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Journal of the Optical Society of America

Calculation of highly excited Rydberg states of ytterbium atoms

E. P. Vidolova-Angelova, Л. Н. Иванов, Vladilen S Letokhov

Published Jun 1, 1981• 14 citations
Publisher

Abstract

Asymptotically exact calculations (with n → ∞) for the positions of the Rydberg states 4f14 6s1/2nlj of Yb have been carried out. The calculations have been performed by using the relativistic-perturbation theory with a model zeroth-order approximation. The proposed approach is more universal than the usually applied quantum-defect method, and, in contrast to the latter, it does not require the availability of experimental data about the low-lying states of the considered Rydberg series. It is shown that singlet–triplet splitting increases with increasing nuclear charge, and, for sufficiently heavy atoms, this splitting may exceed the distance between adjacent Rydberg states of the same series. The results have made it possible to change the accepted interpretation of the experimental spectrum. The difference between the theoretical and experimental quantum-defect spectrum monotonically decreases as n increases and is about 0.2 for n = 45.

DOI
10.1364/josa.71.000699

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Asymptotically exact calculations (with n → ∞) for the positions of the Rydberg states 4f14 6s1/2nlj of Yb have been carried out. The calculations have been performed by using the relativistic-perturbation theory with a model zeroth-order approximation. The proposed approach is more universal than the usually applied quantum-defect method, and, in contrast to the latter, it does not require the availability of experimental data about the low-lying states of the considered Rydberg series. It is shown that singlet–triplet splitting increases with increasing nuclear charge, and, for sufficiently heavy atoms, this splitting may exceed the distance between adjacent Rydberg states of the same series. The results have made it possible to change the accepted interpretation of the experimental spectrum. The difference between the theoretical and experimental quantum-defect spectrum monotonically decreases as n increases and is about 0.2 for n = 45.
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^{174}174Yb in 6sns 1S06sns\,^1S_06sns1S0​ Rydberg states across nearly two decades in principal quantum number nnn 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 sss-wave scattering length and the positions of two spin-orbit split ppp-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 6s23f 1F36s23f\, ^1F_36s23f1F3​ 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.
By combining the quantum theory of radiative transition with multichannel quantum-defect theory, we have derived a general formula to calculate the lifetimes of highly excited states for atoms. As an example, we have evaluated the lifetimes for the perturbed 6snd 1D2^{1}D_{2}1D2​ (n=8--40) and 6snd 3D2^{3}D_{2}3D2​ (n=10--26) Rydberg levels, and the perturbers of the ytterbium atom. We have not only obtained results that are in perfect agreement with the recent measurements, but also predicted the lifetimes of 18 other highly excited states. The results indicate that the dramatic variation for lifetimes of Rydberg states in the vicinity of perturbing states is due to the strong channel interaction.
In the study of Yb atomic Rydberg states, new members of 6sns 1 S 0 series for n=23, 24, 66-116 and 6snd 1 D 2 series for n=81-114 were observed. The data are in excellent agreement with the MQDT analysing results. The autoionizing Rydberg series 6p 1 2 /n's ( 1/2 , 1/2 ) 1 0 were investigated by three-step laser excitation. The ICE model was used to explain the experimental spectrum, and it has been proved to be suitable for describing the excitation of the autoionizing Rydberg states with a weakly-excited core.
The measurements of microwave (μw) and radio-frequency (RF) radiation quantitative parameters may be based on the quantum–optical approach to determine the spectral characteristics of radiation transitions between the Rydberg states of atoms. Frequencies and matrix elements are calculated for dipole transitions between opposite-parity Rydberg states nL 1L and n′L±1 1L±1 (where n′= n,n±1,n±2) of the singlet series in the alkaline–earth–metal-like atoms of group IIb (Zn, Cd, Hg) and Yb. The matrix elements determine the shifts of Rydberg-state energy levels in the field of resonance μw or RF radiation, splitting the resonance of electromagnetically induced transparency (EIT) for intensely absorbed probe radiation. Numerical computations based on the single-electron quantum defect method (QDM) and the Fues’ model potential (FMP) approach with the use of the most reliable data from the current literature on quantum defect values are performed for frequencies and matrix elements of transitions between singlet Rydberg states of 1S0-, 1P1-, 1D2-, and 1F3-series in Zn, Cd, Hg, and Yb atoms. The calculated data are approximated by polynomials in the powers of the principal quantum numbers. The polynomial coefficients are determined with the use of a standard curve-fitting interpolation polynomial procedure for numerically calculated functions. These approximation expressions provide new possibilities for accurately evaluating the frequencies and matrix elements of dipole transitions between Rydberg states over a wide range of quantum numbers n >> 1, accompanied by the emission and absorption of μw and RF photons.