A K-Rb-$^{21}$Ne Comagnetometer for Tests of Fundamental Symmetries and Inertial Rotation Sensing

The K-$^3$He noble gas comagnetometer has already set the most stringent limit on possible Lorentz and CPT violation coupling to nuclear spin and on long-range nuclear spin-dependant forces. The comagnetometer is mounted on a rotating platform for reorientation of the sensitive axis in the horizontal plane that is a key to improved tests of spatial isotropy. Replacement of $^3$He with $^{21}$Ne provides an order of magnitude improvement in sensitivity to non-magnetic nuclear spin interactions due the smaller gyromagnetic ratio of $^{21}$Ne. Because $^{21}$Ne has $I=3/2$, the experiment is also sensitive to tensor Lorentz-violating effects that do not break CPT symmetry. The comagnetometer also works as a sensitive gyroscope that is potentially competitive with fiber-optic and atomic Sagnac interferometers. We will describe our current development of the K-Rb-$^{21}$Ne comagnetometer as a gyroscope and a precision measurement tool. Finally, we discuss the advantage and future plans for Lorentz Violation tests at the South Pole for removal of Earth's rotation rate as a background systematic effect.