Increased sensitivity of spin noise spectroscopy using homodyne detection in $n$-doped GaAs

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.