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arXiv:1610.08150 · Physical Review A

Polarizabilities and tune-out wavelengths of the hyperfine ground states of Rb87,85

Xia Wang, Jun Jiang, Lu-You Xie, Denghong Zhang, Chenzhong Dong

Published Nov 23, 2016• 13 citations
arXivHTMLPDF

Abstract

The static and dynamic polarizabilities and the tune-out wavelengths of the ground state of Rb and the hyperfine ground states of $^{87,85}\mathrm{Rb}$ have been calculated by using the relativistic configuration interaction plus core polarization (RCICP) approach. It is found that the first primary tune-out wavelengths of the $5{s}_{1/2},F=1,2$ states of $^{87}\mathrm{Rb}$ are 790.018187(193) and 790.032602(193) nm, respectively, where the calculated result for the $5{s}_{1/2},F=2$ state is in good agreement with the latest high-precision measurement 790.032388(32) nm [R. H. Leonard et al., Phys. Rev. A 92, 052501 (2015)]. Similarly, the first primary tune-out wavelengths of the $5{s}_{1/2},F=2,3$ states of $^{85}\mathrm{Rb}$ are 790.023515(218) and 790.029918(218) nm, respectively. Furthermore, the tune-out wavelengths for the different magnetic sublevels ${M}_{F}$ of each hyperfine level $F$ are also determined by considering the contributions of tensor polarizabilities.

DOI
10.1103/physreva.94.052510

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The static and dynamic polarizabilities and the tune-out wavelengths of the ground state of Rb and the hyperfine ground states of 87,85Rb^{87,85}\mathrm{Rb}87,85Rb have been calculated by using the relativistic configuration interaction plus core polarization (RCICP) approach. It is found that the first primary tune-out wavelengths of the 5s1/2,F=1,25{s}_{1/2},F=1,25s1/2​,F=1,2 states of 87Rb^{87}\mathrm{Rb}87Rb are 790.018187(193) and 790.032602(193) nm, respectively, where the calculated result for the 5s1/2,F=25{s}_{1/2},F=25s1/2​,F=2 state is in good agreement with the latest high-precision measurement 790.032388(32) nm [R. H. Leonard et al., Phys. Rev. A 92, 052501 (2015)]. Similarly, the first primary tune-out wavelengths of the 5s1/2,F=2,35{s}_{1/2},F=2,35s1/2​,F=2,3 states of 85Rb^{85}\mathrm{Rb}85Rb are 790.023515(218) and 790.029918(218) nm, respectively. Furthermore, the tune-out wavelengths for the different magnetic sublevels MF{M}_{F}MF​ of each hyperfine level FFF are also determined by considering the contributions of tensor polarizabilities.
The influence of hyperfine interactions on the tune-out wavelengths of the 39{}^{39}39K, 40{}^{40}40K, and 41{}^{41}41K isotopes of the potassium atom was investigated. The hyperfine interaction of the 4s1/24{s}_{1/2}4s1/2​ ground state results in a shift and splitting of the primary tune-out wavelength near 769 nm. The 4s1/24{s}_{1/2}4s1/2​ state hyperfine splittings of the primary tune-out wavelength were almost equal to the hyperfine splittings of the ground states. The splittings in the wavelengths were 0.0009, 0.0026, and 0.0005 nm for 39{}^{39}39K, 40{}^{40}40K, and 41{}^{41}41K, respectively. The hyperfine splitting of the npJn{p}_{J}npJ​ levels leads to the creation of additional tune-out wavelengths. The additional tune-out wavelengths could be difficult to detect due to very small differences from the transition wavelengths to the 4pJ,F4{p}_{J,F}4pJ,F​ states. The hyperfine Stark shift for the ground states of all three isotopes was also computed, and the value for 39{}^{39}39K was found to be compatible with the previous experiments and the most recent calculation using relativistic many-body perturbation theory.
We report on a precision measurement of the DDD line tune-out wavelength of 87Rb^{87}\text{Rb}87Rb in the hyperfine ground state $\left|F=1,{m}_{F}=0,\ifmmode\pm\else\textpm\fi{}1\right\ensuremath{\rangle}$ manifold at 790nm790\phantom{\rule{0.16em}{0ex}}\mathrm{nm}790nm, where the scalar ac Stark shifts of the D1{D}_{1}D1​ and the D2{D}_{2}D2​ lines cancel. This wavelength is sensitive to usually neglected contributions from vector and tensor ac Stark shifts, transitions to higher principle quantum numbers, and core electrons. The ac Stark shift is probed by Kapitza-Dirac scattering of a rubidium Bose-Einstein condensate in a one-dimensional optical lattice in free space and controlled magnetic environment. The tune-out wavelength of the magnetically insensitive mF=0{m}_{F}=0mF​=0 state was determined to 790.01858(23)nm790.01858(23)\phantom{\rule{0.16em}{0ex}}\mathrm{n}\mathrm{m}790.01858(23)nm with sub-pm accuracy. An in situ absolute polarization, and magnetic background field measurement is performed by employing the ac vector Stark shift for the ${m}_{F}=\ifmmode\pm\else\textpm\fi{}1$ states. Comparing our findings to theory, we get quantitative insight into atomic physics beyond commonly used two-level atom approximations or the neglect of inner shell contributions.
The five longest tune-out wavelengths for the rubidium atom are predicted from existing experimental and theoretical information by using an approximation formula. The formula is derived from the analysis of a non-relativistic configuration-interaction plus core polarization (CICP) calculation of the tune-out wavelengths for rubidium. The differences between the wavelengths predicted from the approximation formula and the exact CICP calculation are at the 10 −3 nm level. The predicted five longest tune-out wavelengths are 790.115 nm, 423.155 nm, 421.111 nm, 359.429 nm, and 359.022 nm, respectively.
We report a precision measurement of a tune-out wavelength for 87Rb^{87}\mathrm{Rb}87Rb using circularly polarized light. A tune-out wavelength characterizes a zero in the electric polarizability of the atom. For circularly polarized light, the total polarizability depends on both the scalar and vector polarizability components. This shifts the location of the tune-out wavelength and makes it sensitive to different combinations of atomic dipole matrix elements than the scalar polarizability alone. Using ${\ensuremath{\sigma}}_{\ensuremath{-}}$ polarized light with a purity of 0.9931(1), we observe a tune-out wavelength of 785.1522(3) nm, which agrees with theoretical expectations when small contributions from the core electrons and off-resonant valence states are taken into account.