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Long-lived double periodic patterns in dipolar cigar-shaped Bose–Einstein condensates in an optical lattice

Periodic patterns with doubled lattice periodicity (DPP) that originate from the modulationally unstable continuous-wave (CW)-type state are found in dipolar Bose–Einstein condensates loaded into a deep one-dimensional optical lattice. The DPP can be created in the presence of any type of contact and/or dipole–dipole (DD) interaction in the system. The main finding is the possibility of creating the stable DPP branch from the CW solution via supercritical pitchfork bifurcation in a condensate with the repulsive contact and certain values of the repulsive DD interaction parameters. In all other combinations of interaction types, we showed that close to the anticontinuum limit DPPs are long-lived, while the instability grows with an increase of the inter-site coupling.