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arXiv:2412.19710 · Physical Review Letters

High Precision Spectroscopy of Trilobite Rydberg Molecules

Markus Exner, Rohan Srikumar, Richard Blättner, Matthew T. Eiles, Peter Schmelcher, Herwig Ott

Published Jun 4, 2025• 8 citations
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Abstract

We perform three-photon photoassociation to obtain high resolution spectra of ^{87}Rb trilobite dimers for the principal quantum numbers n=22, 24, 25, 26, and 27. The large binding energy of the molecules in combination with a relative spectroscopic resolution of 10^{-4} provides a rigorous benchmark for existing theoretical models. A recently developed Green's function framework, which circumvents the convergence issues that afflicted previous studies, is employed to theoretically reproduce the vibrational spectrum of the molecule with high accuracy. The relatively large molecular binding energy is primarily determined by the low-energy S-wave electron-atom scattering length, thereby allowing us to extract the ^{3}S_{1} scattering phase shift with unprecedented accuracy, at low-energy regimes inaccessible to free electrons.

DOI
10.1103/physrevlett.134.223401

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We perform three-photon photoassociation to obtain high resolution spectra of ^{87}Rb trilobite dimers for the principal quantum numbers n=22, 24, 25, 26, and 27. The large binding energy of the molecules in combination with a relative spectroscopic resolution of 10^{-4} provides a rigorous benchmark for existing theoretical models. A recently developed Green's function framework, which circumvents the convergence issues that afflicted previous studies, is employed to theoretically reproduce the vibrational spectrum of the molecule with high accuracy. The relatively large molecular binding energy is primarily determined by the low-energy S-wave electron-atom scattering length, thereby allowing us to extract the ^{3}S_{1} scattering phase shift with unprecedented accuracy, at low-energy regimes inaccessible to free electrons.
In trilobite Rydberg molecules, an atom in the ground state is bound by electron-atom scattering to a Rydberg electron that is in a superposition of high angular momentum states. This results in a homonuclear molecule with a permanent electric dipole moment in the kilo-debye range. Trilobite molecules have previously been observed only with admixtures of low-l states. Here we report on the observation of two vibrational series of pure trilobite Rubidium-Rydberg molecules that are nearly equidistant. They are produced by three-photon photoassociation and lie energetically more than 15 GHz below the atomic 22F state of rubidium. We show that these states can be used to measure the electron-atom scattering length at low energies in order to benchmark current theoretical calculations. In addition to measuring their kilo-Debye dipole moments, we also show that the molecular lifetime is increased compared to the 22F state due to the high-l character. The observation of an equidistant series of vibrational states opens the way to observe coherent molecular wave packet dynamics.
We report on a novel method for the photoassociation of strongly polar trilobite Rydberg molecules. This exotic ultralong-range dimer, consisting of a ground-state atom bound to the Rydberg electron via electron-neutral scattering, inherits its polar character from the admixture of high-angular-momentum electronic orbitals. The absence of low-L character hinders standard photoassociation techniques. Here, we show that for suitable principal quantum numbers the resonant coupling of the orbital motion with the nuclear spin of the perturber, mediated by electron-neutral scattering, hybridizes the trilobite molecular potential with the more conventional S-type molecular state. This provides a general path to associate trilobite molecules with large electric dipole moments, as demonstrated via high-resolution spectroscopy. We find a dipole moment of 135(45) D for the trilobite state. Our results are compared to theoretical predictions based on a Fermi model.
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.
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.
We observe long-range 85Rb^{85}\mathrm{Rb}85Rb and 87Rb^{87}\mathrm{Rb}87Rb (24DJ+5S1/224{D}_{J}+5{S}_{1/2}24DJ​+5S1/2​) Rydberg molecules for eight different spin couplings, with binding energies up to 440 MHz and subpercent relative uncertainty. Isotopic effects of the molecular binding energies arise from the different masses and nuclear spins. Because the vibrational states involve different spin configurations and cover a wide range of internuclear separations, the states have different dependencies on the sss-wave and ppp-wave scattering phase shifts for singlet and triplet scattering. Fitting the spectroscopic data, we comprehensively determine all four scattering length functions over the relevant energy range as well as the zero-energy scattering lengths of the two sss-wave channels. Our unusually high temperature and low density (180 $\ensuremath{\mu}\mathrm{K}$, $1\ifmmode\times\else\texttimes\fi{}{10}^{11}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$) suggest that the molecule excitation occurs through photoassisted collisions.
Rydberg molecules, often exemplified by long-range ``trilobite'' molecules, are a subject of much recent interest at high principal quantum number nnn. States that use the same bonding mechanism can exist at much lower nnn and less-extreme internuclear separations that are still quite long range. We use a high-resolution pulsed amplifier to study previously detected transitions to a low-nnn Rydberg molecular state near the 5s+7p5s+7p5s+7p asymptote in 85Rb2^{85}\mathrm{Rb}_{2}85Rb2​. The observed line structure is modeled using precise ground-state positions and a lower bound of $\ensuremath{\tau}>1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ s is set on the excited-state autoionization lifetime.