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Cross-correlation spin noise spectroscopy of heterogeneous interacting spin systems

We develop and apply a minimally invasive approach for characterization of inter-species spin interactions by detecting spin fluctuations alone. We consider a heterogeneous two-component spin ensemble in thermal equilibrium that interacts via binary exchange coupling, and we determine cross-correlations between the intrinsic spin fluctuations exhibited by the two species. Our theoretical predictions are experimentally confirmed using `two-color' optical spin noise spectroscopy on a mixture of interacting Rb and Cs alkali vapors. The results allow us to explore the rates of spin exchange and total spin relaxation under conditions of strict thermodynamic equilibrium.