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arXiv:1808.07723 · Physical Review A

Near-threshold bound states of the dipole-dipole interaction

Tijs Karman, Matthew D. Frye, John D. Reddel, Jeremy M. Hutson

Published Dec 4, 2018• 6 citations
arXivHTMLPDF

Abstract

We study the two-body bound states of a model Hamiltonian that describes the interaction between two field-oriented dipole moments. This model has been used extensively in the many-body physics of ultracold polar molecules and magnetic atoms, but its few-body physics has been explored less fully. With a hard-wall short-range boundary condition, the dipole-dipole bound states are universal and exhibit a complicated pattern of avoided crossings between states of different character. For more realistic Lennard--Jones short-range interactions, we consider parameters representative of magnetic atoms and polar molecules. For magnetic atoms, the bound states are dominated by the Lennard--Jones potential, and the perturbative dipole-dipole interaction is suppressed by the special structure of van der Waals bound states. For polar molecules, we find a dense manifold of dipole-dipole bound states with many avoided crossings as a function of induced dipole or applied field, similar to those for hard-wall boundary conditions. This universal pattern of states may be observable spectroscopically for pairs of ultracold polar molecules.

DOI
10.1103/physreva.98.062502

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We study the two-body bound states of a model Hamiltonian that describes the interaction between two field-oriented dipole moments. This model has been used extensively in the many-body physics of ultracold polar molecules and magnetic atoms, but its few-body physics has been explored less fully. With a hard-wall short-range boundary condition, the dipole-dipole bound states are universal and exhibit a complicated pattern of avoided crossings between states of different character. For more realistic Lennard--Jones short-range interactions, we consider parameters representative of magnetic atoms and polar molecules. For magnetic atoms, the bound states are dominated by the Lennard--Jones potential, and the perturbative dipole-dipole interaction is suppressed by the special structure of van der Waals bound states. For polar molecules, we find a dense manifold of dipole-dipole bound states with many avoided crossings as a function of induced dipole or applied field, similar to those for hard-wall boundary conditions. This universal pattern of states may be observable spectroscopically for pairs of ultracold polar molecules.
We explore on-site interaction energies UUU for pairs of shielded ultracold molecules on the same lattice site. We use 2-dimensional effective potentials appropriate for microwave shielding, which have dipole-dipole character at long range but feature a very large repulsive core when the two molecules come close together. This causes very strong correlation between the motions of two molecules on the same site. We find behavior very different from that for ultracold atoms: in particular, there are states for which UUU is negative for weak lattices but crosses zero to positive values as the lattice strength increases. This behavior is found for both unbound pairs and 2-body bound states. The latter will give access to previously unexplored types of strongly dipolar Hubbard physics with multiple site occupancy.
Progress in ultracold experiments with polar molecules requires a clear understanding of their interactions and reactivity at ultralow collisional energies. Two important theoretical steps in this process are the characterization of interaction potentials between molecules and the modeling of the reactive scattering mechanism. Here, we report on the ab initio calculation of isotropic and anisotropic van der Waals interaction potentials for polar KRb and RbCs colliding with each other or with ultracold atoms. Based on these potentials and two short-range scattering parameters, we then develop a single-channel scattering model with flexible boundary conditions. Our calculations show that, at low temperatures (and in the absence of an external electric field), the reaction rates between molecules or between molecules and atoms have a resonant character as a function of the short-range parameters. We also find that both the isotropic and anisotropic van der Waals coefficients have significant contributions from dipole coupling to excited electronic states. Their values can differ dramatically from those solely obtained from the permanent dipole moment. A comparison with recently obtained reaction rates of fermionic 40 K 87 Rb shows that the experimental data cannot be explained by a model where the short-range scattering parameters are independent of the relative orbital angular momentum or partial wave.
Abstract Using the multipolar expansion of electrostatic and magnetostatic potential energies, we characterize the long-range interactions between two weakly-bound diatomic molecules, taking as an example the paramagnetic Er 2 Feshbach molecules which were produced recently. Since inside each molecule individual atoms conserve their identity, the intermolecular potential energy can be expanded as the sum of pairwise atomic potential energies. In the case of Er 2 Feshbach molecules, we show that the interaction between atomic magnetic dipoles gives rise to the usual term of the multipolar expansion, where R is the intermolecular distance, but also to additional terms scaling as and so on. Those terms are due to the interaction between effective molecular multipole moments, and are strongly anisotropic with respect to the orientation of the molecules. Similarly, the atomic pairwise van der Waals interaction results in ... terms in the intermolecular potential energy. By calculating the reduced electric-quadrupole moment of erbium ground level a.u., we also demonstrate that the electric–quadrupole interaction energy is negligible with respect to the magnetic dipole and van der Waals interaction energies. The general formalism presented in this article can be applied to calculate the long-range potential energy between arbitrary charge distributions composed of almost free subsystems.
We report on the five-body repulsive and attractive van der Waals interactions between the strongly dipole-dipole coupled Rydberg states. Compared to four-body van der Waals interactions, five-body van der Waals interactions show more energy levels and more potential wells caused by avoided crossings. This research bridges the few-body physics and many-body physics. Other disciplines, such as chemistry, biology, and medical fields, will also benefit from better understanding van der Waals interactions.
We design dipolar quantum many-body Hamiltonians that will facilitate the realization of exotic quantum phases under current experimental conditions achieved for polar molecules. The main idea is to modulate both single-body potential barriers and two-body dipolar interactions on a spatial scale of tens of nanometers to strongly enhance energy scales and, therefore, relax temperature requirements for observing new quantum phases of engineered many-body systems. We consider and compare two approaches. In the first, nanoscale barriers are generated with standing-wave optical light fields exploiting optical nonlinearities. In the second, static electric-field gradients in combination with microwave dressing are used to write nanostructured spatial patterns on the induced electric dipole moments, and thus dipolar interactions. We study the formation of interlayer and interface bound states of molecules in these configurations, and provide detailed estimates for binding energies and expected losses for present experimental setups.
Few-body interactions offer the opportunity to study the isolated atom to few-body coupled molecules, and to condensed matter transitions. Atoms in molecules and in condensed matters are coupled by different orders of multipole–multipole interactions, which all stem from different orders of approximations from coulomb interactions between multiple charges. The lowest order multipole–multipole interaction is the dipole–dipole interaction, which is proportional to the size of the dipole. In this article, we use Rydberg atoms, which have more than 1000 times greater electric dipoles than the ground state atoms, to study the van der Waals interaction between few bodies. In addition to the large dipoles, the kinetic energy of the atoms is significantly reduced by reducing the temperature, which makes these interactions stable and observable. Here, we report on the 2D and 3D few-body interaction potentials and possible ways of creating semistable molecules in such an ultracold Rydberg gas with a temperature of ≈100 nK. Although we use Rydberg atoms in this article, this calculation can be applied to other states too. The results reported here are useful for studying repulsive van der Waals interactions and creating ultracold molecules.