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Photonics

Precision Spectroscopy of Radiation Transitions between Singlet Rydberg States of the Group IIb and Yb Atoms

Igor L. Glukhov, Aleksandr A. Kamenski, Vitaly D. Ovsiannikov, Vitaly G. Palchikov

Published Oct 13, 2023• 5 citations
Publisher

Abstract

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.

DOI
10.3390/photonics10101153

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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.
The high-precision determination of microwave radiation parameters may be based on measurements of the spectral characteristics of radiation transitions between the Rydberg states of atoms. Frequencies and matrix elements are calculated for dipole transitions from even-parity nS1/2 and nD5/2 to odd-parity n′P3/2 and n′F7/2 (where n′ = n, n ± 1, n ± 2) for the Rydberg states of alkali-metal atoms. The matrix elements determine the splitting of Rydberg-state energy levels in the field of a resonance microwave (μw) radiation, which results in the splitting of the resonance in electromagnetic induced transparency (EIT). 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 of the current literature on quantum defect values were performed for the 2S, 2P, 2D and 2F series of the Rydberg states of Li, Na, K, Rb and Cs atoms. The calculated data were approximated by quadratic polynomials of the principal quantum number. The polynomial coefficients were determined with the use of a standard curve-fitting interpolation polynomial procedure for numerically presented functions. The approximation equations may be used for the accurate evaluation of the frequencies and matrix elements of μw transitions in wide ranges of the Rydberg-state quantum numbers n >> 1.
Numerical values of quantum defects us ed for calculations of frequencies and matrix elements of dipole radiation transitions in the microwave range between triplet Rydberg states n 3 S 1, n 3 P 1, n 3 D 2 and n 3 F 3 series of Group IIb atoms with large principal quantum numbers have been determined n > 20. The calculation results within semi-empirical methods of quantum defect theory and Fues model potential are approximated by quadratic polynomials. The polynomial coefficients are tabulated along with numerical values of frequencies and matrix elements and can be used for measuring field strengths through microwave-induced splitting of electromagnetically induced transparency resonance, for development and planning of studies of microwave radiation characteristics using Rydberg atoms.
Abstract Background of the electromagnetically induced transparency (EIT) resonance splitting by millimeter-wave radiation was investigated and so were calculated frequencies and amplitudes of radiation transitions between Rydberg states in alkaline earth atoms of IIA group elements, which are necessary for precise measurements of electric field magnitude at millimeter-wave (mmw) frequencies. Numerical values of the frequencies and matrix elements are approximated by asymptotic polynomials and tabulated for dipole transitions between singlet nS, nP, nD, and nF states with large values of principal quantum number n.
We calculated the frequencies and amplitudes of the microwave (µw) dipole transitions between triplet Rydberg states of n 3 S 1 , n 3 P 1 , n 3 D 2 , and n 3 F 3 series in the alkaline-earth atoms. Numerical values of the amplitudes determine the µw electric-field-dependent Rabi frequency of the Rydberg level shift in the field of a resonance radiation. This shift, observed as splitting of resonance in electromagnetically induced transparency for intensely absorbed probe radiation, enables measuring the µw electric field strength. For numerical calculations, we used single-electron methods and the most reliable data on quantum defect values from the literature. We derived the asymptotic approximation formulas of the µw frequencies and amplitudes.
Background of the electromagnetically induced transparency (EIT) resonance splitting by millimeter-wave radiation was investigated and so were calculated frequencies and amplitudes of radiation transitions between Rydberg states in alkaline earth atoms of IIA group elements, which are necessary for precise measurements of electric field magnitude at millimeter-wave (mmw) frequencies. Numerical values of the frequencies and matrix elements are approximated by asymptotic polynomials and tabulated for dipole transitions between singletnS,nP,nD, andnF states with large values of principal quantum numbern.
Rydberg atoms have a long history of scientific research, but they have recently seen a resurgence in popularity due to their advantages when dealing with coupled internal Rydberg states, or externally-coupled Rydberg atoms. The use of convenient RF and/or microwave generation techniques allows for straightforward coupling of many nearby Rydberg states, enabling quantum simulation studies, such as the generation of a synthetic lattice. Strontium is particularly attractive for Rydberg atom studies due to its optically active core, which allows for two-electron excited states and its conveniently accessible transition frequencies that match those available using commercial diode lasers. Before these experiments and applications can be realized however, precise knowledge of Rydberg state energies and quantum defects is required. Therefore, this work undertakes an extensive study of the quantum defects of both singly and doubly-excited strontium Rydberg atoms for a wide range of n and l. Precision microwave spectroscopy between nearby Rydberg states produces an improved self-consistent set of quantum defects for singly-excited 1S0, 1P1, 1D2, and 1F3 states, described by their corresponding Rydberg-Ritz parameters. Quantum defects and lifetimes for autoionizing two-electron-states are also presented. These elucidate the effects of core penetration by the “outer” excited Rydberg electron on transitions within the core ion and on the Rydberg level itself.