Revealing Electron-Ytterbium Interactions through Rydberg Molecular Spectroscopy

TL;DR

This work develops and applies ultralong-range Rydberg-molecule spectroscopy of $^{174}$Yb to extract low-energy electron–Yb scattering phase shifts, including the zero-energy $s$-wave scattering length $a_s(0)$ and two $p$-wave shape resonances, while providing strong evidence that Yb$^-$ is not bound. By combining a Coulomb Green's-function approach with LS-coupled single-channel quantum defect treatment, the authors map Born–Oppenheimer PECs and vibrational spectra across a wide range of $n$, enabling precise refinement of the $^1F_3$ quantum defect to $\nu_{^1F_3}=21.73253\pm0.00004$ and an accurate determination of the polarizability and resonance positions. The results show excellent agreement between experiment and theory (within ~10% for bound states) and demonstrate the power of ULRMs as high-precision probes of electron–atom interactions in divalent atoms. Collectively, these findings establish Yb ULRMs as a versatile platform for probing low-energy scattering, core physics, and near-degenerate Rydberg manifolds, with prospects for multichannel extensions and future Rydberg-based quantum technologies.

Abstract

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 $^{174}$Yb in $6sns\,^1S_0$ 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 refine the value for the $6s23f\, ^1F_3$ quantum defect. 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.

Figures (7)

• Figure 1: (a) Schematic drawing of an ultralong-range Rydberg molecule consisting of one (or several) ground-state atom(s) (blue) bound to a Rydberg atom (ionic core in red and electronic wave function of Rydberg electron in gray). (b) Scheme of the photoassociation of Yb Rydberg molecules in the $6sns\,^1S_0$ manifold. We use a detuning from the intermediate state $6s6p\,^1P_1$ of $\Delta=1GHz$. Varying the detuning of the $399nm$ laser allows control over the two-photon detuning $\delta$. (c) Schematic of the experimental setup. The pulsed excitation light at $399nm$ and at $\SIrange[range-phrase = -]{395}{397}{\nano\meter}$ (depending on the Rydberg state) is focused onto the dense atomic cloud (green). The Rydberg molecules or atoms are field ionized after each excitation pulse by high-voltage electrodes (orange) above the atomic cloud. The ions are guided towards a microchannel plate (MCP) detector using a deflection electrode.
• Figure 2: (a) Overall PEC landscape between the $\nu=31$ and $\nu=32$ degenerate high-$\ell$ manifolds, with the energy axis referenced to the $6s36s\, ^1S_0$ level. The Bohr radius is denoted $a_0$. All dissociation thresholds corresponding to Rydberg $\nu\,^{2S_R+1}{L_R}_J$ states included are shown; on this scale, the corresponding PECs are essentially flat. The dominant features are the twin butterfly PECs. (b) Close-up of the region near the $\nu=32$ high-$\ell$ hydrogenic manifold with the nearby $^3F_J$ and $^{1,3}G_J$ levels. (c) Close-up of the $6s36s\, ^1S_0$ PEC.
• Figure 3: Spectra near the atomic $6sns\,^1 S_0$ state for $n=27$, $n=36$ and $n=44$. Blue points show the mean ion counts versus detuning $\delta$ from the atomic Rydberg line at $\delta=0$; error bars indicate statistical uncertainties. A multi-Lorentzian fit (black) models the atomic transition, the dimer lines, and polyatomic molecular lines (trimers and tetramers) at binding energies given by sums of integer multiples of the corresponding dimer binding energies. Atomic and dimer contributions are highlighted as shaded curves, and the polyatomic binding energies are marked by points below the data. The vertical axis for $n=36$ is scaled by a factor of 4.0 for $\delta<-25MHz$ to enhance visibility.
• Figure 4: Calculated PEC (black) and vibrational wave functions near the $^1S_0$ asymptote for $n=33$ and $n=40$. The Green's function formalism was used to obtain these PECs. The amplitude of each wave function is shown at its corresponding eigenenergy. The color scheme identifies different classes of molecular states (see main text). The measured spectra (blue) and the fitted experimental energies (gray dashed lines) are shown for comparison. The insets provide a zoomed-in view of the region between the atomic line and the outermost-well ground state.
• Figure 5: Measured and calculated molecular binding energies for $n=\SIrange[]{26}{45}{}$. Measured energies are shown as black points, while calculated energies are indicated by colored circles following the color code defined in Fig. \ref{['fig:exp_theo_comp']}. The straight blue line shows a power-law fit to the measured binding energies of the ground state in the outermost potential well $A0$. Light-brown curves highlight systematic scalings of the deeply bound states localized in the $p_{1/2}$ "butterfly" wells. Gray points mark lines missing in the model prediction that are likely bound in the $p_{3/2}$ "butterfly" wells (see main text). Error bars on the experimental energies represent the $1\sigma$ confidence intervals of the fit and are mostly smaller than the marker size. Experimentally unexplored regions are shaded in gray.