Pump-Probe Faraday Rotation and Ellipticity in an Ensemble of Singly Charged Quantum Dots

A description of spin Faraday rotation, Kerr rotation and ellipticity signals for single- and multi-layer ensembles of singly charged quantum dots (QDs) is developed. The microscopic theory considers both the single pump-pulse excitation and the effect of a train of such pulses, which in the case of long resident-electron spin coherence time leads to a stationary distribution of the electron spin polarization. The calculations performed for single-color and two-color pump-probe setups show that the three experimental techniques: Faraday rotation, Kerr rotation and ellipticity measurements provide complementary information about an inhomogeneous ensemble of QDs. The microscopic theory developed for a three-dimensional ensemble of QDs is shown to agree with the phenomenological description of these effects. The typical time-dependent traces of pump-probe Faraday rotation, Kerr rotation and ellipticity signals are calculated for various experimental conditions.