Super-frustration in a dipolar Bose-Einstein condensate introduced by an optical lattice

Dipolar Bose-Einstein condensates can form arrays of spatially distinct droplets with hexagonal symmetry on top of a small background density in what's known as the supersolid phase. Here we consider the application of a square optical lattice to such a system. The 4-fold symmetry of the lattice, and the spacing set by it, competes with the intrinsic 6-fold symmetry and spacing of the dipolar droplets in the unperturbed ground state. By developing a graphics processing unit enhanced solver to the extended Gross-Pitaevskii equation, we find that the application of the lattice can lead to frustration for certain lattice parameters while maintaining phase coherence between droplets, and thus we consider such states super-frustrated. We additionally see second-order phase transitions as a function of lattice depth and glassiness characterized by a deeply degenerate ground state manifold.