arXiv:1507.06570

The magic road to precision

Marianna S. Safronova, Z. Zuhrianda, Marianna S. Safronova, Charles W. Clark

Published Jul 23, 2015• 4 citations

Abstract

We predict a sequence of magic-zero wavelengths for the Sr excited $5s5p~ ^3P_0$ 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 $5s^2\ ^1S_0 - 5s5p\ ^3P_0$ Sr clock transition between 350 nm and 500 nm which can also serve as precision benchmarks.

DOI: 10.48550/arxiv.1507.06570

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arXiv:1507.06570

The magic road to precision

Marianna S. Safronova, Z. Zuhrianda, Marianna S. Safronova, Charles W. Clark

Published Jul 23, 2015• 4 citations

arXiv HTML PDF

Abstract

We predict a sequence of magic-zero wavelengths for the Sr excited

5s5p~ ^3P_0

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

5s^2\ ^1S_0 - 5s5p\ ^3P_0

Sr clock transition between 350 nm and 500 nm which can also serve as precision benchmarks.

DOI: 10.48550/arxiv.1507.06570

Related papers

Extracting transition rates from zero-polarizability spectroscopy

Marianna S. Safronova, Z. Zuhrianda, Marianna S. Safronova +1 more

We predict a sequence of magic-zero wavelengths for the Sr excited $5s5p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}$ 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 $5s5p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}$ 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.

Physical Review AOct 6, 201531 citations

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

Grady Kestler, Khang Ton, Dmytro Filin +2 more

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.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.

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Magic wavelength at 477 nm for the strontium clock transition

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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.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.

arXiv:2507.04532Physical Review AppliedNov 10, 20251 citation

Precision Measurement of Transition Matrix Elements via Light Shift Cancellation

Creston D. Herold, Varun Vaidya, Xiao Li +3 more

We present a method for accurate determination of atomic transition matrix elements at the 10(-3) level. Measurements of the ac Stark (light) shift around "magic-zero" wavelengths, where the light shift vanishes, provide precise constraints on the matrix elements. We make the first measurement of the 5s - 6p matrix elements in rubidium by measuring the light shift around the 421 and 423 nm zeros through diffraction of a condensate off a sequence of standing wave pulses. In conjunction with existing theoretical and experimental data, we find 0.3235(9)ea(0) and 0.5230(8)ea(0) for the 5s - 6p(1/2) and 5s - 6p(3/2) elements, respectively, an order of magnitude more accurate than the best theoretical values. This technique can provide needed, accurate matrix elements for many atoms, including those used in atomic clocks, tests of fundamental symmetries, and quantum information.We present a method for accurate determination of atomic transition matrix elements at the 10(-3) level. Measurements of the ac Stark (light) shift around "magic-zero" wavelengths, where the light shift vanishes, provide precise constraints on the matrix elements. We make the first measurement of the 5s - 6p matrix elements in rubidium by measuring the light shift around the 421 and 423 nm zeros through diffraction of a condensate off a sequence of standing wave pulses. In conjunction with existing theoretical and experimental data, we find 0.3235(9)ea(0) and 0.5230(8)ea(0) for the 5s - 6p(1/2) and 5s - 6p(3/2) elements, respectively, an order of magnitude more accurate than the best theoretical values. This technique can provide needed, accurate matrix elements for many atoms, including those used in atomic clocks, tests of fundamental symmetries, and quantum information.

