Detection and manipulation of nuclear spin states in fermionic strontium

Fermionic ⁸⁷Sr has a nuclear spin of $I=9/2$, higher than any other element with a similar electronic structure. This large nuclear spin has many applications in quantum simulation and computation, for which preparation and detection of the spin state are requirements. For an ultracold ⁸⁷Sr cloud, we show two complementary methods to characterize the spin-state mixture: optical Stern-Gerlach state separation and state-selective absorption imaging. We use these methods to optimize the preparation of a variety of spin-state mixtures by optical pumping and to measure an upper bound of the ⁸⁷Sr spin-relaxation rate.