Birefringence and dichroism effects in the spin noise spectra of a spin-1 system

We perform spin noise spectroscopy experiments in metastable helium atoms at room temperature, with a probe light whose frequency is blue detuned from the D _0 line. Both circular birefringence fluctuations (Faraday noise) and linear birefringence fluctuations (ellipticity noise) are explored theoretically and experimentally. In particular, it is shown that in both cases but for different optical detunings, two noise resonances are isolated at the Larmor frequency and at twice the Larmor frequency with a behavior, which strongly depends on the orientation of the probe field polarization. The simple structure of metastable helium allows us to probe, model and explain the changes in the behavior of these peaks in terms of circular and linear dichroisms and birefringences as well as in terms of spin oscillation modes.