  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.
