``Listening" to the spin noise of electrons and holes in semiconductor quantum dots*

The coherence and dynamical properties of spins in semiconductors are usually studied with powerful techniques based on optical pump-probe or spin resonance methods. Such methods are necessarily perturbative, in that one measures the (dissipative) response of the spins resulting from an external drive or excitation field (\emph{eg}, free-induction decays). However, in accord with the fluctuation-dissipation theorem, the intrinsic fluctuations of the spin system - if experimentally measurable - can also reveal the same dynamical properties (such as $g$-factors and decoherence times) without ever perturbing the spin ensemble from thermal equilibrium. This talk describes how we measure electron and hole spin dynamics in semiconductors by passively ``listening'' to these small spin noise signals [1]. We employ a spin noise spectrometer based on a sensitive optical Faraday rotation magnetometer that is coupled to a digitizer and field-programmable gate array (FPGA), to acquire noise spectra from 0-1 GHz in real time with picoradian/root-Hz sensitivity. In doped (In,Ga)As/GaAs quantum dots, both electron and hole spin fluctuations generate distinct noise peaks whose shift and broadening with magnetic field directly reveal their $g$-factors and dephasing rates. A large, energy-dependent anisotropy of in-plane hole $g$-factors is clearly exposed, reflecting systematic variations in the average confinement potential. In contrast with conventional pump-probe studies, noise signals increase as the probed volume shrinks, suggesting possible routes towards non-perturbative, sourceless magnetic resonance of few-spin systems.\\[4pt][1] PRL \textbf{104}, 036601 (2010); PRB \textbf{79}, 035208 (2009).