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arXiv:2111.04812 · Physical Review A

Magic wavelengths of the Sr ( 5s2 S01 – 5s5p P13 ) intercombination transition near the 5s5p P13 – 5p2 P23 transition

Grady Kestler, Khang Ton, Dmytro Filin, Marianna S. Safronova, Julio T. Barreiro

Published Jan 31, 2022• 9 citations
arXivHTMLPDF

Abstract

Predicting magic wavelengths accurately requires precise knowledge of electric dipole matrix elements of nearby atomic transitions. As a result, measurements of magic wavelengths allow us to test theoretical predictions for the matrix elements that frequently cannot be probed by any other methods. Here, we calculate and measure a magic wavelength near 473 nm of the $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}{S}_{0}\ensuremath{-}5s5p\phantom{\rule{0.16em}{0ex}}^{3}{P}_{1}$ intercombination transition of $^{88}\mathrm{Sr}$. Experimentally, we find 473.371(6) nm for $\mathrm{\ensuremath{\Delta}}m=0$ ($\ensuremath{\pi}$ transition) and 473.117(15) nm for $\mathrm{\ensuremath{\Delta}}m=\ensuremath{-}1$ (${\ensuremath{\sigma}}^{\ensuremath{-}}$ transition). Theoretical calculations yield 473.375(22) and 473.145(20) nm, respectively. Determining magic wavelengths nearby the dominant 461-nm probe transition of $^{88}\mathrm{Sr}$ holds promise for state insensitive interfacing of strontium atoms and nanophotonic devices with a narrow band of operating wavelengths. Furthermore, the $^{3}{P}_{1}$ polarizability is dominated by the contributions to the $5{p}^{2}\phantom{\rule{0.16em}{0ex}}^{3}P$ levels, and excellent agreement of theory and experiment validates both theoretical values of these matrix elements and estimates of their uncertainties.

