Period-doubled Bloch states in a Bose-Einstein condensate

TL;DR

This paper investigates the formation and stability of period-doubled Bloch states in a weakly interacting Bose-Einstein condensate within a one-dimensional optical lattice, revealing their growth from linear states and inherent instabilities.

Contribution

It provides a systematic numerical and analytical study of nonlinear period-doubled Bloch states and their instabilities in a Bose-Einstein condensate in an optical lattice.

Findings

Nonlinear period-doubled states emerge from linear states as interaction increases.

All studied states exhibit both Landau and dynamical instabilities.

States grow out of linear states at a quarter of the Brillouin zone center.

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 $\psi_k=e^{ikx}\phi_k(x)$, 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.