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arXiv:1503.07300 · Physical Review A

Dynamic dipole polarizabilities for the low-lying triplet states of helium

Yong-Hui Zhang, Li-Yan Tang, Xian Zhou Zhang, Ting-Yun Shi

Published Jul 24, 2015• 28 citations
arXivHTMLPDF

Abstract

The dynamic dipole polarizabilities for the four lowest triplet states ($2{\phantom{\rule{0.16em}{0ex}}}^{3}S, 3{\phantom{\rule{0.16em}{0ex}}}^{3}S, 2{\phantom{\rule{0.16em}{0ex}}}^{3}P$, and $3{\phantom{\rule{0.16em}{0ex}}}^{3}P$) of helium are calculated using the $B$-spline configuration interaction method. Present values of the static dipole polarizabilities in the length, velocity, and acceleration gauges are in good agreement with the best Hylleraas results. Also the tune-out wavelengths in the range 400 nm--4.2 $\ensuremath{\mu}\mathrm{m}$ for the four lowest triplet states are identified, and the magic wavelengths in the range 460 nm--3.5 $\ensuremath{\mu}\mathrm{m}$ for the $2{\phantom{\rule{0.16em}{0ex}}}^{3}S\ensuremath{\rightarrow}3{\phantom{\rule{0.16em}{0ex}}}^{3}S, 2{\phantom{\rule{0.16em}{0ex}}}^{3}S\ensuremath{\rightarrow}2{\phantom{\rule{0.16em}{0ex}}}^{3}P$, and $2{\phantom{\rule{0.16em}{0ex}}}^{3}S\ensuremath{\rightarrow}3{\phantom{\rule{0.16em}{0ex}}}^{3}P$ transitions are determined. We show that the tune-out wavelength of $2{\phantom{\rule{0.16em}{0ex}}}^{3}S$ state is $413.038\phantom{\rule{0.16em}{0ex}}28(3)$ nm, which corroborates the value of Mitroy and Tang [Phys. Rev. A 88, 052515 (2013)], and the magic wavelength around 1066 nm for the $2{\phantom{\rule{0.16em}{0ex}}}^{3}S\ensuremath{\rightarrow}3{\phantom{\rule{0.16em}{0ex}}}^{3}P$ transition can be expected for precision measurement to determine the ratio of transition matrix elements $(2{\phantom{\rule{0.16em}{0ex}}}^{3}S\ensuremath{\rightarrow}2{\phantom{\rule{0.16em}{0ex}}}^{3}P)/(3{\phantom{\rule{0.16em}{0ex}}}^{3}P\ensuremath{\rightarrow}6{\phantom{\rule{0.16em}{0ex}}}^{3}S)$.

DOI
10.1103/physreva.92.012515

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Magic wavelengths (${\ensuremath{\lambda}}_{\mathrm{magic}}$) for the $7{S}_{1/2}\ensuremath{-}7{P}_{1/2,3/2}$ transitions (D lines) in Fr were reported by Dammalapati et al. [U. Dammalapati, K. Harada, and Y. Sakemi, Phys. Rev. A 93, 043407 (2016)]. These ${\ensuremath{\lambda}}_{\mathrm{magic}}$ were determined by plotting dynamic polarizabilities ($\ensuremath{\alpha}$) of the involved states with the above transitions against a desired range of wavelengths. Electric dipole (E1) matrix elements listed in [J. E. Sansonetti, J. Phys. Chem. Ref. Data 36, 497 (2007)], from the measured lifetimes of the 7P1/2,3/27{P}_{1/2,3/2}7P1/2,3/2​ states and from the calculations considering core-polarization effects in the relativistic Hartree-Fock (HFR) method, were used to determine $\ensuremath{\alpha}$. However, contributions from core correlation effects and from the E1 matrix elements of the $7P\ensuremath{-}7S, 7P\ensuremath{-}8S$, and $7P\ensuremath{-}6D$ transitions to $\ensuremath{\alpha}$ of the 7P7P7P states were ignored. In this work, we demonstrate importance of these contributions and improve accuracies of $\ensuremath{\alpha}$ further by replacing the E1 matrix elements taken from the HFR method by the values obtained employing relativistic coupled-cluster theory. Our static $\ensuremath{\alpha}$ are found to be in excellent agreement with the other available theoretical results, whereas substituting the E1 matrix elements used by Dammalapati et al. gives very small $\ensuremath{\alpha}$ values for the 7P7P7P states. Owing to this, we find disagreement in ${\ensuremath{\lambda}}_{\mathrm{magic}}$ reported by Dammalapati et al. for linearly polarized light, especially at wavelengths close to the D lines and in the infrared region. As a consequence, a ${\ensuremath{\lambda}}_{\mathrm{magic}}$ reported at 797.75 nm which was seen supporting a blue detuned trap in their work is now estimated at 771.03 nm and is supporting a red detuned trap. Also, none of our results match with the earlier results for circularly polarized light. Moreover, our static values of $\ensuremath{\alpha}$ will be very useful for guiding experiments to carry out their measurements.
The dynamic dipole polarizabilities for the 3s3s3s state of the Li atom are computed using Hylleraas and semiempirical approaches. This enables the calculation of the 7{}^{7}7Li($2s\ensuremath{\rightarrow}3s$) Stark shift at photon wavelengths of 610.5 nm and 735.1 nm. They are calculated to be 834.7(5) and $\ensuremath{-}686.7(25)$ a03{a}_{0}^{3}a03​, respectively. The first two tune-out frequencies for the 7{}^{7}7Li(2s2s2s) ground state are determined to be 670.971626(1)670.971\phantom{\rule{0.16em}{0ex}}626(1)670.971626(1) nm and 324.192(2)324.192(2)324.192(2) nm, respectively.