Period-doubled Bloch states in a Bose-Einstein condensate

Abstract

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 ${\psi }_k=e^{ikx}{\varphi }_k(x)$, where ${\varphi }_k(x)$ 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.

5 pages, 5 figures