Spectroscopy of spontaneous spin noise as a probe of spin dynamics and magnetic resonance

Not all noise in experimental measurements is unwelcome. Certain fundamental noise sources contain valuable information about the system itself -- a notable example being the inherent voltage fluctuations that exist across any resistor (Johnson noise), from which temperature may be determined[1,2]. In magnetic systems, fundamental noise can exist in the form of random spin fluctuations[3,4]. Felix Bloch noted in 1946 that statistical fluctuations of N paramagnetic spins should generate measurable noise of order \sqrt{N} spins, even in zero magnetic field[5,6]. Here we address precisely these same spin fluctuations, using off-resonant Faraday rotation to passively[7,8] "listen" to the magnetization noise in an equilibrium ensemble of paramagnetic alkali atoms. 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 system away from thermal equilibrium. These noise signatures scale inversely with interaction volume, suggesting routes towards non-perturbative, sourceless magnetic resonance of small systems.