Probing semiconductor carrier kinetics with ultrafast nonlinear Faraday rotation

We demonstrate that in semiconductors with strong Coulomb exchange correlations, transient nonlinear Faraday rotation spectroscopy (FRS) more accurately probes the ultrafast carrier relaxation than the widely used differential transmission spectroscopy (DTS). We calculate nonlinear FRS and DTS by solving the six-band semiconductor Bloch equations for magnetic ${\mathrm{Cd}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ and CdTe quantum wells. We show that for highly excited carriers, nonlinear FRS rotation spectra closely monitor the ultrafast thermalization of the carrier distribution, unlike DTS signals. We further show that the magnetic band tuning capabilities (giant Zeeman splitting) of dilute magnetic semiconductors allows one to investigate the electron kinetics in selective bands.