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arXiv:1709.06881 · Physical Review A

Angular-momentum couplings in ultra-long-range giant dipole molecules

Thomas Stielow, Stefan Scheel, Markus Kurz

Published Feb 6, 2018• 2 citations
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Abstract

In this article we extend the theory of ultra-long-range giant dipole molecules, formed by an atom in a giant dipole state and a ground-state alkali-metal atom, by angular-momentum couplings known from recent works on Rydberg molecules. In addition to $s$-wave scattering, the next higher order of $p$-wave scattering in the Fermi pseudopotential describing the binding mechanism is considered. Furthermore, the singlet and triplet channels of the scattering interaction as well as angular-momentum couplings such as hyperfine interaction and Zeeman interactions are included. Within the framework of Born-Oppenheimer theory, potential energy surfaces are calculated in both first-order perturbation theory and exact diagonalization. Besides the known pure triplet states, mixed-spin character states are obtained, opening up a whole new landscape of molecular potentials. We determine exact binding energies and wave functions of the nuclear rotational and vibrational motion numerically from the various potential energy surfaces.

DOI
10.1103/physreva.97.022501

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In this article we extend the theory of ultra-long-range giant dipole molecules, formed by an atom in a giant dipole state and a ground-state alkali-metal atom, by angular-momentum couplings known from recent works on Rydberg molecules. In addition to sss-wave scattering, the next higher order of ppp-wave scattering in the Fermi pseudopotential describing the binding mechanism is considered. Furthermore, the singlet and triplet channels of the scattering interaction as well as angular-momentum couplings such as hyperfine interaction and Zeeman interactions are included. Within the framework of Born-Oppenheimer theory, potential energy surfaces are calculated in both first-order perturbation theory and exact diagonalization. Besides the known pure triplet states, mixed-spin character states are obtained, opening up a whole new landscape of molecular potentials. We determine exact binding energies and wave functions of the nuclear rotational and vibrational motion numerically from the various potential energy surfaces.
We study angular-momentum couplings in 87Rb2^{87}\mathrm{Rb}{}_{2}87Rb2​ Rydberg molecules formed between a Rydberg and 5S1/25{S}_{1/2}5S1/2​ ground-state atom. We use a Fermi model that includes SSS-wave and PPP-wave singlet and triplet scattering of the Rydberg electron with the 5S1/25{S}_{1/2}5S1/2​ atom, along with the fine-structure coupling of the Rydberg atom and hyperfine-structure coupling of the 5S1/25{S}_{1/2}5S1/2​ atom. We discuss the effects of these couplings on the adiabatic molecular potentials. We obtain bound-state energies, lifetimes, and electric and magnetic dipole moments for the vibrational ground states of the 87Rb(nD+5S1/2)^{87}\mathrm{Rb}(nD+5{S}_{1/2})87Rb(nD+5S1/2​) molecules in all adiabatic potentials, with fine and hyperfine structure included. The hyperfine structure gives rise to mixed singlet-triplet potentials. We also study the effect of the hyperfine structure on the deep 3S{}^{3}S3S-wave- and 3P{}^{3}P3P-wave-dominated adiabatic molecular potentials, which support high-$\ensuremath{\ell}$ 87Rb2^{87}\mathrm{Rb}{}_{2}87Rb2​ Rydberg molecules.
We show the existence of ultra-long-range giant dipole molecules formed by a neutral alkali ground state atom that is bound to the decentered electronic wave function of a giant dipole atom. The adiabatic potential surfaces emerging from the interaction of the ground state atom with the giant dipole electron possess a rich topology depending on the degree of electronic excitation. Binding energies and the vibrational motion in the energetically lowest surfaces are analyzed by means of perturbation theory and exact diagonalization techniques. The resulting molecules are truly giant with internuclear distances up to several μm. Finally, we demonstrate the existence of intersection manifolds of excited electronic states that potentially lead to a vibrational decay of the ground state atom dynamics.