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Magic wavelengths and triple magic trapping conditions for $5s^2~^1\!S_0$ and $5s5p~^3\!P_{0,2}$ states of Sr atomsMagic wavelengths and triple magic trapping conditions for $5s^2~^1\!S_0$ and $5s5p~^3\!P_{0,2}$ states of Sr atoms

Yan-Min Wang, Qing-Yi Liu, Yong-Bo Tang +4 more

The static and dynamic electric dipole polarizabilities of the $5s^2~^1\!S_0$ and $5s5p~^3\!P_{0,2}$ states of Sr atoms are calculated using the relativistic configuration interaction plus the many-body perturbation theory (RCI+MBPT) method. Magic wavelengths are determined for the transitions $5s^2~^1\!S_0\rightarrow 5s5p~^3\!P_{0}$ , $5s^2~^1\!S_0\rightarrow 5s5p~^3\!P_{2}$ , and $5s5p~^3\!P_0\rightarrow 5s5p~^3\!P_{2}$ . A comprehensive study is conducted on the dependence of magic wavelengths on the angle between the laser polarization and the magnetic field. Furthermore, the conditions for realizing triple magic trapping at 813.4~nm for the $5s^2~^1\!S_0$ , $5s5p~^3\!P_{0}$ and $5s5p~^3\!P_{2}$ states are investigated. In the case of linearly polarized light, when the angle ( $θ_p$ ) between the laser polarization direction and the magnetic field is $79.1(0.7)^\circ$ , triple magic trapping for the $5s^2~^1\!S_0$ , $5s5p~^3\!P_{0}$ , and $5s5p~^3\!P_{2}~M=0$ states can be achieved. This result agrees well with the recent experimental measurement (78.49(3) $^\circ$ )[Phys. Rev. Lett. 135, 143401 (2025)]. Meanwhile, triple magic trapping involving the $5s5p~^3\!P_{2}~M=2$ state can be achieved when $θ_p= 37.4(0.3)^\circ$ . The conditions for achieving triple magic trapping with circularly and arbitrarily elliptically polarized light are also presented.The static and dynamic electric dipole polarizabilities of the $5s^2~^1\!S_0$ and $5s5p~^3\!P_{0,2}$ states of Sr atoms are calculated using the relativistic configuration interaction plus the many-body perturbation theory (RCI+MBPT) method. Magic wavelengths are determined for the transitions $5s^2~^1\!S_0\rightarrow 5s5p~^3\!P_{0}$, $5s^2~^1\!S_0\rightarrow 5s5p~^3\!P_{2}$, and $5s5p~^3\!P_0\rightarrow 5s5p~^3\!P_{2}$. A comprehensive study is conducted on the dependence of magic wavelengths on the angle between the laser polarization and the magnetic field. Furthermore, the conditions for realizing triple magic trapping at 813.4~nm for the $5s^2~^1\!S_0$, $5s5p~^3\!P_{0}$ and $5s5p~^3\!P_{2}$ states are investigated. In the case of linearly polarized light, when the angle ($θ_p$) between the laser polarization direction and the magnetic field is $79.1(0.7)^\circ$, triple magic trapping for the $5s^2~^1\!S_0$, $5s5p~^3\!P_{0}$, and $5s5p~^3\!P_{2}~M=0$ states can be achieved. This result agrees well with the recent experimental measurement (78.49(3)$^\circ$)[Phys. Rev. Lett. 135, 143401 (2025)]. Meanwhile, triple magic trapping involving the $5s5p~^3\!P_{2}~M=2$ state can be achieved when $θ_p= 37.4(0.3)^\circ$. The conditions for achieving triple magic trapping with circularly and arbitrarily elliptically polarized light are also presented.