DOI
10.1103/physreva.105.012821

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Predicting magic wavelengths accurately requires precise knowledge of electric dipole matrix elements of nearby atomic transitions. As a result, measurements of magic wavelengths allow us to test theoretical predictions for the matrix elements that frequently cannot be probed by any other methods. Here, we calculate and measure a magic wavelength near 473 nm of the 5s21S0\ensuremath−5s5p3P15{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}{S}_{0}\ensuremath{-}5s5p\phantom{\rule{0.16em}{0ex}}^{3}{P}_{1}5s21S0​\ensuremath−5s5p3P1​ intercombination transition of 88Sr^{88}\mathrm{Sr}88Sr. Experimentally, we find 473.371(6) nm for \ensuremathΔm=0\mathrm{\ensuremath{\Delta}}m=0\ensuremathΔm=0 (\ensuremathπ\ensuremath{\pi}\ensuremathπ transition) and 473.117(15) nm for \ensuremathΔm=\ensuremath−1\mathrm{\ensuremath{\Delta}}m=\ensuremath{-}1\ensuremathΔm=\ensuremath−1 (\ensuremathσ\ensuremath−{\ensuremath{\sigma}}^{\ensuremath{-}}\ensuremathσ\ensuremath− transition). Theoretical calculations yield 473.375(22) and 473.145(20) nm, respectively. Determining magic wavelengths nearby the dominant 461-nm probe transition of 88Sr^{88}\mathrm{Sr}88Sr holds promise for state insensitive interfacing of strontium atoms and nanophotonic devices with a narrow band of operating wavelengths. Furthermore, the 3P1^{3}{P}_{1}3P1​ polarizability is dominated by the contributions to the 5p23P5{p}^{2}\phantom{\rule{0.16em}{0ex}}^{3}P5p23P levels, and excellent agreement of theory and experiment validates both theoretical values of these matrix elements and estimates of their uncertainties.
We calculate and measure the magic wavelengths for the $6{s}^{2}^{1}S_{0}\ensuremath{-}6s6p\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ intercombination transition of the neutral ytterbium atom. The calculation is performed with the ab initio configuration interaction +++ all-order method. The measurement is done with laser spectroscopy on cold atoms in an optical dipole trap. The magic wavelengths are determined to be 1035.68(4) nm for the $\ensuremath{\pi}$ transition $(\mathrm{\ensuremath{\Delta}}m=0)$ and 1036.12(3) nm for the $\ensuremath{\sigma}$ transitions $(|\mathrm{\ensuremath{\Delta}}m|=1)$ in agreement with the calculated values. Laser cooling on the narrow intercombination transition could achieve better results for atoms in an optical dipole trap when the trap wavelength is tuned to near the magic wavelength.
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.
We demonstrate magic wavelengths for the 6s 2S1/2−6p 2P3/2,1/26s ~ {^2}S_{1/2}-6p ~ {^2}P_{3/2,1/2}6s 2S1/2​−6p 2P3/2,1/2​ transitions in the Cs atom due to the circularly polarized light. In addition, we also obtain magic wavelengths using the linearly polarized light in order to verify the previously reported values and make a comparative study with the values obtained for the circularly polarized light. Most of these wavelengths are found to be in the optical region and could be of immense interest to the experimentalists for carrying out high precision measurements. To obtain these wavelengths, we have calculated dynamic dipole polarizabilities of the ground, 6p 2P1/26p ~{^2}P_{1/2}6p 2P1/2​ and 6p 2P3/26p ~{^2}P_{3/2}6p 2P3/2​ states. We use the available precise values of the electric dipole (E1) matrix elements for the most dominantly contributing transitions from the lifetime measurements of the above excited states and obtain other relevant important E1 matrix elements by employing a relativistic coupled-cluster method approximating at the singles and doubles level. Accuracies in these quantities are substantiated by comparing our evaluated scalar polarizability values with the corresponding experimental results.
We predict a sequence of magic-zero wavelengths for the Sr excited 5s5p3P05s5p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}5s5p3P0​ state, and provide a general roadmap for extracting transition matrix elements using precise frequency measurements. We demonstrate that such measurements can serve as a global benchmark of the spectroscopic accuracy that is required for the development of high-precision predictive methods. These magic-zero wavelengths are also needed for state-selective atom manipulation for implementation of quantum logic operations. We also identify five magic wavelengths of the $5{s}^{2}{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}\text{\ensuremath{-}}5s5p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}$ Sr clock transition between 350 and 500 nm which can also serve as precision benchmarks.
We predict a sequence of magic-zero wavelengths for the Sr excited 5s5p 3P05s5p~ ^3P_05s5p 3P0​ state, and provide a general roadmap for extracting transition matrix elements using precise frequency measurements. We demonstrate that such measurements can serve as a best global benchmark of the spectroscopic accuracy that is required for the development of high-precision predictive methods. These magic-zero wavelengths are also needed for state-selective atom manipulation for implementation of quantum logic operations. We also identify five magic wavelengths of the 5s2 1S0−5s5p 3P05s^2\ ^1S_0 - 5s5p\ ^3P_05s2 1S0​−5s5p 3P0​ Sr clock transition between 350 nm and 500 nm which can also serve as precision benchmarks.
We report the experimental measurement of a magic wavelength at 476.823 62(8) nm for the ${}^{88}\mathrm{Sr}\phantom{\rule{0.2em}{0ex}}5{s}^{2}{\phantom{\rule{0.1em}{0ex}}}^{1}{\mathrm{S}}_{0}\ensuremath{\rightarrow}5s5p{\phantom{\rule{0.1em}{0ex}}}^{3}{\mathrm{P}}_{0}$ clock transition. The magic wavelength is determined through an ac Stark shift spectroscopy of atoms in an optical dipole trap. The value is in reasonable agreement with the theoretical prediction, differing by 0.061(54) nm. This magic wavelength, being shorter than the commonly used one at 813 nm, will be important for applications such as Bragg-pulse matter-wave interferometry involving both clock states. This work also paves the way for quantum simulation with a shorter lattice constant.