Molecular bonds can be divided into four primary types: ionic, covalent, van der Waals and hydrogen bonds. At ultralow temperatures a novel binding type emerges paving the way for novel molecules and ultracold chemistry [1,2]. The underlying mechanism for this new type of chemical bond is low-energy electron scattering of Rydberg electrons from polarisable ground state atoms [3]. This quantum scattering process can generate an attractive potential that is able to bind the ground state atom to the Rydberg atom at a well localized position within the Rydberg electron wave function. The resulting giant molecules can have an internuclear separation of several thousand Bohr radii, which places them among the largest known molecules to date. Their binding energies are much smaller than the Kepler frequencies of the Rydberg electrons i.e. the atomic Rydberg electron state is essentially unchanged by the bound ground state atom. Ultracold and dense samples of atoms enable the creation of these molecules via Rydberg excitation. In this paper we present spectroscopic evidence for the vibrational ground and first excited state of a Rubidium dimer Rb(5S)-Rb(nS). We apply a Born-Oppenheimer model to explain the measured binding energies for principal quantum numbers n between 34 and 40 and extract the s-wave scattering length for electron-Rb(5S) scattering in the relevant low energy regime Ekin < 100 meV. We also determine the lifetimes and the polarisabilities of these molecules. P-wave bound states [2], Trimer states [4] as well as bound states for large angular momentum of the Rydberg electron - socalled trilobite molecules [1] - are within reach in the near future and will further refine our conceptual understanding of the chemical bond.
An operator that generates an approximate symmetry of long-range Rydberg molecules (LRRMs) formed by two alkali atoms, one in a Rydberg state and the other in the ground state, is identified. This is first done by evaluating the natural orbitals associated with a variational calculation of the binding wave function within the Born-Oppenheimer description of the molecule including s and p Fermi pseudopotential and the hyperfine structure energy terms. The resulting orbitals with the highest occupation number are shown to be identical to those obtained by a perturbative model for high angular momentum—trilobite and butterfly—LRRMs. Whenever the slight dependence of the quantum defects of the Rydberg electron on its total momentum j⃗=ℓ⃗+s⃗1 can be neglected, the symmetry operator of the high angular momentum LRRMs orbitals is identified as the sum of the spin of the Rydberg electron s⃗1 , spin of the valence electron s⃗2 , and the spin of nucleus i⃗ of the ground-state atom, N⃗=s1⃗+s2⃗+i⃗ . The spin orbitals that diagonalize N⃗ define compact basis sets for the description of LRRMs beyond the aforementioned approximations. The matrix elements of the Hamiltonian in these basis sets have simple expressions, so that the relevance of triplet and singlet contributions can be directly estimated. The expected consequences of this approximate spin-symmetry on the spectra of LRRMs are briefly described. Published by the American Physical Society 2024
We present high-resolution spectroscopy of Rb2{\mathrm{Rb}}_{\text{2}}Rb2​ ultralong-range Rydberg molecules bound by mixed singlet-triplet electron-neutral atom scattering. The mixing of the scattering channels is a consequence of the hyperfine interaction in the ground-state atom, as predicted recently by Anderson et al. [Phys. Rev. A 90, 062518 (2014)]. Our experimental data enable the determination of the effective zero-energy singlet sss-wave scattering length for Rb. We show that an external magnetic field can tune the contributions of the singlet and the triplet scattering channels and therefore the binding energies of the observed molecules. This mixing of molecular states via the magnetic field results in observed shifts of the molecular line which differ from the Zeeman shift of the asymptotic atomic states. Finally, we calculate molecular potentials using a full diagonalization approach including the ppp-wave contribution and all orders in the relative momentum kkk, and compare the obtained molecular binding energies to the experimental data.
Ultralong-range Rydberg molecules, composed of an excited Rydberg atom and a ground-state atom, are characterized by large bond lengths, dipole moments, sensitivity to external fields, and an unusual binding mechanism based on low-energy elastic electron scattering. Although Rydberg molecules formed between alkali atoms have received the most attention, the additional complexity found in atoms with more than a single valence electron poses new theoretical challenges as well as new possibilities for control and design of the molecular structure. In this paper, we extend the theory of Rydberg molecules to include the additional spin coupling of the Rydberg states of a multivalent atom. We employ this theory to describe the properties of Rydberg molecules composed of mercury atoms. We calculate the potential energy curves of both heteronuclear (Hg∗Rb{\mathrm{Hg}}^{*}\mathrm{Rb}Hg∗Rb) and homonuclear (Hg∗Hg{\mathrm{Hg}}^{*}\mathrm{Hg}Hg∗Hg) molecules. In the former case, we propose the realization of long-range spin entanglement and remote spin flip. In the latter, we show how long-lived metastable molecular states of Hg∗Hg{\mathrm{Hg}}^{*}\mathrm{Hg}Hg∗Hg exist as resonances above the dissociation threshold.