Mean-field phases of an ultracold gas in a quasicrystalline potential

The recent experimental advancement to realize ultracold gases scattering off an eightfold optical potential [K. Viebahn, M. Sbroscia, E. Carter, J.-C. Yu, and U. Schneider, Phys. Rev. Lett. 122, 110404 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.110404] heralds the beginning of a new technique to study the properties of quasicrystalline structures. Quasicrystals possess long-range order but are not periodic, and are still little studied in comparison to their periodic counterparts. Here, we consider an ultracold bosonic gas in an eightfold symmetric lattice and assume a toy model where the atoms occupy the ground states of the local minima of the potential. The ground-state phases of the system are studied, with particular interest in the local nature of the phases. The usual Mott-insulator, density wave, and supersolid phases of the standard and extended Bose-Hubbard model are observed. For nonzero long-range interactions, we find that density wave states can spontaneously break the eightfold symmetry, and may even possess no rotational symmetry. We find the local variation in the number of nearest neighbors to play a vital role in the phase transitions, local structure, and global symmetries of the ground states. This variation in the number of nearest neighbors is not a unique property of the considered eightfold lattice, and we expect our results to be generalizable to any quasicrystalline potential where there are only small position dependent variations in the site energy, tunneling, and interactions.