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.
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