Spatiotemporal Spin Noise Spectroscopy.

We report on the potential of a new spin noise spectroscopy approach by demonstrating all-optical probing of spatiotemporal spin fluctuations. This is achieved by homodyne mixing of a spatially phase-modulated local oscillator with spin-flip scattered light, from which the frequency and wave vector dependence of the spin noise power is unveiled. As a first application of the method we measure the spatiotemporal spin noise in weakly n-doped CdTe layers, from which the electron spin diffusion constant and spin relaxation rates are determined. The absence of spatial spin correlations is also shown for this particular system.