  We study the influence of nuclei-induced frequency focusing on the mode
locking of spin coherence in quantum dots subjected to a periodic train of
optical pulses. In particular, we address the question whether or not
nuclei-induced frequency focusing always enhances the effect of spin mode
locking. We combine two advanced semiclassical approaches and extend the
resulting model by including the full dynamics of the optically excited trion
state. In order to reduce the discrepancy to a full quantum model, we establish
a nondeterministic pulse description by interpreting each pump pulse as a
measurement. Both extensions lead to significant qualitative changes of the
physics. Their combination improves the description of the corresponding
experiments. Importantly, we observe the emergence of dynamic nuclear
polarization, i.e., the formation of a nonzero average polarization of the
nuclear spin bath, leading to a certain increase of the coherence time.
