The behavior of ultra-cold atoms in two-dimensional optical lattices with asymmetric periodic pinning potentials

We examine the disorder effect of the pinning potential acting on ultracold atoms in the optical lattice based on the expanded Bose–Hubbard model for soft-core bosons. Using Quantum Monte Carlo simulation with local optimal Worm algorithm, we obtain three additional crystal-like phase types at commensurate densities, ρ = 1/2, 1, and 3/2 besides two basic phases which are superfluid and Mott insulator phases as observed in the bare soft-core boson model. In the presence of disorder, the superfluid and the charge-density wave coexist in the sandwiched regions between the superfluid and the solid orders around the commensurate densities. This observation signifies our work because it has not been revealed previously in other models of the soft-core bosons. •Three different types of charge-density-wave (CDW) orders are observed at commensurate particle densities.•The superfluid and solid phases simultaneously exist in the neighboring regions of solid densities.•The asymmetric pining potential induces an anisotropic superfluid, proposing the quasi-one-dimensional superfluid in the two-dimensional optical lattice.