Coherent Propagation of Spin Helices in a Quantum-Well Confined Electron Gas

We use phase-resolved transient grating spectroscopy to measure the propagation of spin helices in a high mobility $n$-GaAs/AlGaAs quantum well with an applied in-plane electric field. At relatively low fields helical modes crossover from overdamped excitations where the spin-precession period exceeds the spin lifetime, to a regime of coherent propagation where several spin-precession periods can be observed. We demonstrate that the envelope of a spin polarization packet reaches a current-driven velocity of 10$^7$ cm s$^{-1}$ in an applied field of 70 V cm$^{-1}$.