${}^3\mathrm{He}\text{−}{}^{129}\mathrm{Xe}$ Comagnetometery using ${}^{87}\mathrm{Rb}$ Detection and Decoupling

We describe a ${}^3\mathrm{He}\text{−}{}^{129}\mathrm{Xe}$ comagnetometer using ${}^{87}\mathrm{Rb}$ atoms for noble-gas spin polarization and detection. We use a train of ${}^{87}\mathrm{Rb}$ $\pi$ 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 ${}^3\mathrm{He}$ and ${}^{129}\mathrm{Xe}$ 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 ${}^3\mathrm{He}$ to ${}^{129}\mathrm{Xe}$ spin precession frequencies with sufficient absolute accuracy to resolve Earth’s rotation without changing the orientation of the comagnetometer. A frequency resolution of 7 nHz is achieved after integration for 8 h without evidence of significant drift.

Figure 1

(a) The pulse-train ${}^{87}\mathrm{Rb}$ magnetometer uses $\widehat{y}$-axis $\pi$ pulses with a ${\sigma }^{+}-{\sigma }^{-}$ pump beam along $\widehat{z}$ and a linearly polarized probe beam along $\widehat{x}$ (see inset). A $B_y$ field gives a paramagnetic Faraday rotation signal detected with a lock-in. (b) Using a ${}^{87}\mathrm{Rb}\text{−}{\mathrm{N}}_2$ cell at $103°\mathrm{C}$ and low laser power, we measure the magnetometer linewidth in zero bias field (stars) and for $B_0=5\mathrm{mG}$ (circles) as a function of the $\pi$-pulse repetition rate. For comparison we also show a Bell-Bloom magnetometer linewidth (square) that is limited by Rb-Rb spin-exchange relaxation.

Figure 2

The Rb back polarization from spin exchange with ${}^{129}\mathrm{Xe}$ is reduced by a factor of $10^4$ by increasing the pulse repetition rate, in agreement with predictions from a Rb density matrix model including Rb-Rb spin exchange. The inset shows the current flowing through the coil to generate typical $\pi$ pulses.

Figure 3

(a) The Ramsey scheme with an inset showing a ${}^3\mathrm{He}\text{−}{}^{129}\mathrm{Xe}$ lock-in signal pattern and the fit residuals $\times 100$. (b) Allan deviation of the rotation rate ${\mathrm{\Omega }}_z$ with an 7 nHz (${10}^{-2}\mathrm{deg}/\mathrm{h}$) upper limit of the rotation rate stability.

Figure 4

(a) Frequency ratio $f_r={\omega }_{\mathrm{He}}/{\omega }_{\mathrm{Xe}}$ measured with a ${}^{87}\mathrm{Rb}$ depolarizing $\widehat{x}-\widehat{y}$ pulse train using $\pi$, $3\pi /4$, and $\pi /2$ pulses and rotating at frequency ${\omega }_r$ for two directions of the bias magnetic field $B_0=5.3\mathrm{mG}$. The stars show the intersection points where the effect of the pulses is canceled. Inset: rotating $\widehat{x}-\widehat{y}$ pulse train. (b) Frequency ratio ${\omega }_{\mathrm{He}}/{\omega }_{\mathrm{Xe}}$ at the intersection points (note a factor of 10 expanded vertical scale) as a function of $B_0$. Solid and dashed lines show prediction from Eq. (1) due to projection of Earth’s rotation on $B_0$.