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Journal of Optics B Quantum and Semiclassical Optics

Black-body radiation effects and light shifts in atomic frequency standards

V G Pal chikov, Yu. S. Domnin, A. V. Novoselov

Published Apr 1, 2003• 27 citations
Publisher

Abstract

A general method is presented for calculating the higher-order terms of series in powers of the black-body radiation field for the Stark-state wavefunctions, dipole transition matrix elements and corresponding frequency shifts of hyperfine splitting in the ground states for Cs and Rb atoms. A numerical method for calculating the light shifts in Sr atoms is described. It is based on the Green function method for summation over all intermediate states and exact Dirac–Fock wavefunctions for the resonant transitions to the first excited s-, p- and d-states. By comparing the calculated Stark shift with results of measurements employing atomic frequency standards, the black-body radiation effects on the ground state are analysed.

DOI
10.1088/1464-4266/5/2/370

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A general method is presented for calculating the higher-order terms of series in powers of the black-body radiation field for the Stark-state wavefunctions, dipole transition matrix elements and corresponding frequency shifts of hyperfine splitting in the ground states for Cs and Rb atoms. A numerical method for calculating the light shifts in Sr atoms is described. It is based on the Green function method for summation over all intermediate states and exact Dirac–Fock wavefunctions for the resonant transitions to the first excited s-, p- and d-states. By comparing the calculated Stark shift with results of measurements employing atomic frequency standards, the black-body radiation effects on the ground state are analysed.
The light frequency shifts induced by an external laser field are calculated for the spin-forbidden 3 P J — 1 S 0 transitions in Mg, Sr, and Yb atoms. The calculations are performed within the framework of the perturbation theory using experimentally measured transition energies. The calculations of the higher-order dynamic Stark effect were initiated by precision measurements of trapped and cooled atoms as well as by the development of a highly stable optical atomic clock. The dispersion properties of the polarisability and hyperpolarisability components are analysed in the vicinity of resonances and so-called cross points for the ground and excited atomic levels. The radial matrix elements were calculated by the Green function method for the model potential.
We present the results of studying the characteristics of Rydberg alkali atomic systems in a black-body (BBR; thermal) radiation field, in particular, BBR induced Stark shift coefficient k. As theoretical approach the combined generalized relativistic energy approach and relativistic many-body perturbation theory (PT) with ab initio Dirac zeroth approximation is applied. Application of theory to computing the spectral parameters of studied atomic systems have demonstrated physically reasonable agreement between the theoretical and experimental data. carefully. It should be noted that our method takes carefully into account such important factors as the implementation of a gauge invariance principle when calculating the corresponding matrix elements, the correct degree of consideration of complex exchange-correlation effects (primarily, the effect of polarization of the core), and also generates a fairly optimal one-quasiparticle representation in within the limits of many-body relativistic PT with ab initio zeroth Dirac-Fock (Kohn-Sham) approximation. In any case, the formalism developed in this work, as it follows from the given results, can be used for precise calculations of the Stark shift coefficient k, the BBR shift parameter β, and other parameters.
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.
Higher-order perturbation theory is used to study frequency shifts of the spin-forbidden 3 P J - 1 S 0 transitions for Mg, Sr and Yb atoms in an external laser field. Calculations of the higher-order dynamic Stark effect have been performed in connection with precise measurements on cooled and trapped atoms and the design of ultra stable optical clock in an engineered light shift trap. The form of the model potential of the valence electrons suggested by Simons is used for the calculation of atomic dynamic characteristics given by second- and fourth-order perturbation theory for the interaction of the atoms with the electromagnetic field. Dispersion properties of the polarizability and hyperpolarizability components and their behavior in the vicinity of both resonances and so-called magic wavelengths for the upper and lower atomic states, are analyzed. Calculations of ac multipole polarizabilities and dipole hyperpolarizabilities for the 3 P 0 - 1 S 0 clock transition in 87 Sr indicate that the contribution of the higher- order light shifts can be reduced to less than 1 mHz, allowing for a projected accuracy of better than 10 -17 .
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.
A general method is presented for calculating the higher-order terms of series in powers of the DC field for the hydrogen Stark-state wavefunctions, dipole transition matrix elements and corresponding line intensities. Analytical expressions are derived for the second-order Stark effect on the matrix elements and intensities of the Stark lines. Simple formulae for transitions to states with zero parabolic quantum numbers are given. The numerical data for the Lyman and Balmer series and for some transitions between Rydberg levels are analysed in detail.