Using quantum-defect theory wave functions, we have computed dipole radial matrix elements involving Rydberg states of the singly-ionized alkaline-earth atoms. In order to test the results, we have calculated a set of transition probabilities, absorption oscillator strengths and radiative lifetimes for S, P, D, and F states up to n ∼30. Transition probabilities are in good agreement with available data. We report the lifetimes in terms of scaling relations of type τnl=τ0(n*)α. The variation of oscillator strengths with respect to the effective principal quantum number n* is discussed.
Using quantum-defect theory wave functions, we have computed dipole radial matrix elements involving Rydberg states of the singly-ionized alkaline-earth atoms. In order to test the results, we have calculated a set of transition probabilities, absorption oscillator strengths and radiative lifetimes for S, P, D, and F states up to n ∼30. Transition probabilities are in good agreement with available data. We report the lifetimes in terms of scaling relations of type τnl=τ0(n*)α. The variation of oscillator strengths with respect to the effective principal quantum number n* is discussed.
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.
We have presented an effective relativistic approach for sensing and calculating energy of levels, probabilities and oscillator strengths (transition amplitudes, lifetimes) of a number of radiative transitions in the spectra of heavy Rydberg atoms of alkaline elements. It represents a new version of the relativistic model potential method. The approach is based on the relativistic many-body gauge-invariant perturbation theory with the improved Dirac-Kohn-Sham zeroth approximation and relativistic energy approach (S-matrix adiabatic Gell-Mann and Low formalism). We have shown that that during computing the energy and spectroscopic characteristics of the multielectron Rydberg atomic systems a new approach provides a precise accounting exchange-correlation effects, including effect of essentially non-Coulomb grouping of Rydberg levels, pressure continuum. There are received precise data on energy and spectroscopic parameters energy, radiation width, amplitude transitions, the lifetime) for Rydberg atoms Rb, Cs, Fr, particularly, transitions nS½→n’P½,3/2 (n=5,6; n’=10-70), nP½,3.2→n’D3/2,5/2 (n=5,6; n’=10-80) in the Rb, Cs spectra; for Rydberg Fr there are in most first calculated and predicted spectroscopic data on transition amplitude, lifetime of Rydberg states and transitions 7S½-nP½,3/2, 7P½,3.2-nD3/2,5/2 (n=20-80). Regarding the application of the obtained data it can be indicated on carrying out new types of radiative quantum sensors and frequency standards, quantum electronics and different quantum devices.
Rates of depopulation by blackbody radiation (BBR) and effective lifetimes of alkali-metal nS, nP, and nD Rydberg states have been calculated in a wide range of principal quantum numbers $n\ensuremath{\le}80$ at the ambient temperatures of 77, 300, and 600 K. Quasiclassical formulas were used to calculate the radial matrix elements of the dipole transitions from Rydberg states. Good agreement of our numerical results with the available theoretical and experimental data has been found. We have also obtained simple analytical formulas for estimates of effective lifetimes and BBR-induced depopulation rates, which well agree with the numerical data.
Once created, an ensemble of atoms in their identical Rydberg states immediately experiences significant variations of its structure and corresponding properties. The variation is caused by the inevitable radiation transitions of highly excited states into different states of higher or lower energies. In particular, the change of a uniform definite-state population for another kind of population of different states will change the long-range interaction between atoms, even transforming the van der Waals interaction, Δ E vdW =− C 6 / R 6 , into dipole–dipole interaction with a different dependence on the interatomic distance, Δ E d−d =− C 3 / R 3 . In this paper, the most important—dipole radiation transitions from Rydberg states to higher- or lower-energy | n ′ 1 P 1 ⟩ states—are considered, both spontaneous and induced by the blackbody radiation (BBR) of the environment. The total transition probability rate, which is usually determined as the natural width, equals the imaginary part of the Rydberg-state energy Γ n S /2=−Im E n S . The probabilities of the | n ′ 1 P 1 ⟩-state populations W n S ( n ′ P, T ), which depend on the BBR temperature T , on the lifetime scale are also rather important optical characteristics of the ensemble of the Rydberg-state atoms. The value of W n S ( n ′ P, T ) is determined as the ratio of a particular transition probability rate Γ n S→ n ′ P sp +Γ n S→ n ′ P BBR ( T ) to the sum of all possible radiative transition rates, which include spontaneous and BBR-induced rates, where the latter depend on the temperature T of the environment. Numerical values of W n S ( n ′ P, T ) are calculated and presented in wide regions of the principal quantum numbers n , n ′ , and BBR temperatures T .
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.
Apropos to the growing interest in the study of long-range interactions which for their applications in cold atom physics, we have performed theoretical calculation for the two-dipole C6 and three-dipole C9 dispersion coefficients involving alkaline-earth atoms with alkaline-earth atoms and alkaline-earth ions. The C6 and C9 coefficients are expressed in terms of the dynamic dipole polarizabilities, which are calculated using relativistic methods. Thereafter, the calculated C6 coefficients for the considered alkaline-earth atoms among themselves are compared with the previously reported values. Due to unavailability of any other earlier theoretical or experimental results, for the C6 coefficients for alkaline-earth atoms with alkaline-earth ions and the C9 coefficients, we have performed separate fitting calculations and compared. Our calculations match in an excellent manner with the fitting calculations. We have also reported the oscillator strengths for the leading transitions and static dipole polarizabilities for the ground states of the alkaline-earth ions, i.e., Mg+, Ca+, Sr+, and Ba+ as well as the alkaline-earth atoms, i.e., Mg, Ca, Sr, and Ba. These, when compared with the available experimental results, show good agreement.