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arXiv:2502.10555

Ultracold long-range van der Waals Rydberg trimer

Mateo Londoño, V. C. Olaya-Agudelo, Felipe Herrera, Jesús Pérez‐Ríos

Published Feb 14, 2025• 0 citations
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Abstract

Rydberg molecules, Rydberg-atom or Rydberg-molecule, are an essential ingredient of cold molecular sciences. However, due to the richness of Rydberg-neutral interactions, new kinds of Rydberg molecules and binding mechanisms are still to be discovered. In this work, we predict the existence of ultra-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 new binding mechanism gives rise to trimers with sizes between 5-500~nm and binding energies between 2 MHz and 0.2 kHz depending on the atomic principal quantum number $n$ and orbital angular momentum $L$. We show that these molecules can be produced via two-photon photoassociation, with rates on the order of (10$^{-13}$ - 10$^{-11}$) cm$^{3}$s$^{-1}$ for temperatures in the range of (0.5 $μK$ - 10$μK$), and discuss the feasibility of observing trimer resonances.

DOI
10.48550/arxiv.2502.10555

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•Jan 1, 2010•1 citation
Rydberg molecules, Rydberg-atom or Rydberg-molecule, are an essential ingredient of cold molecular sciences. However, due to the richness of Rydberg-neutral interactions, new kinds of Rydberg molecules and binding mechanisms are still to be discovered. In this work, we predict the existence of ultra-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 new binding mechanism gives rise to trimers with sizes between 5-500~nm and binding energies between 2 MHz and 0.2 kHz depending on the atomic principal quantum number nnn and orbital angular momentum LLL. We show that these molecules can be produced via two-photon photoassociation, with rates on the order of (10−13^{-13}−13 - 10−11^{-11}−11) cm3^{3}3s−1^{-1}−1 for temperatures in the range of (0.5 μKμKμK - 10μKμKμK), and discuss the feasibility of observing trimer resonances.
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.
We study ultracold long-range collisions of heteronuclear alkali-metal dimers with a reservoir gas of alkali-metal Rydberg atoms in a two-photon laser excitation scheme. In a low density regime where molecules remain outside the Rydberg orbits of the reservoir atoms, we show that the two-photon photoassociation (PA) of the atom-molecule pair into a long-range bound trimer state is efficient over a broad range of atomic Rydberg channels. As a case study, we obtain the PA lineshapes for the formation of trimers composed of KRb molecules in the rovibrational ground state and excited Rb atoms in the asymptotic Rydberg levels n2Sjn^{2}S_jn2Sj​ and n2Djn^{2}D_jn2Dj​, for n=20−80n=20-80n=20−80. We predict atom-molecule binding energies in the range 10−10310-10^310−103 kHz for the first vibrational state below threshold. The average trimer formation rate is order 108 s−110^8\, {\rm s}^{-1}108s−1 at 1.0 μμμK, and depends weakly on the principal quantum number nnn. Our results set the foundations for a broader understanding of exotic long range collisions of dilute molecules in ultracold atomic Rydberg reservoirs.
Summary form only given. The discovery of ultracold and dilute ensembles of atoms and molecules in magneto-optical traps (MOT) and in atomic Bose-Einstein condensates (BECs) has ushered in a new era of precision atomic and molecular spectroscopy. Since the atoms in such cold environments predominantly interact via long-range forces, the creation of BECs and dilute atomic samples has made the study of very long-range molecular states possible. In this work (Greene et al, Phys. Rev. Lett. vol. 85, p. 2458, 2000), we discuss a particular interatomic arrangement that should be favored in modern-day MOT and BEC setups and should result in the production of molecular Rydberg states whose vibrational wave functions are localized at internuclear distances of order n/sup 2/ Bohr radii, where n is the principal quantum number. The vibrational binding energies of these molecules for n=20-50 fall in the MHz and GHz range, for molecules excited from /sup 87/Rb ultracold atomic gas. We predict two distinct classes of molecular Rydberg states. The nonpolar class of Rydberg molecules form from the interaction between a Rb(nl/sub j/) Rydberg atom with low orbital angular momentum l/sub j//spl les/2 and a distant Rb ground state atom. Rydberg molecules of the second class form from the interaction between an excited Rb atom in high (l/sub j/>2) orbital angular momentum states with a ground state Rb atom.
Ultra-cold long-range Rydberg-ground molecule consisting of a Rydberg atom and one or more ground-state atoms is formed by low-energy scattering between the Rydberg electron and ground-state atoms located inside the Rydberg electron’s wave function. The low-energy scattering interaction, initially investigated by Fermi and Omont, has been predicted to lead to molecular binding in a novel type of Rydberg molecules, including the trilobite and butterfly molecules. Their unconventional binding mechanism, which is unlike covalent, or ionic, or van der Waals bonds, results in loosely bound molecules with bond lengths on the order of thousands of Bohr radius. This kind of molecule with large size and huge permanent electric dipole moment is a good candidate for realizing the certain strongly correlated many-body gases and for quantum information processing, as well as for dipolar quantum gases and spin systems with long-range interactions. Consequently, these molecules have received considerable attention in recent years. In this paper, we review the recent theoretical and experimental investigations of ultra-cold long-range Rydberg-ground molecules, including the scattering interaction between the Rydberg electron and ground-state atom and the resulting adiabatic potential curves, experimental observations of photo-associated Rydberg-ground molecules spectra, as well as the measurements of permanent electric dipole moment. Ultra-cold long-range Rydberg-ground molecules are prepared by photoassociation in a high-density cold atom sample. Therefore, the Rydberg electron can bind several ground-state atoms to form a polyatomic Rydberg-ground molecule. The permanent molecular electric-dipole moments are revealed by spectral line broadening in the electric fields. The latest research pointed out that the permanent electric dipole moments of the Cs nDJ -type Rydberg-ground molecules are negative, which is different from the previous reports (the electric dipole moments are positive). The negative sign reflects a deficiency of Rydberg-electron density near the ground-state perturber, which is caused by electronic configuration mixing.
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.
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.