Zero-field spin noise spectrum of an alkali vapor with strong spin-exchange coupling

We study the zero-field optical spin noise spectra (OSN) for a thermal state hot 87Rb vapor with strong spin exchange coupling. Our main findings are: (1) The OSN spectrum consists of two components representing a positive and a negative hyperfine spin correlation (HSC), the relative power of which varies dramatically with the detuning frequency of the probe. (2) There exist two polar frequencies at which the OSN spectrum is completely polarized with one type of HSC. (3) At the limit of far detuning, the power ratio of the positive and negative HSC component of the OSN is 4:5. (4) The total power of the OSN is independent of the strength of SE coupling. (5) We give a simple way of deriving the OSN using the eigensolution of the density matrix equation.