Dipolar and scalar ${}^3$He and ${}^{129}$Xe frequency shifts in mm-sized cells

We describe a ${}^3$He-${}^{129}$Xe comagnetometer operating in stemless anodically bonded cells with a 6 mm${}^3$ volume and a ${}^{129}$Xe spin coherence time of 300 sec. We use a ${}^{87}$Rb pulse-train magnetometer with co-linear pump and probe beams to study the nuclear spin frequency shifts caused by spin polarization of ${}^3$He. By systematically varying the cell geometry in a batch cell fabrication process we can separately measure the cell shape dependent and independent frequency shifts. We find that a certain aspect ratio of the cylindrical cell can cancel the effects of ${}^3$He magnetization that limit the stability of vapor-cell comagnetometers. Using this control we also observe for the first time a scalar ${}^3$He-${}^{129}$Xe collisional frequency shift characterized by an enhancement factor $\kappa_{$\text{HeXe}$} = -0.011\pm0.001$.