The fast dephasing of electron spins in an ensemble of quantum dots is detrimental for applications in quantum information processing. We show here that dephasing can be overcome by using a periodic train of light pulses to synchronize the phases of the precessing spins, and we demonstrate this effect in an ensemble of singly charged (In,Ga)As/GaAs quantum dots. This mode locking leads to constructive interference of contributions to Faraday rotation and presents potential applications based on robust quantum coherence within an ensemble of dots.

The hyperfine interaction of an electron with the nuclei is considered as the primary obstacle to coherent control of the electron spin in semiconductor quantum dots. We show, however, that the nuclei in singly charged quantum dots act constructively by focusing the electron spin precession about a magnetic field into well-defined modes synchronized with a laser pulse protocol. In a dot with a synchronized electron, the light-stimulated fluctuations of the hyperfine nuclear field acting on the electron are suppressed. The information about electron spin precession is imprinted in the nuclei and thereby can be stored for tens of minutes in darkness. The frequency focusing drives an electron spin ensemble into dephasing-free subspaces with the potential to realize single frequency precession of the entire ensemble.

Electron spin coherence has been generated optically in $n$-type modulation doped $(\mathrm{In},\mathrm{Ga})\mathrm{As}/\mathrm{GaAs}$ quantum dots (QDs) which contain on average a single electron per dot. The coherence arises from resonant excitation of the QDs by circularly polarized laser pulses, creating a coherent superposition of an electron and a trion. Time dependent Faraday rotation is used to probe the spin precession of the optically oriented electrons about a transverse magnetic field. The coherence generation can be controlled by pulse intensity, being most efficient for $(2n+1)\pi$ pulses.

We measure the frequency spectra of random spin fluctuations, or “spin noise,” in ensembles of $(\mathrm{In},\mathrm{Ga})\mathrm{As}/\mathrm{GaAs}$ quantum dots (QDs) at low temperatures. We employ a spin noise spectrometer based on a sensitive optical Faraday rotation magnetometer that is coupled to a digitizer and field-programmable gate array, to measure and average noise spectra from 0–1 GHz continuously in real time with $\mathrm{\text{subnanoradian}}/\sqrt{\mathrm{Hz}}$ sensitivity. Both electron and hole spin fluctuations generate distinct noise peaks, whose shift and broadening with magnetic field directly reveal their $g$ factors and dephasing rates within the ensemble. A large, energy-dependent anisotropy of the in-plane hole $g$ factor is clearly exposed, reflecting systematic variations in the average QD confinement potential.

The Zeeman splitting and the underlying $g$ factor for conduction-band electrons in $\mathrm{Ga}\mathrm{As}∕{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum wells have been measured by spin-beat spectroscopy based on a time-resolved Kerr rotation technique. The experimental data are plotted as functions of the lowest band-to-band optical transition energy, i.e., the effective band gap of the quantum wells. The model calculations suggest that in the tracked range of transition energies $E$ from $1.52\text{to}2.0\mathrm{eV}$, the component of electron $g$ factor along the growth axis follows closely the universal dependence $g_{\Vert }\left(E\right)\approx 0.445+3.38(E-1.519)-2.21{(E-1.519)}^2$ (with $E$ given in eV), and this universality also embraces ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ alloys. On the other hand, the in-plane $g$ factor component deviates in a systematic way from this universal curve, with the degree of deviation controlled by the structural anisotropy. The experimental data are in good agreement with the theoretical predictions.