping rates ranging over 2 orders of magnitude. Our study gives the maximum field response as a function of duty cycle and pumping rate. Especially, for a fixed duty cycle, the maximum field response is obtained when the time averaged pumping rate, which is the product of pumping rate and duty cycle, is equal to the transverse relaxation rate in the dark. By using a combination of small duty cycle and large pumping rate, one can increase the maximum field response by up to a factor of 2 or π/2, relative to that of the sinusoidal modulation or the 50% duty cycle square-wave modulation respectively. We further show that the same pumping condition is also practically optimal for the sensitivity due to the fact that the signal at resonance is insensitive to the fluctuations of pumping rate and duty cycle.