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

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.

22 pages, 6 figures

References in corpus (29)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• The density-matrix renormalization group in the age of matrix product states
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• A High Phase-Space-Density Gas of Polar Molecules
• Bose-Einstein condensation of chromium
• Realizing a lattice spin model with polar molecules
• Bose-Einstein Condensation of Erbium
• Strongly correlated 2D quantum phases with cold polar molecules: controlling the shape of the interaction potential
• Quantum degenerate dipolar Fermi gas
• Exponential localization of Wannier functions in insulators
• Spontaneously modulated spin textures in a dipolar spinor Bose-Einstein condensate
• Radial and angular rotons in trapped dipolar gases
• Dual-Species Bose-Einstein Condensate of ${}^{87}$Rb and ${}^{133}$Cs
• Ultracold Fermionic Feshbach Molecules of ${}^{23}$Na${}^{40}$K
• Superfluid behaviour of a two-dimensional Bose gas
• Applying matrix product operators to model systems with long-range interactions
• Suppressing the loss of ultracold molecules via the continuous quantum Zeno effect
• Anisotropic Polarizability of Ultracold Polar ${}^{40}$K${}^{87}$Rb Molecules
• Observation of interspecies Li-Cs Feshbach resonances
• Tensor operators: constructions and applications for long-range interaction systems
• Ultracold mixtures of atomic Li-6 and Cs-133 with tunable interactions
• Bose-Hubbard model with occupation dependent parameters
• Simulating quantum magnets with symmetric top molecules
• Meta-nematic, smectic and crystalline phases of dipolar fermions in an optical lattice
• Dipolar confinement-induced resonances of ultracold gases in waveguides
• A high phase-space density mixture of ${}^{87}$Rb and ${}^{133}$Cs: towards ultracold heteronuclear molecules
• The Molecular Hubbard Hamiltonian: Field Regimes and Molecular Species
• Strongly interacting fermions in an optical lattice

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• Observing the two-dimensional Bose glass in an optical quasicrystal
• Observation of generalized t-J spin dynamics with tunable dipolar interactions
• Accuracy of quantum simulators with ultracold dipolar molecules: a quantitative comparison between continuum and lattice descriptions
• Superfluid phases induced by the dipolar interactions
• Quantum simulator of link models using spinor dipolar ultracold atoms
• Recent progress on quantum simulations of non-standard Bose-Hubbard models
• Lattice control of non-ergodicity in a polar lattice gas
• Detecting quadrupole interactions in ultracold Fermi gases
• Controlling the dynamics of ultracold polar molecules in optical tweezers
• Multi-mode Bose-Hubbard model for quantum dipolar gases in confined geometries
• Transversal effects on the ground-state of hard-core dipolar bosons in one-dimensional optical lattices
• Beyond-mean-field corrections for dipolar bosons in an optical lattice
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• The role of interaction-induced tunneling in the dynamics of polar lattice bosons
• On cold gases with anisotropic interactions