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Periodic laser pulsing of singly charged semiconductor quantum dots in anexternal magnetic field leads to a synchronization of the spin dynamics withthe optical excitation. The pumped electron spins partially rephase prior toeach laser pulse, causing a revival of electron spin polarization with itsmaximum at the incidence time of a laser pulse. The amplitude of this revivalis amplified by the frequency focusing of the surrounding nuclear spins. Twocomplementary theoretical approaches for simulating up to 20 million laserpulses are developed and employed that are able to bridge between 11 orders ofmagnitude in time: a fully quantum mechanical description limited to smallnuclear bath sizes and a technique based on the classical equations of motionapplicable for a large number of nuclear spins. We present experimental data ofthe nonmonotonic revival amplitude as function of the magnetic field appliedperpendicular to the optical axis. The dependence of the revival amplitude onthe external field with a profound minimum at $4\;$T is reproduced by both ofour theoretical approaches and is ascribed to the nuclear Zeeman effect. Sincethe nuclear Larmor precession determines the electronic resonance condition, italso defines the number of electron spin revolutions between pump pulses, theorientation of the electron spin at the incidence time of a pump pulse, and theresulting revival amplitude. The magnetic field of $4\;$T, for example,corresponds to half a revolution of nuclear spins between two laser pulses.

Magnetic field dependence of the electron spin revival amplitude in periodically pulsed quantum dots