  We implement the homodyne detection scheme for an increase of the
polarimetric sensitivity in spin noise spectroscopy. Controlling the laser
intensity of the local oscillator, which is guided around the sample and does
not perturb the measured spin system, we are able to improve the
signal-to-noise ratio. The opportunity of additional amplification of the
measured signal strength allows us to reduce the probe laser intensity incident
onto the sample and therefore to approach the non-perturbative regime. The
efficiency of this scheme with signal enhancement by more than a factor of 3 at
low probe powers is demonstrated on bulk $n$-doped GaAs where the reduced
electron-spin relaxation rate is shown experimentally. Additionally, the
control of the optical phase provides us with the possibility to switch between
the measurement of Faraday rotation and ellipticity without changes in the
optical setup.
