  We study systematically the period-doubled Bloch states for a weakly
interacting Bose-Einstein condensate in a one-dimensional optical lattice. This
kind of state is of form $\psi_k=e^{ikx}\phi_k(x)$, where $\phi_k(x)$ is of
period twice the optical lattice constant. Our numerical results show how these
nonlinear period-doubled states grow out of linear period-doubled states at a
quarter away from the Brillouin zone center as the repulsive interatomic
interaction increases. This is corroborated by our analytical results. We find
that all nonlinear period-doubled Bloch states have both Landau instability and
dynamical instability.
