Cross-correlation spin noise spectroscopy of heterogeneous interacting spin systems

Interacting multi-component spin systems are ubiquitous in nature and in the laboratory. As such, investigations of inter-species spin interactions are of vital importance. Traditionally, they are studied by experimental methods that are necessarily perturbative: e.g., by intentionally polarizing or depolarizing one spin species while detecting the response of the other(s). Here, we describe and demonstrate an alternative approach based on multi-probe spin noise spectroscopy, which can reveal inter-species spin interactions--under conditions of strict thermal equilibrium--by detecting and cross-correlating the stochastic fluctuation signals exhibited by each of the constituent spin species. Specifically, we consider a two-component spin ensemble that interacts via exchange coupling, and we determine cross-correlations between their intrinsic spin fluctuations. The model is experimentally confirmed using "two-color" optical spin noise spectroscopy on a mixture of interacting Rb and Cs vapors. Noise correlations directly reveal the presence of inter-species spin exchange, without ever perturbing the system away from thermal equilibrium. These non-invasive and noise-based techniques should be generally applicable to any heterogeneous spin system in which the fluctuations of the constituent components are detectable.