Spatial period-doubling in Bose-Einstein condensates in an optical lattice

TL;DR

This paper explores the existence and properties of period-doubled stationary states in Bose-Einstein condensates within optical lattices, revealing their relation to soliton trains and dynamical instabilities.

Contribution

It introduces the concept of period-doubled states in BECs in optical lattices and analyzes their energy bands using both discrete models and the Gross-Pitaevskii equation.

Findings

Period-doubled states exist beyond the usual Bloch states.

Onset of dynamical instability coincides with the emergence of period-doubled states.

Period-doubled states are related to soliton trains.

Abstract

We demonstrate that there exist stationary states of Bose-Einstein condensates in an optical lattice that do not satisfy the usual Bloch periodicity condition. Using the discrete model appropriate to the tight-binding limit we determine energy bands for period-doubled states in a one-dimensional lattice. In a complementary approach we calculate the band structure from the Gross-Pitaevskii equation, considering both states of the usual Bloch form and states which have the Bloch form for a period equal to twice that of the optical lattice. We show that the onset of dynamical instability of states of the usual Bloch form coincides with the occurrence of period-doubled states with the same energy. The period-doubled states are shown to be related to periodic trains of solitons.