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.
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.
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.
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.
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.
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.
Authors: E.F. Stelmashenko(1), O.A. Klezovich(1), V.N. Baryshev(1), V.A. Tischenko(1), I.Yu. Blinov(1), V.G.Palchikov (1,2(, V. D. Ovsiannikov (1,3) Affiliation: (1)National Research Institute for Physical-Technical and Radiotechnical Measurements, Mendeleevo, Moscow Region , Russia (2)National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow, Russia (3)Voronezh State University, University sq.1, 394018, Voronezh, Russia Abstract: Spectral characteristics are determined for the resonance electromagnetically induced transparency (EIT) effect on atomic rubidium vapours, induced by an intense radiation of the wavelength in the region from 479 to 486 nm in presence of a microwave (MW) radiation of a frequency from 1 to 300 GHz, which splits the energy of transition from the 5P3/2 state to a Rydberg state nD5/2 . The magnitude of the EIT peak splitting is proportional to the MW-radiation electric field. Simple approximation equations are derived for evaluating numerically the amplitude of transition between Rydberg nD5/2 and (n+1)P3/2 states with high principal quantum numbers n. An experimental setup is constructed for measuring the MW electric field on the basis of the EIT resonance-splitting measurements in absorption spectra of a probe radiation.