  The periodic optical orientation of electron spins in (In,Ga)As/GaAs quantum
dots leads to the formation of electron spin precession modes about an external
magnetic field which are resonant with the pumping periodicity. As the electron
spin is localized within a nuclear spin bath, its polarization imprints onto
the spin polarization of the bath. The latter acts back on the electron spin
polarization. We implement a pulse protocol where a train of laser pulses is
followed by a long, dark gap. It allows us to obtain a high-resolution
precession mode spectrum from the free evolution of the electron spin
polarization. Additionally, we vary the number of pump pulses in a train to
investigate the build-up of the precession modes. To separate out nuclear
effects, we suppress the nuclear polarization by using a radio-frequency field.
We find that a long-living nuclear spin polarization imprinted by the periodic
excitation significantly speeds up the buildup of the electron spin
polarization and induces the formation of additional electron spin precession
modes. To interpret these findings, we extend an established dynamical nuclear
polarization model to take into account optically detuned quantum dots for
which nuclear spins activate additional electron spin precession modes.
