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Physical Review A

Photoassociation of Sr 84 n 1 D 2 ultralong-range Rydberg dimers

C. Wang, Ang Li, S. K. Kanungo, T. C. Killian, F. B. Dunning, S. Yoshida

Published Apr 7, 2026• 1 citation
Publisher

Abstract

Measurements of the production of 5 s n d 1 D 2 – 5 s 2 1 S 0 ultralong-range Rydberg dimers through photoassocation in an ultracold Sr 84 atomic gas are reported. The molecular potential associated with the Rydberg D state is anisotropic and the molecular states are characterized by the vibrational quantum number ν and the total angular momentum K ⃗ = L ⃗ + N ⃗ , where L ⃗ and N ⃗ are the electronic orbital angular momentum and rotational angular momentum, respectively. The measured molecular binding energies agree reasonably well with theoretical predictions. Additionally, the electron-atom scattering leads to broader line shapes in the photoassociation spectrum than might be expected simply from the angular momentum of the initial colliding cold-atom pairs.

DOI
10.1103/ppv2-mlfd

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•Jan 1, 2010•1 citation
Measurements of the production of 5 s n d 1 D 2 – 5 s 2 1 S 0 ultralong-range Rydberg dimers through photoassocation in an ultracold Sr 84 atomic gas are reported. The molecular potential associated with the Rydberg D state is anisotropic and the molecular states are characterized by the vibrational quantum number ν and the total angular momentum K ⃗ = L ⃗ + N ⃗ , where L ⃗ and N ⃗ are the electronic orbital angular momentum and rotational angular momentum, respectively. The measured molecular binding energies agree reasonably well with theoretical predictions. Additionally, the electron-atom scattering leads to broader line shapes in the photoassociation spectrum than might be expected simply from the angular momentum of the initial colliding cold-atom pairs.
Spectroscopic measurements of the rotational distribution of 84Sr^{84}\mathrm{Sr}84Sr and 86Sr5sns1S0^{86}\mathrm{Sr}\phantom{\rule{4pt}{0ex}}\phantom{\rule{0.16em}{0ex}}5sns{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}86Sr5sns1S0​ ultralong-range Rydberg molecular dimers created via photoassociation in a cold gas are reported. The dimers are produced by two-photon excitation via the 5s5p5s5p5s5p 1P1^{1}P_{1}1P1​ intermediate state. The use of singlet states permits detailed study of the roles that the initial atom-atom interaction, photon momentum transfer during Rydberg excitation, and sample temperature play in determining the spectral line shape and final dimer rotational distribution. The results are in good agreement with the predictions of a model that includes these effects. The present work further highlights the sensitivity of ultralong-range Rydberg molecule formation to the state of the initial cold gas.
Photoassociation of 5 s n d 1 D 2 − 5 s 2 1 S 0 ultralong-range Rydberg dimers from an ultracold Sr 84 atomic gas in a magnetic field is studied. In the absence of magnetic fields, the electronic wave function is aligned along the rotating molecular axis through electron-atom scattering. With increasing magnetic field strength, the symmetry axis of the electron wave function becomes determined by the applied field. While the ground-state atom has no spin or net charge to interact directly with the magnetic field, the dimer wave function in the limit of strong magnetic field becomes aligned along the applied field. Photoassociation spectra show that with increasing field, an increasing number of rovibrational states are excited, indicating strong coupling between rotational states within the Rydberg dimer.
Anomalies in the rotational structure of 86Sr^{86}\mathrm{Sr}86Sr 3S1^{3}S_{1}3S1​ dimer ultralong-range Rydberg molecules created in a cold strontium gas by two-photon excitation via the intermediate 5s5p5s5p5s5p 3P1^{3}P_{1}3P1​ state are reported. Measurements reveal that the distribution of product rotational states is sensitive to intermediate state detuning. Comparative studies using 84Sr^{84}\mathrm{Sr}84Sr 1S0^{1}S_{0}1S0​ and 3S1^{3}S_{1}3S1​, and 86Sr^{86}\mathrm{Sr}86Sr 1S0^{1}S_{0}1S0​ dimers display no similar behavior, indicating that the observed behavior is peculiar to 86Sr^{86}\mathrm{Sr}86Sr triplet dimers. While we have no definitive hypothesis as to the physical mechanism responsible for this behavior, possible explanations might involve the very different scattering lengths for 84Sr^{84}\mathrm{Sr}84Sr and 86Sr^{86}\mathrm{Sr}86Sr, or the interchange of spin and rotational angular momentum.
Abstract Photoexcitation rates for creation of ultralong-range Rydberg molecules with 31 ≲ n ≲ 41 in both ground and excited vibrational levels in cold ( T ∼ 900 nK) gases of polarized and unpolarized 87 Sr are presented. The measured production rates of the ν = 0, 1 and 2 vibrational levels reveal rather different n dependences which are analyzed by evaluating the Franck–Condon factors associated with excitation of the different vibrational levels and molecular rotational states. In particular, for gases of spin-polarized fermions, only Rydberg dimers with odd rotational quantum numbers are excited due to the requirement that their wave functions be anti-symmetric with respect to exchange. The data also demonstrate that measurements of the formation of vibrationally-excited ν = 1 molecules can furnish a probe of pair correlations over intermediate length scales.
We report experimental observations of the rotational structure in photoassociative spectroscopy of ultralong-range Rydberg molecules (ULRRMs) in an ultracold gas of 86Sr^{86}\mathrm{Sr}86Sr. ULRRM spectroscopy probes scattering wave functions at much larger internuclear separations than photoassociative spectroscopy of low-lying electronic states. At such separations photon recoil momentum can lead to the transfer of significant angular momentum to the Rydberg molecule, evidence of which is provided through the distribution of excited rotational states. The visibility of the rotational structure is enhanced because, for collisions between ground-state 86Sr^{86}\mathrm{Sr}86Sr atoms, the large, near-resonant s-wave scattering length approaches the size of the ULRRM. Similar enhancement is not seen for 84Sr^{84}\mathrm{Sr}84Sr, which has a much smaller scattering length. Results are interpreted with the aid of a theory that accounts for the recoil momentum associated with photoexcitation and the large sss-wave scattering length in the entrance channel. While the observed rotational splittings and the qualitative trends in the relative intensities of the spectral features are well described by theory, the effects of recoil momentum are more prominent in the measured data than in the theory.
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.