  Theoretical description of electron spin orientation and detection by short
optical pulses is proposed for the ensembles of the singly charged
semiconductor nanocrystals. The complex structure of the valence band in
spherical nanocrystals is taken into account. We demonstrate that the direction
of electron spin injected by the pump pulse depends on both the pump pulse
helicity and the pump pulse power. It is shown that the train of the optical
pulses can lead to the complete orientation of the resident electron spin. The
microscopic theory of the spin Faraday, Kerr and ellipticity effects is
developed and the spectral sensitivity of these signals is discussed. We show
that under periodic pumping the pronounced mode-locking of electron spins takes
place and manifests itself as significant spin signals at negative delays
between pump and probe pulses.
