$^{3}$He-$^{129}$Xe Comagnetometery using $^{87}$Rb Detection and Decoupling

We describe a $^{3}$He-$^{129}$Xe comagnetometer using $^{87}$Rb atoms for noble-gas spin polarization and detection. We use a train of $^{87}$Rb $\pi$ pulses and $\sigma^+/\sigma^-$ optical pumping to realize a finite-field Rb magnetometer with suppression of spin-exchange relaxation. We suppress frequency shifts from polarized Rb by measuring the $^{3}$He and $^{129}$Xe spin precession frequencies in the dark, while applying $\pi$ pulses along two directions to depolarize Rb atoms. The plane of the $\pi$ pulses is rotated to suppress the Bloch-Siegert shifts for the nuclear spins. We measure the ratio of $^{3}$He to $^{129}$Xe spin precession frequencies with sufficient absolute accuracy to resolve the Earth's rotation without changing the orientation of the comagnetometer. A frequency resolution of 7 nHz is achieved after integration for 8 hours without evidence of significant drift.