Theory of optically detected spin noise in nanosystems

The theory of spin noise in low-dimensional systems and bulk semiconductors is reviewed. Spin noise is usually detected by optical means continuously measuring the rotation angle of the polarization direction of a probe beam passing through a sample. Spin noise spectra yield rich information about the spin properties of the system, for example, $g$-factors of the charge carriers, spin relaxation times, parameters of the hyperfine interaction, spin-orbit coupling constants, frequencies and widths of the optical resonances. The review describes basic models of spin noise, methods to theoretically describe it, and thier relation to experimental results. We also discuss the relation between spin noise spectroscopy and strong and weak quantum measurements, as well as spin flip Raman scattering, and analyze similar effects, including manifestations of the charge, current, and valley polarization fluctuations in the optical response. Possible directions for further development of spin noise spectroscopy are outlined.