We show that the small AC response of the bulk spin current and the optical spin conductivity, which is elusive in condensed matter systems, can be measured in ultracold atoms. By analyzing experimentally achievable systems such as spin 1/2 superfluid Fermi gases, spin 1 Bose Einstein condensates, and Tomonaga Rattinger liquids, we demonstrate that this conductivity contains a wealth of information about quantum states. To do. The obtained conductivity spectra, absent in the Drude conductivity, reflect quasiparticle excitations and non-Fermi liquid properties. Accessible physical quantities include superfluid gaps and contacts in superfluid Fermi gases, gapped and gapless spin excitations, and quantum depletion in Bose-Einstein condensates, and the elusive Tomonaga-Rattinger liquid parameter in cold atom experiments. contains the spin portion of Unlike their mass transport counterparts, spin conductivity serves as a probe applicable to clean atomic gases without disorder or lattice potential. Our formalism can be generalized to various systems, such as spin-orbit coupled systems and non-equilibrium systems.

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