Dipole-dipole interactions in optical lattices do not follow an inverse cube power law

TL;DR

This paper reveals that effective dipole-dipole interactions in optical lattices deviate from the inverse cube law of free space, showing non-algebraic short-range behavior and a long-range tail, significantly affecting many-body physics.

Contribution

It demonstrates the non-algebraic nature of lattice dipole interactions and quantifies deviations from free-space behavior based on confinement asymmetry.

Findings

Interaction differs by up to 36% from free-space at nearest neighbors

Effective interactions are non-algebraic at short to medium distances

Results are applicable to both bosonic and fermionic dipolar gases

Abstract

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 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-1D 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.