Search for Spin-Gravity Interactions with a $^{3}$He-$^{21}$Ne Co-magnetometer using Microwave Controlled Rb Magnetometer Readout*

Nuclear spin co-magnetometry possesses ultrahigh precision in resolving spin energy levels and holds the potential for long-term stability, rendering it an ideal tool for probing spin-dependent new physics beyond the Standard Model. Here, we present the latest advancements in our Ramsey-type pulsed $^{3}$He-$^{21}$Ne co-magnetometer, including methods for active control of Rb polarization with strong microwaves at 6.8 GHz. Furthermore, we will discuss the application of the co-magnetometer to search for spin-gravity couplings at the sub-nHz level.