Ultralong-range Rydberg molecules, formed by the interaction between a highly excited Rydberg atom and a ground-state atom, provide a unique platform for exploring quantum phenomena spanning nanometer-to-micrometer distances as well as exotic few-body interactions. The formation mechanisms and resultant physical properties differ markedly between s-wave and p-wave scattering channels. Here we report the experimental observation of node-dependent p-wave molecular signals in Rb(nS)-Rb(5S) Rydberg molecular spectra, where variations in the principal quantum number n directly reveal the shift of molecular binding energies induced by the moving nodal structure of the Rydberg electron wavefunction. This node-dependence is attributed to a cooperative effect between the local gradient of the nS-electron wavefunction and the energydependent p-wave scattering length. In addition, resolving two p-wave bound states associated with adjacent nodes highlights the remarkable sub-nanometer spatial resolution achieved in our experiment. Our findings reveal a more profound quantum control mechanism, wherein the principal quantum number acts as a switch for nodal-selective molecular bound states, and the reported method provides a sensitive spectroscopic probe of electron-atom scattering.
Ultralong-range Rydberg molecules, formed by the interaction between a highly excited Rydberg atom and a ground-state atom, provide a unique platform for exploring quantum phenomena spanning nanometer-to-micrometer distances as well as exotic few-body interactions. The formation mechanisms and resultant physical properties differ markedly between s-wave and p-wave scattering channels. Here we report the experimental observation of node-dependent p-wave molecular signals in Rb(nS)-Rb(5S) Rydberg molecular spectra, where variations in the principal quantum number n directly reveal the shift of molecular binding energies induced by the moving nodal structure of the Rydberg electron wavefunction. This node-dependence is attributed to a cooperative effect between the local gradient of the nS-electron wavefunction and the energydependent p-wave scattering length. In addition, resolving two p-wave bound states associated with adjacent nodes highlights the remarkable sub-nanometer spatial resolution achieved in our experiment. Our findings reveal a more profound quantum control mechanism, wherein the principal quantum number acts as a switch for nodal-selective molecular bound states, and the reported method provides a sensitive spectroscopic probe of electron-atom scattering.
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 present high-resolution spectroscopy of 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 s-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 p-wave contribution and all orders in the relative momentum k, and compare the obtained molecular binding energies to the experimental data.
Divalent atoms have emerged as powerful alternatives to alkalis in ultracold atom platforms, offering unique advantages arising from their two-electron structure. Among these species, ytterbium (Yb) is especially promising, yet its anionic properties and its Rydberg spectrum remain comparatively unexplored. In this work, we perform a first and comprehensive experimental and theoretical investigation of ultralong-range Rydberg molecules (ULRMs) of 174Yb in 6sns1S0 Rydberg states across nearly two decades in principal quantum number n and three orders of magnitude in molecular binding energy. Using the Coulomb Green's function formalism, we compute Born-Oppenheimer molecular potentials describing the Rydberg atom in the presence of a ground-state perturber and achieve quantitative agreement with high-resolution molecular spectra. This enables the extraction of low-energy electron-Yb scattering phase shifts, including the zero-energy s-wave scattering length and the positions of two spin-orbit split p-wave shape resonances. Our results provide strong evidence that the Yb− anion exists only as a metastable resonance.% We additionally show the sensitivity of ULRM spectra to the atomic quantum defects, using this to determine the quantum defect of the 6s23f1F3 state. Together, these findings establish Yb ULRMs as a powerful probe of electron-Yb interactions and lay essential groundwork for future Rydberg experiments with divalent atoms.
We observe the formation of long-range Cs2 Rydberg molecules consisting of a Rydberg and a ground-state atom by photoassociation spectroscopy in an ultracold Cs gas near 6s1/2(F=3,4)→np3/2 resonances (n=26-34). The spectra reveal two types of molecular states recently predicted by D. A. Anderson, S. A. Miller, and G. Raithel [Phys. Rev. A 90, 062518 (2014)]: states bound purely by triplet s-wave scattering with binding energies ranging from 400 MHz at n=26 to 80 MHz at n=34, and states bound by mixed singlet-triplet s-wave scattering with smaller and F-dependent binding energies. The experimental observations are accounted for by an effective Hamiltonian including s-wave scattering pseudopotentials, the hyperfine interaction of the ground-state atom, and the spin-orbit interaction of the Rydberg atom. The analysis enables the characterization of the role of singlet scattering in the formation of long-range Rydberg molecules and the determination of an effective singlet s-wave scattering length for low-energy-electron-Cs collisions.
Rydberg molecule, formed by one or more Rydberg atoms, exhibits remarkable properties, including an exceptionally large spatial extent, rich rovibrational level structures, permanent electric dipole moments, and a pronounced sensitivity to external fields. Based on the underlying binding mechanisms, Rydberg molecules can be divided into three categories, the ground-Rydberg molecule that is bound via a low-energy electron-atom scattering interaction between ground atom and Rydberg electron, the Rydberg-Rydberg molecule that is bound via a long-range electrostatic interaction between Rydberg atoms, and the ion-Rydberg molecule that is bound via single- or multi-polar interactions between Rydberg atom and ion. This review focuses on recent theoretical and experimental advances in diatomic Rydberg molecules, covering their formation and binding mechanisms, potential energy curves, experimental observations, and spectroscopic properties, with the aim of providing a comprehensive overview of the current state and future prospects of this rapidly developing field.