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arXiv:2102.02146 · Physical Review A

Magnetic moments of lanthanide van der Waals dimers

Joseph McCann, John L. Bohn, Lucie D. Augustovičová

Published Apr 15, 2021• 2 citations
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Abstract

Loosely bound van der Waals dimers of lanthanide atoms, as might be obtained in ultracold atom experiments, are investigated. These molecules are known to exhibit a degree of quantum chaos due to the strong anisotropic mixing of their angular spin and rotation degrees of freedom. Within a model of these molecules, we identify different realms of this anisotropic mixing, depending on whether the spin, the rotation, or both are significantly mixed by the anisotropy. These realms are in turn generally correlated with the resulting magnetic moments of the states.

DOI
10.1103/physreva.103.042812

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Loosely bound van der Waals dimers of lanthanide atoms, as might be obtained in ultracold atom experiments, are investigated. These molecules are known to exhibit a degree of quantum chaos due to the strong anisotropic mixing of their angular spin and rotation degrees of freedom. Within a model of these molecules, we identify different realms of this anisotropic mixing, depending on whether the spin, the rotation, or both are significantly mixed by the anisotropy. These realms are in turn generally correlated with the resulting magnetic moments of the states.
A systematic study of the leading isotropic van der Waals coefficients for the alkali-metal atom+molecule and molecule+molecule systems is presented. Dipole moments and static and dynamic dipole polarizabilities are calculated employing high-level quantum chemistry calculations. The dispersion, induction, and rotational parts of the isotropic van der Waals coefficient are evaluated. The known van der Waals coefficients are then used to derive characteristics essential for simple models of the collisions involving the corresponding ultracold polar molecules.
Abstract The electronic structure of magnetic lanthanide atoms is fascinating from a fundamental perspective. They have electrons in a submerged open 4f shell lying beneath a filled 6s shell with strong relativistic correlations leading to a large magnetic moment and large electronic orbital angular momentum. This large angular momentum leads to strong anisotropies, i. e. orientation dependencies, in their mutual interactions. The long-ranged molecular anisotropies are crucial for proposals to use ultracold lanthanide atoms in spin-based quantum computers, the realization of exotic states in correlated matter, and the simulation of orbitronics found in magnetic technologies. Short-ranged interactions and bond formation among these atomic species have thus far not been well characterized. Efficient relativistic computations are required. Here, for the first time we theoretically determine the electronic and ro-vibrational states of heavy homonuclear lanthanide Er 2 and Tm 2 molecules by applying state-of-the-art relativistic methods. In spite of the complexity of their internal structure, we were able to obtain reliable spin–orbit and correlation-induced splittings between the 91 Er 2 and 36 Tm 2 electronic potentials dissociating to two ground-state atoms. A tensor analysis allows us to expand the potentials between the atoms in terms of a sum of seven spin–spin tensor operators simplifying future research. The strengths of the tensor operators as functions of atom separation are presented and relationships among the strengths, derived from the dispersive long-range interactions, are explained. Finally, low-lying spectroscopically relevant ro-vibrational energy levels are computed with coupled-channels calculations and analyzed.
Lanthanide atoms have an unusual electron configuration, with a partially filled shell of fff orbitals. This leads to a set of characteristic properties that enable enhanced control over ultracold atoms and their interactions: large numbers of optical transitions with widely varying wavelengths and transition strengths, anisotropic interaction properties between atoms and with light, and a large magnetic moment and spin space present in the ground state. These features in turn enable applications ranging from narrow-line laser cooling and spin manipulation to evaporative cooling through universal dipolar scattering, to the observation of a rotonic dispersion relation, self-bound liquid-like droplets stabilized by quantum fluctuations, and supersolid states. In this short review, we describe how the unusual level structure of lanthanide atoms leads to these key features, and provide a brief and necessarily partial overview of experimental progress in this rapidly developing field.
Abstract Rydberg molecules are an essential ingredient of cold molecular sciences. Due to the richness of interactions between Rydberg atoms and neutral atoms, new kinds of Rydberg molecules and binding mechanisms are still to be discovered. In this work, we predict the existence of long-range van der Waals trimers in dilute atom-gas mixtures. These are bound states of a Rydberg atom and a diatomic polar molecule mediated by the long-range van der Waals interaction. This binding mechanism gives rise to trimers with sizes between 5 and 500 nm and binding energies between 0.2 kHz and 2 MHz depending on the atomic principal quantum number n and orbital angular momentum L. We show that these trimers can be produced via two-photon photoassociation, with rates on the order of (10−13 - 10−11) cm3s−1 for temperatures in the range of (0.5 μ K - 10 μ K), and discuss the feasibility of observing trimer resonances.
The long-range part of the interatomic interactions plays a substantial role in the collisional dynamics of ultracold gases. Here, we report on the calculation of the isotropic and anisotropic C6{C}_{6}C6​ coefficients characterizing the van der Waals interaction between dysprosium or erbium atoms in the two lowest energy levels and the ground-state alkali-metal (Li, Na, K, Rb, Cs, Fr) or alkaline-earth-metal (Be, Mg, Ca, Sr, Ba) atoms. The calculations are done using the integral of dynamic dipole polarizabilities at so-called imaginary frequencies of the two interacting atoms. For all atom pairs, we find that the isotropic C6{C}_{6}C6​ coefficients are two or three orders of magnitude larger than the anisotropic ones. Those coefficients are essential for modeling collisional properties of heteronuclear quantum mixtures containing highly magnetic dysprosium or erbium atoms and alkali-metal or alkaline-earth-metal atoms.
We present high-precision trap loss spectroscopy of excited molecules obtained by the photoassociation of ultracold sodium atoms. Near the dissociation limit, hyperfine and rotational (Coriolis-type) interactions cause significant mixing of states of different nominal Hund's case (c) symmetry resulting in a complex pattern of spectral lines. We construct a theoretical model of the large, slowly rotating molecule starting from a long-range, atomic viewpoint. Interaction potentials are derived from the known long-range resonant dipole and van der Waals forces between atoms, supplemented at short range by the results of electronic-structure calculations. Spin-dependent interactions coupling the various angular momenta---nuclear spin, electron spin, electron orbit, and the mechanical rotation of the molecule as a whole---are derived from known atomic parameters. We avoid imposing approximate symmetries or coupling schemes and consequently include all nonadiabatic mixing of different degrees of freedom. Quantitative agreement between experiment and theory for both line positions and intensities is found. Specifically, we observe and calculate mixing of levels of , , and symmetry bound by below the asymptote.