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We observe the noise spectrum of electron spins in bulk GaAs by Faraday-rotation noise spectroscopy. The experimental technique enables the undisturbed measurement of the electron-spin dynamics in semiconductors. We measure exemplarily the electron-spin relaxation time and the electron Landé g factor in -doped GaAs at low temperatures and find good agreement of the measured noise spectrum with a theory based on Poisson distribution probability.

In this Letter, the first spin noise spectroscopy measurements in semiconductor systems of reduced effective dimensionality are reported. The nondemolition measurement technique gives access to the otherwise concealed intrinsic, low temperature electron spin relaxation time of n-doped GaAs (110) quantum wells and to the corresponding low temperature anisotropic spin relaxation. The Brownian motion of the electrons within the spin noise probe laser spot becomes manifest in a modification of the spin noise line width. Thereby, the spatially resolved observation of the stochastic spin polarization uniquely allows to study electron dynamics at equilibrium conditions with a vanishing total momentum of the electron system.

Semiconductor spin noise spectroscopy (SNS) has emerged as a unique experimental tool that utilizes spin fluctuations to provide profound insight into undisturbed spin dynamics in doped semiconductors and semiconductor nanostructures. The technique maps ever present stochastic spin polarization of free and localized carriers at thermal equilibrium via the Faraday effect onto the light polarization of an off-resonant probe laser and was transferred from atom optics to semiconductor physics in 2005. The inimitable advantage of spin noise spectroscopy to all other probes of semiconductor spin dynamics lies in the fact that in principle no energy has to be dissipated in the sample, i.e., SNS exclusively yields the intrinsic, undisturbed spin dynamics and promises optical non-demolition spin measurements for prospective solid state based optical spin quantum information devices. SNS is especially suitable for small electron ensembles as the relative noise increases with decreasing number of electrons. In this review, we first introduce the basic principles of SNS and the difference in spin noise of donor bound and of delocalized conduction band electrons. We continue the introduction by discussing the spectral shape of spin noise and prospects of spin noise as a quantum interface between light and matter. In the main part, we give a short overview about spin relaxation in semiconductors and summarize corresponding experiments employing SNS. Finally, we give in-depth insight into the experimental aspects and discuss possible applications of SNS.

We have measured the electron spin relaxation rate and the integrated spin noise power in ndoped GaAs for temperatures between 4 K and 80 K and for doping concentrations ranging from 2.7 × 10 −15 cm −3 to 8.8 × 10 −16 cm −3 using spin noise spectroscopy. The temperature dependent measurements show a clear transition from localized to free electrons for the lower doped samples and confirm mainly free electrons at all temperatures for the highest doped sample. While the sample at the metal-insulator-transition shows the longest spin relaxation time at low temperatures, a clear crossing of the spin relaxation rates is observed at 70 K and the highest doped sample reveals the longest spin relaxation time above 70 K.