Two approaches for nuclear spin co-magnetometry*

I will discuss two methods commonly used for nuclear spin co-magnetometry in fundamental physics measurements. One technique uses a comparison between magnetic fields measured by nuclear and alkali-metal spins, another approach compares the precession frequencies of two nuclear spin species. Alkali-nuclear spin comparison achieves the highest energy resolution at short time scales, but does not have high absolute stability. We recently investigated a pulsed pump laser approach to understand the limitations of absolute stability. A comparison of two nuclear spin precession frequencies provides better long-term stability and has a potential for further improvement by many orders of magnitude in sensitivity before reaching fundamental quantum limits. We recently focused on comparison between $^{3}$He and $^{21}$Ne spins that have hour-long coherence times and weak spin-interaction effects.