Period-Doubled Bloch States in a Bose–Einstein Condensate**Supported by the National Key Research and Development Program of China under Grant Nos 2016YFA0301501 and 2017YFA0303302, and the National Natural Science Foundation of China under Grants Nos 11334001, 61727819, 61475007 and 91736208.

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 ψk = eikx ϕk(x), where ϕk(x) is of a 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.