Random spin fluctuations in an equilibrium ensemble of paramagnetic spins are shown to contain valuable information about the system itself. We use off-resonant Faraday rotation to passively and sensitively "listen" to the random magnetization fluctuations (spin noise) in atomic alkali vapors. These random fluctuations generate spontaneous spin coherences which precess and decay with the same characteristic energy and time scales as the macroscopic magnetization of an intentionally polarized or driven ensemble. Correlation spectra of the measured spin noise reveals g-factors, nuclear spin, isotope abundance ratios, hyperfine splittings, nuclear moments, and spin coherence lifetimes -- without having to excite, optically pump, or otherwise drive the spin system away from thermal equilibrium. These noise signatures scale inversely with interaction volume, suggesting routes towards non-perturbative, sourceless magnetic resonance of small solid state spin systems.
We discuss non-trivial effects which emerge when a single spin is embedded in various (normal and Josephson) junctions and discuss a new experimental technique to probe single spin dynamics. We show that current may be influenced by the presence of a single spin and the converse. New spin nutations in a Josephson junction are predicted. We discuss a new general exerimental technique to probe single spin dynamics via noise spectroscopy- by carefully monitoring the current noise, important information can be extracted regarding a single spin motion.