| Popis: |
We study the effective dipole–dipole interactions in ultracold quantum gases on optical lattices as a function of asymmetry in confinement along the principal axes of the lattice. In particular, we study the matrix elements of the dipole–dipole interaction in the basis of lowest band Wannier functions which serve as a set of low-energy states for many-body physics on the lattice. We demonstrate that, for shallow lattices in quasi-reduced dimensional scenarios, the effective interaction between dipoles in an optical lattice is non-algebraic in the inter-particle separation at short to medium distance on the lattice scale and has a long-range power-law tail, in contrast to the pure power-law behavior of the dipole–dipole interaction in free space. The modifications to the free-space interaction can be sizable; we identify differences of up to 36% from the free-space interaction at the nearest-neighbor distance in quasi-one-dimensional arrangements. The interaction difference depends essentially on asymmetry in confinement, due to the d-wave anisotropy of the dipole–dipole interaction. Our results do not depend on statistics, applying to both dipolar Bose–Einstein condensates and degenerate Fermi gases. Using matrix product state simulations, we demonstrate that use of the correct lattice dipolar interaction leads to significant deviations from many-body predictions using the free-space interaction. Our results are relevant to up and coming experiments with ultracold heteronuclear molecules, Rydberg atoms and strongly magnetic atoms in optical lattices. |
