  We advance all optical spin noise spectroscopy (SNS) in semiconductors to
detection bandwidths of several hundred gigahertz by employing an ingenious
scheme of pulse trains from ultrafast laser oscillators as an optical probe.
The ultrafast SNS technique avoids the need for optical pumping and enables
nearly perturbation free measurements of extremely short spin dephasing times.
We employ the technique to highly n-doped bulk GaAs where magnetic field
dependent measurements show unexpected large g-factor fluctuations.
Calculations suggest that such large g-factor fluctuations do not necessarily
result from extrinsic sample variations but are intrinsically present in every
doped semiconductor due to the stochastic nature of the dopant distribution.
