We report a measurement of the ratio of electric dipole transition matrix elements of cesium for the $6p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}\ensuremath{\rightarrow}7s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and $6p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}\ensuremath{\rightarrow}7s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ transitions. We determine this ratio of matrix elements through comparisons of two-color, two-photon excitation rates of the
7s2S1/2 state using laser beams with polarizations parallel to one another vs perpendicular to one another. Our result of $R\ensuremath{\equiv}\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{3/2}\ensuremath{\rangle}/\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{1/2}\ensuremath{\rangle}=1.5272(17)$ is in excellent agreement with a theoretical prediction of
R=1.5270(27). Moreover, the accuracy of the experimental ratio is sufficiently high to differentiate between various theoretical approaches. To our knowledge, there are no prior experimental measurements of
R. Combined with our recent determination of the lifetime of the
7s2S1/2 state, we determine reduced matrix elements for these two transitions, $\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{3/2}\ensuremath{\rangle}=\ensuremath{-}6.489(5)\phantom{\rule{4pt}{0ex}}{a}_{0}$ and $\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{1/2}\ensuremath{\rangle}=\ensuremath{-}4.249(4)\phantom{\rule{4pt}{0ex}}{a}_{0}$. These matrix elements are also in excellent agreement with theoretical calculations. These measurements improve knowledge of Cs properties needed for parity violation studies and provide benchmarks for tests of high-precision theory.
The interaction between light and an atom causes perturbations in the atom's energy levels, known as the light shift. These light shifts are a key source of inaccuracy in atomic clocks, and can also deteriorate their precision. We present a study of light shifts and associated dynamic polarizabilities for a two-photon atomic clock based on the
5S1/2--
5D5/2 transition in rubidium-87 over the range 770--800 nm. We determine experimental and theoretical values for a magic wavelength in this range and the electric dipole (E1) matrix element for the
5P3/2--
5D5/2 transition. We find a magic wavelength of 776.179(5) nm (experimental) and 776.21 nm (theoretical) in the vicinity of the
5P3/2--
5D5/2 resonance, and the corresponding reduced E1 matrix element
1.80(6)ea0 (experimental) and
1.96(15)ea0 (theoretical). These values resolve a previous discrepancy between theory and experiment.
Light shift in a state due to the applied laser in an atomic system vanishes at tune-out wavelengths (λTs). Similarly, differential light shift in a transition vanishes at the magic wavelengths (λmagics). In many of the earlier studies, values of the electric dipole (E1) matrix elements were inferred precisely by combining measurements and calculations of λmagic. Similarly, the λT values of an atomic state can be used to infer the E1 matrix element, as it involves dynamic electric dipole (α) values of only one state whereas the λmagic values require evaluation of α values for two states. However, both the λmagic and λT values depend on angular momenta and their magnetic components (M) of states. Here, we report the λmagic and λT values of many S1/2 and D3/2,5/2 states, and transitions among these states of the Mg+, Ca+, Sr+ and Ba+ ions that are independent of M values. It is possible to infer a large number of E1 matrix elements of the above ions accurately by measuring these values and combining with our calculations.