Spin noise of localized electrons interacting with optically cooled nuclei

A microscopic theory of spin fluctuations of localized electrons interacting with optically cooled nuclear spin bath has been developed. Since nuclear spin temperature may stay low enough for macroscopically long time, the nuclear spin system becomes very sensitive to an external magnetic field. This strongly affects electron spin noise spectrum. It has been shown that in the case of weak fields/relatively high nuclear spin temperature, a small degree of nuclear spin polarization affect the electron spin fluctuations in the same way as an additional external magnetic field. By contrast, the high degree of nuclear polarization realized in relatively strong magnetic field and low nuclear spin temperature leads to a suppression of hyperfine field fluctuations and to a dramatic narrowing of precession-induced peak in the spin noise spectrum. The experimental possibilities of nuclear spin system investigation by means of spin noise spectroscopy are discussed.