  We study the effect of bias voltage on the nuclear spin polarization of a
ballistic wire, which contains electrons and nuclei interacting via hyperfine
interaction. In equilibrium, the localized nuclear spins are helically
polarized due to the electron-mediated Ruderman-Kittel-Kasuya-Yosida (RKKY)
interaction. Focusing here on non-equilibrium, we find that an applied bias
voltage induces a uniform polarization, from both helically polarized and
unpolarized spins available for spin flips. Once a macroscopic uniform
polarization in the nuclei is established, the nuclear spin helix rotates with
frequency proportional to the uniform polarization. The uniform nuclear spin
polarization monotonically increases as a function of both voltage and
temperature, reflecting a thermal activation behavior. Our predictions offer
specific ways to test experimentally the presence of a nuclear spin helix
polarization in semiconducting quantum wires.
