An efficient method to study highly excited states at the ab initio level has been introduced and applied to ultralong Rydberg CsNe molecules. Vibrational properties of Rydberg CsNe molecules are investigated on corresponding potential energy curves obtained by perturbation theory. The Rydberg CsNe molecules are associated with a Rydberg Cs(ns∕np) atom (n = 20-60) and a ground state Ne((1)S0) atom. The starting point for the perturbation treatment of corresponding Rydberg molecular potential energy curves is to generate accurate atomic Rydberg states from realistic ab initio effective core potential. According to the authors' knowledge this is a good reference for ultralong range molecules (order of 1000 Bohr radii) to be studied at the ab initio level.
An efficient method to study highly excited states at the ab initio level has been introduced and applied to ultralong Rydberg CsNe molecules. Vibrational properties of Rydberg CsNe molecules are investigated on corresponding potential energy curves obtained by perturbation theory. The Rydberg CsNe molecules are associated with a Rydberg Cs(ns∕np) atom (n = 20-60) and a ground state Ne((1)S0) atom. The starting point for the perturbation treatment of corresponding Rydberg molecular potential energy curves is to generate accurate atomic Rydberg states from realistic ab initio effective core potential. According to the authors' knowledge this is a good reference for ultralong range molecules (order of 1000 Bohr radii) to be studied at the ab initio level.
Vibrational properties of ultralong Rydberg Cs2 molecules are investigated on corresponding potential curves obtained by perturbation theory. The Rydberg Cs2 molecules are associated by a Rydberg Cs(nS/nP) atom (n=30−70) and a ground state Cs(6s) atom. The starting point for the perturbation treatment of corresponding Rydberg molecular potential curves is to generate accurate atomic Rydberg states from realistic {\it ab initio} effective core potential. The calculated results have similar characteristics with available experimental and theoretical investigations on Rydberg Rb2 molecules. And this is the first time that Rydberg molecules are studied at the {\it ab initio} level.
Abstract Ultralong-range Rydberg molecules (ULRMs) have attracted significant interest due to their unique formation mechanisms and distinctive properties. We theoretically investigate the formation and characteristics of heteronuclear ULRMs, focusing on Rb-Cs systems. We calculate the vibrational energy levels of nS heteronuclear ULRMs and extend our analysis to polyatomic systems, tracing the evolution of binding energies as the molecular configuration changes. Our theoretical results are presented in terms of potential energy curves and the associated vibrational spectra, providing insight into the formation dynamics of these systems. These results also provide a framework for experimental efforts in probing heteronuclear ULRMs, which serve as a sensitive platform for investigating the fundamental properties of Rydberg atoms and their interactions with ground-state atoms, while providing a benchmark for \textit{ab initio} calculations.
In this work the existence of a novel type of molecule is shown whose binding is based solely on electron-atom scattering. These molecules are composed of a Rydberg atom and a ground state atom - here Rb(ns) and Rb(5s) - where the binding arises from scattering of the Rydberg electron from the ground state atom. The ground state atom is bound to the Rydberg wavefunction, which has radii on the order of 100nm, and thus these molecules are of long-range. Although the theoretical description of this interaction goes back to the famous work of Fermi in the year 1934 which was expanded in the following decades by Omont and Greene, the experimental proof of their existence was still missing. Up to now, experimental evidence for the ultralong-range Rydberg molecules was found only in spectral line broadenings. The present experiments have demonstrated the direct photoassociation of these ultralong-range Rydberg molecules for Rb(ns)-Rb(5s) triplet states from a cold and dense sample of rubidium 87 atoms for a range of principal quantum numbers, n, between 34 and 40. The high-resolution photoassociation spectra allowed for the observation of several vibrational states separated by only a few Megahertz. Based on the model by Greene the vibrational ground states v=0 are assigned and the dependence of their binding energy on the principal quantum number, n, is used to extract the triplet s-wave scattering length for electron-Rb(5s) collisions from the data. The remarkably good agreement between experiment and theory for the vibrational ground state v=0 over a range of principal quantum numbers attests to the accuracy of Fermi's original pseudopotential approach in describing interactions in excited multi-atom systems. Aside from this good agreement for the state v=0, the measurements also show that contributions from p-wave scattering cannot be neglected, as a number of excited vibrational states is observed in the experiment that are not predicted from the theory assuming only s-wave scattering. Calculations of Li, Pohl and coworkers have shown that a full solution of the electron-atom scattering is necessary for the assignment of all vibrational states. This work finds the molecular bound states to be very sensitive to both s-wave as well as p-wave electron-atom scattering and the Rydberg molecules turn out to be an accurate experimental platform to study electron-atom collisions in a previously inaccessible ultralow-energy regime. In general, the ultralong-range Rydberg molecules investigated here for rubidium are expected for all species with negative scattering length for electron-atom interaction, e. g. the other alkali atoms. Rydberg atom and ground state atom do not even have to be of the same chemical element, the only requirement is a negative scattering length of the ground state atom for electron scattering. Moreover, the binding force of the Rydberg electron is not restricted to a single ground state atom and molecules with more than one ground state atom can be created. The fact that these exotic molecules have huge bond lengths but nevertheless a vibrational spectrum with several states make a new type of ultracold Rydberg chemistry feasible. In the future, larger polymers or even heteronuclear molecules can be realized, where the number of atoms, the constituent atomic elements and the addressed Rydberg state allow to precisely select the properties of the long-range molecule.
We study long range interactions between two Rydberg atoms and predict the existence of ultralong range Rydberg dimers with equilibrium distances of many thousands of Bohr radii. We calculate the dispersion coefficients C5, C6, and C8 for two rubidium atoms in the same excited level np and find that they scale like n(8), n(11), and n(15), respectively. We show that for certain molecular symmetries these coefficients lead to long range potential wells that can support molecular bound levels. Such macrodimers would be very sensitive to their environment and could probe weak interactions. We suggest experiments to detect these macrodimers.
Ultralong-range Cs 2 Rydberg-ground molecules ( nD 5/2 + 6 S 1/2 F ) (33 ≤ n ≤ 39, F = 3 or 4) are investigated by a two-photon photo-association spectroscopy of an ultracold Cs gas. Two vibrational ground molecular spectra of triplet 3 Σ and hyperfine mixed singlet-triplet 1,3 Σ molecular states and their corresponding binding energies are attained. The experimental observations are simulated by an effective Hamiltonian including low energy electron scattering pseudopotentials, the spin-orbit interaction of the Rydberg atom, and the hyperfine interaction of the ground-state atom. The zero-energy singlet and triplet s-wave scattering lengths are extracted by comparing the experimental observations and calculations. Dependences of the measured binding energies on the effective principal quantum number, n eff = n − δ D ( δ D is the quantum defect of Rydberg D state), yield the scaling of n eff − 5.60 ± 0.16 ( 3 Σ , F = 3 ) , n eff − 5.62 ± 0.16 ( 3 Σ , F = 4 ) for deep triplet potential and n eff − 5.65 ± 0.38 ( 1 , 3 Σ , F = 3 ) , n eff − 6.19 ± 0.14 ( 1 , 3 Σ , F = 4 ) for shallow mixed singlet-triplet potential well. The simulations of low-energy Rydberg electron scattering show agreement well with the experimental measurements.
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) and homonuclear (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 exist as resonances above the dissociation threshold.