We present analysis of low-
n long-range molecular Rydberg states in
85Rb
2, based on high-resolution spectra. The weakly bound states are accessed by bound-bound transitions from high-
v levels of the
a,3Sigmau+ state, which are prepared by photoassociation of laser-cooled atoms. Single-photon transitions to target states near the
5s+7p asymptote are excited by a frequency-doubled pulse-amplified CW laser with a narrow linewidth, under 200 MHz. The long-range portion of the bonding potential is dominated by the elastic scattering interaction of the Rydberg electron of a perturbed
7p atom and a nearby ground-state atom, in much the same manner as trilobite states. We use time of flight to selectively measure molecular ions, which are formed via autoionization. This technique gives a two orders-of-magnitude improvement in linewidth over our previous work, reported in Ref. [1]. We also present calculations of a proposed scheme for STIRAP transfer from the current
v′′=35 level of the
a,3Sigmau+ state to the
v′′=39 level. The long-range states accessible to us are defined in large part by the Franck-Condon factors, which are dominated by the outer lobe of the wavefunction. Thus, choosing a
v′′ sets
R, and determines the Franck-Condon window. The proposed
v′′=39 level has a classical outer turning point at
sim72,a0, and will provide access to higher-
n states with longer-range wells. This work is supported by the NSF and AFOSR.\ noindent [1] M. A. Bellos textit{et al.}, Phys. Rev. Lett. textbf{111}, 053001 (2013)
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 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.
We investigate triatomic molecules that consist of two ground-state atoms and a highly excited Rydberg atom, bound at large internuclear distances of thousands of angstroms. In the molecular state the Rydberg electron is in a superposition of high angular momentum states whose probability densities resemble the form of trilobite fossils. The associated potential-energy landscape has an oscillatory shape and supports a rich variety of stable geometries with different bond angles and bond lengths. Based on an electronic structure investigation we analyze the molecular geometry systematically and develop a simple building principle that predicts the triatomic equilibrium configurations. As a representative example we focus on
87Rb trimers correlated to the
n=30 Rydberg state. Using an exact diagonalization scheme we determine and characterize localized vibrational states in these potential minima with energy spacings on the order of 100 $\mathrm{MHz}\ifmmode\times\else\texttimes\fi{}h$.
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.
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.