The polarization and the fundamental sensitivity of $^{39}$K ($^{133}$Cs)-$^{85}$Rb-$^{4}$He hybrid optical pumping spin exchange relaxation free atomic magnetometers

Abstract: The hybrid optical pumping spin exchange relaxation free (SERF) atomic magnetometers can realize ultrahigh sensitivity measurement of magnetic field and inertia. We have studied the $^{\text{85}}$Rb polarization of two types of hybrid optical pumping SERF magnetometers based on $^{\text{39}}$K-$^{\text{85}}$Rb-$^{\text{4}}$He and $^{\text{133}}$Cs-$^{\text{85}}$Rb-$^{\text{4}}$He respectively. Then we found that $^{\text{85}}$Rb polarization varies with the number density of buffer gas $^{\text{4}}$He and quench gas N$_{\text{2}}$, pumping rate of pump beam and cell temperature respectively, which will provide an experimental guide for the design of the magnetometer. We obtain a general formula on the fundamental sensitivity of the hybrid optical pumping SERF magnetometer due to shot-noise. The formula describes that the fundamental sensitivity of the magnetometer varies with the number density of buffer gas and quench gas, the pumping rate of pump beam, external magnetic field, cell effective radius, measurement volume, cell temperature and measurement time. We obtain a highest fundamental sensitivity of $1.5073$ $aT/Hz^{1/2}$ ($1$ $aT=10^{-18}$ $T$) with $^{\text{39}}$K-$^{\text{85}}$Rb-$^{\text{4}}$He magnetometer between above two types of magnetometers when $^{\text{85}}$Rb polarization is $0.1116$. We estimate the fundamental sensitivity limit of the hybrid optical pumping SERF magnetometer to be superior to $1.8359\times10^{-2}$ $aT/Hz^{1/2}$, which is higher than the shot-noise-limited sensitivity of $1$ $aT/Hz^{1/2}$ of K SERF atomic magnetometer.