  We imaged the transport of current-induced spin coherence in a
two-dimensional electron gas confined in a triple quantum well. Nonlocal Kerr
rotation measurements, based on the optical resonant amplification of the
electrically-induced polarization, revealed a large spatial variation of the
electron g factor and the efficient generation of a current controlled
spin-orbit field in a macroscopic Hall bar device. We observed coherence times
in the nanoseconds range transported beyond half-millimeter distances in a
direction transverse to the applied electric field. The measured long spin
transport length can be explained by two material properties: large mean free
path for charge diffusion in clean systems and enhanced spin-orbit coefficients
in the triple well.
