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

Abstract

The recent experimental advancement to realise ultracold gases scattering off an eight-fold optical potential [Phys. Rev. Lett. 122, 110404 (2019)] 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 eight-fold 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 non-zero long-range interactions, we find that density wave states can spontaneously break the eight-fold symmetry, and may even possess no rotational symmetry. We find the local variation in the number of nearest neighbours 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 neighbours is not a unique property of the considered eight-fold lattice, and we expect our results to be generalisable to any quasicrystalline potential where there are only small position dependent variations in the site energy, tunnelling and interactions.

Mean-field study of the Bose-Hubbard model in Penrose lattice

“…A typical strongly correlated system in optical lattice is the Bose-Hubbard model, where phase transition between Mott insulator (MI) to superfluid (SF) phase appears [39] as experimentally observed [40,41]. Recent achievements in establishing an eight-fold rotationally symmetric optical lattice attract new attention [42], in connection with theoretical investigation of an extended Bose-Hubbard with quasicrystalline confined potential [43], where spontaneous breaking of underlying eight-fold symmetry is observed. However, the effect of aperiodicity in the Bose-Hubbard model is not yet fully understood both theoretically and experimentally.…”

Dipolar Bose-Hubbard Model in finite-size real-space cylindrical lattices

“…Solid order in region III, which has the most extreme spatial variation of interactions and has significant occupation of both the polar and equatorial sublattices due to repulsion along the axis, builds sharply on the polar sublattice and then gradually on the equatorial sublattice. Spatially-diffuse solid-tunnelling transitions in extended Bose-Hubbard models have previously been predicted due to external mechanisms such as inhomogeneous trapping potentials [58] and varying coordination number in quasicrystal lattices [59], but here this effect is driven entirely by interactions.…”

Bulk Localised Transport States in Infinite and Finite Quasicrystals via Magnetic Aperiodicity

“…Another interesting question is how the BLT states would appear or alter the physics in the presence of interactions. The study of the physics of two-dimensional quasicrystals including interactions is an emergent topic [96][97][98]. With the recent advances in many-body numerical techniques [99][100][101], the physics of BLT states and their ramifications in quasicrystalline lattices in the many-body regime could soon be probed.…”