A $^3$He-$^{129}$Xe co-magnetometer probed by alkali metal atoms*

We report the recent progress in the development of a new co-magnetometer using $^3$He and $^{129}$Xe nuclear spins. The co-magnetometer is run as a clock by measuring the precession frequencies of the two nuclear spin species ''in the dark'', with Rb atoms used only to measure the initial and final phases of nuclear spin precession. Using this system we investigated several general classes of systematic effects affecting gas co-magnetometers. We studied the effect of thermal diffusion, which results in a non-uniform relative concentration of $^3$He and $^{129}$Xe in the presense of a temperature gradient. We also investigated the effects of linear and quadratic magnetic field gradients and develped a new theory to model the effects of arbitrary magnetic field gradients on the frequency shifts and nuclear spin relaxation rates. We will present the latest results on the precision and accuracy in the measurements of the ratio between the two nuclear spin precession frequencies. This co-magnetometer has potential applications for many precision measurements, such as searches for spin-gravity couplings, electric dipole moments and nuclear spin gyroscopes.