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

Cross-correlation spin noise spectroscopy of heterogeneous interacting spin systems