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The hybrid optical pumping spin exchange relaxation free (HOPSERF) atomicco-magnetometers make ultrahigh sensitivity measurement of inertia achievable.The wall relaxation rate has a big effect on the polarization and fundamentalsensitivity for the co-magnetometer, but it is often neglected in theexperiments. However, there is almost no work about the systematic analysis ofthe influence factors on the polarization and the fundamental sensitivity ofthe HOPSERF co-magnetometers. Here, we systematically study the polarizationand the fundamental sensitivity of 39K-85Rb-21Ne and 133Cs-85Rb-21Ne HOPSERFco-magnetometers with low polarization limit and the wall relaxation rate. The21Ne number density, the power density and wavelength of pump beam will affectthe polarization greatly by affecting the pumping rate of pump beam. We obtaina general formula on the fundamental sensitivity of the HOPSERFco-magnetometers due to shot-noise and the fundamental sensitivity changes withmultiple systemic parameters, where the suitable number density of buffer gasand quench gas make the fundamental sensitivity highest. The fundamentalsensitivity $7.5355\times10^{-11}$ $\rm rad/s/Hz^{1/2}$ of 133Cs-85Rb-21Neco-magnetometer is higher than the ultimate theoretical sensitivity$2\times10^{-10}$ $\rm rad/s/Hz^{1/2}$ of K-21Ne co-magnetometer.

Polarization and fundamental sensitivity of $^{\text{39}}$K ($^{\text{133}}$Cs)-$^{\text{85}}$Rb-$^{\text{21}}$Ne co-magnetometers