arXiv:2512.23326Dec 29, 20250 citations

Determination of Sr properties for a high-accuracy optical clock

S. G. Porsev, Andrew D. Ludlow, Martin M. Boyd +1 more

We have carried out calculations towards the goal of reducing the inaccuracy of the Sr optical atomic clock to $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ and below. In particular, we focused on ac polarizabilities of the $5{s}^{2}$ $^{1}S_{0}$ and $5s5p$ $^{3}P_{0}^{o}$ clock states that are important for reducing the uncertainty of black-body radiation-induced frequency shifts for the $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{0}^{o}$ clock transition. Four low-lying even-parity states have been identified, whose total contribution to the static polarizability of the $^{3}P_{0}^{o}$ clock state is at the level of 90%. We show that if the contribution of these states is experimentally known with 0.1% accuracy, the same accuracy can be achieved for the total polarizability of the $^{3}P_{0}^{o}$ state. The corresponding uncertainty for the blackbody shift at a fixed room temperature will be below $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$. The calculations are confirmed by a number of experimental measurements on various Sr properties.We have carried out calculations towards the goal of reducing the inaccuracy of the Sr optical atomic clock to $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ and below. In particular, we focused on ac polarizabilities of the $5{s}^{2}$ $^{1}S_{0}$ and $5s5p$ $^{3}P_{0}^{o}$ clock states that are important for reducing the uncertainty of black-body radiation-induced frequency shifts for the $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{0}^{o}$ clock transition. Four low-lying even-parity states have been identified, whose total contribution to the static polarizability of the $^{3}P_{0}^{o}$ clock state is at the level of 90%. We show that if the contribution of these states is experimentally known with 0.1% accuracy, the same accuracy can be achieved for the total polarizability of the $^{3}P_{0}^{o}$ state. The corresponding uncertainty for the blackbody shift at a fixed room temperature will be below $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$. The calculations are confirmed by a number of experimental measurements on various Sr properties.

arXiv:0807.1381Physical Review ASep 5, 200879 citations

We predict a sequence of magic-zero wavelengths for the Sr excited

5s5p~ ^3P_0

5s^2\ ^1S_0 - 5s5p\ ^3P_0

Sr clock transition between 350 nm and 500 nm which can also serve as precision benchmarks.

We predict a sequence of magic-zero wavelengths for the Sr excited

5s5p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}

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.

^{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.

Magic wavelengths and triple magic trapping conditions for

5s^2~^1\!S_0

and

5s5p~^3\!P_{0,2}

states of Sr atoms

The static and dynamic electric dipole polarizabilities of the

5s^2~^1\!S_0

and

5s5p~^3\!P_{0,2}

states of Sr atoms are calculated using the relativistic configuration interaction plus the many-body perturbation theory (RCI+MBPT) method. Magic wavelengths are determined for the transitions

5s^2~^1\!S_0\rightarrow 5s5p~^3\!P_{0}

5s^2~^1\!S_0\rightarrow 5s5p~^3\!P_{2}

, and

5s5p~^3\!P_0\rightarrow 5s5p~^3\!P_{2}

. A comprehensive study is conducted on the dependence of magic wavelengths on the angle between the laser polarization and the magnetic field. Furthermore, the conditions for realizing triple magic trapping at 813.4~nm for the

5s^2~^1\!S_0

5s5p~^3\!P_{0}

and

5s5p~^3\!P_{2}

states are investigated. In the case of linearly polarized light, when the angle (

θ_p

) between the laser polarization direction and the magnetic field is

79.1(0.7)^\circ

, triple magic trapping for the

5s^2~^1\!S_0

5s5p~^3\!P_{0}

, and

5s5p~^3\!P_{2}~M=0

states can be achieved. This result agrees well with the recent experimental measurement (78.49(3)

^\circ

)[Phys. Rev. Lett. 135, 143401 (2025)]. Meanwhile, triple magic trapping involving the

5s5p~^3\!P_{2}~M=2

state can be achieved when

θ_p= 37.4(0.3)^\circ

. The conditions for achieving triple magic trapping with circularly and arbitrarily elliptically polarized light are also presented.

5{s}^{2}

^{1}S_{0}

and

5s5p

^{3}P_{0}^{o}

clock states that are important for reducing the uncertainty of black-body radiation-induced frequency shifts for the $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{0}^{o}$ clock transition. Four low-lying even-parity states have been identified, whose total contribution to the static polarizability of the

^{3}P_{0}^{o}

clock state is at the level of 90%. We show that if the contribution of these states is experimentally known with 0.1% accuracy, the same accuracy can be achieved for the total polarizability of the

^{3}P_{0}^{o}

state. The corresponding uncertainty for the blackbody shift at a fixed room temperature will be below $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$. The calculations are confirmed by a number of experimental measurements on various Sr properties.