The polarization and the fundamental sensitivity of \(^{\text{39}}\)K (\(^{\text{133}}\)Cs)-\(^{\text{85}}\)Rb-\(^{\text{4}}\)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 (\(^{\text{39}}\)K (\(^{\text{133}}\)Cs)-\(^{\text{85}}\)Rb-\(^{\text{4}}\)He, then found that the polarization of \(^{\text{85}}\)Rb varies with the number density of buffer gas (\(^{\text{4}}\)He) and quench gas (N\(_{\text{2}}\)), the optical pumping rate of pump beam (\(^{\text{39}}\)K and \(^{\text{133}}\)Cs) and cell temperature respectively, which will provide an experimental guide for the design of the hybrid optical pumping SERF magnetometer. We obtain a general formula on the fundamental sensitivity of the hybrid optical pumping SERF magnetometer due to the shot-noise of a probe laser, which describes that the fundamental sensitivity of the magnetometer varies with the cell effective radius, the number density of buffer gas and quench gas, the optical pumping rate of pump beam (\(^{\text{39}}\)K and \(^{\text{133}}\)Cs), probe relaxation rate, external magnetic field, measurement volume, cell temperature and measurement time. We obtain a highest fundamental sensitivity of \(25.438 aT/Hz^{1/2}\) (\(1 aT=10^{-18} T\)) with \(^{\text{39}}\)K-\(^{\text{85}}\)Rb-\(^{\text{4}}\)He magnetometer among above two types of magnetometers when the polarization of \(^{\text{85}}\)Rb atom is \(% 0.0121\). Optimizing the magnetometer parameters is advantageous to improve the sensitivity of the hybrid optical pumping SERF magnetometer in measuring weak magnetic field. We estimate the fundamental sensitivity limit of the hybrid optical pumping SERF magnetometer to be superior to \(1.847\times10^{-2} aT/Hz^{1/2}\).