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arXiv:1601.04156 · Physical Review A

Spin-statistic selection rules for multiphoton transitions: Application to helium atoms

Timur A. Zalialiutdinov, Dmitry A. Solovyev, Leonti N Labzowsky, G. Plunien

Published Jan 14, 2016• 8 citations
arXivHTMLPDF

Abstract

A theoretical investigation of the three-photon transition rates $2\phantom{\rule{0.16em}{0ex}}{}^{1}{P}_{1}\ensuremath{\rightarrow}2\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}\phantom{\rule{0.28em}{0ex}},1\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}$ and $2\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{2}\ensuremath{\rightarrow}2\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}\phantom{\rule{0.28em}{0ex}},1\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}$ for the helium atom is presented. Photon energy distributions and precise values of the nonrelativistic transition rates are obtained with employment of correlated wave functions of the Hylleraas type. The possible experiments for the tests of the Bose-Einstein statistics for multiphoton systems are discussed.

DOI
10.1103/physreva.93.012510

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We establish the existence of spin-statistic selection rules (SSSRs) for multiphoton transitions with equal photons in atomic systems. These selection rules are similar to those for systems of many equivalent electrons in atomic theory. The latter are a direct consequence of the Pauli exclusion principle. In this sense, the SSSRs play the role of the exclusion principle for photons: they forbid some particular states for the photon systems. We established several SSSRs for few-photon systems. (i) First rule: two equivalent photons involved in any atomic transition can have only even values of the total angular momentum, JJJ. This selection rule is an extension of the Landau-Yang theorem to the photons involved in atomic transitions. (ii) Second rule: three equivalent dipole photons involved in any atomic transition can have only odd values of the total angular momentum, J=1,3J=1,3J=1,3. (iii) Third rule: four equivalent dipole photons involved in any atomic transition can have only even values of the total angular momentum, J=0,2,4J=0,2,4J=0,2,4. We also suggest a method for a possible experimental test of these SSSRs by means of laser experiments.
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The relativistic configuration interaction plus many-body perturbation (RCI +++ MBPT) method is utilized to calculate the wave functions, energy levels, and reduced E1E1E1 transition matrix elements of Ca atoms in detail. The static and dynamic polarizabilities of the 4s21S0,4s4p1P14{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}, 4s4p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}4s21S0​,4s4p1P1​, and 4s4p3P0,1,24s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{0,1,2}4s4p3P0,1,2​ states are determined by the sum-over-states method. A number of magic-zero wavelengths for the ground and 4s4p3P04s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}4s4p3P0​ states, as well as magic wavelengths for the $4{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}4s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ and $4{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}4s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ transitions, are obtained. We suggest that the measurements of the magic-zero wavelengths of the 4s4p3P04s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}4s4p3P0​ states can be used to determine oscillator strengths with high precision. In addition, the angle-dependent magic wavelengths of each magnetic sublevel transition of the $4{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}4s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ transition are provided, which are of particular interest for optical frequency measurements, Bose-Einstein condensate generation, and superradiant laser technology.