  The intrinsic fluctuations of electron spins in semiconductors and atomic
vapors generate a small, randomly-varying "spin noise" that can be detected by
sensitive optical methods such as Faraday rotation. Recent studies have
demonstrated that the frequency, linewidth, and lineshape of this spin noise
directly reveals dynamical spin properties such as dephasing times, relaxation
mechanisms and g-factors without perturbing the spins away from equilibrium.
Here we demonstrate that spin noise measurements using wavelength-tunable probe
light forms the basis of a powerful and novel spectroscopic tool to provide
unique information that is fundamentally inaccessible via conventional linear
optics. In particular, the wavelength dependence of the detected spin noise
power can reveal homogeneous linewidths buried within inhomogeneously-broadened
optical spectra, and can resolve overlapping optical transitions belonging to
different spin systems. These new possibilities are explored both theoretically
and via experiments on spin systems in opposite limits of inhomogeneous
broadening (alkali atom vapors and semiconductor quantum dots).
