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Liquid-state nuclear spin comagnetometers

We discuss nuclear spin comagnetometers based on ultra-low-field nuclear magnetic resonance in mixtures of miscible solvents, each rich in a different nuclear spin. In one version thereof, Larmor precession of protons and ${\rm ^{19}F}$ nuclei in a mixture of thermally polarized pentane and hexafluorobenzene is monitored via a sensitive alkali-vapor magnetometer. We realize transverse relaxation times in excess of 20 s and suppression of magnetic field fluctuations by a factor of 3400. We estimate it should be possible to achieve single-shot sensitivity of about $5\times{\rm 10^{-9} Hz}$, or about $5\times 10^{-11} {\rm Hz}$ in $\approx 1$ day of integration. In a second version, spin precession of protons and ${\rm ^{129}Xe}$ nuclei in a mixture of pentane and hyperpolarized liquid xenon is monitored using superconducting quantum interference devices. Application to spin-gravity experiments, electric dipole moment experiments, and sensitive gyroscopes is discussed.