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arXiv:2202.07828

Measurement of infrared magic wavelength for an all-optical trapping of $^{40}$Ca$^{+}$ ion clock

Yao Huang, Hua Guan, Chengbin Li, Huaqing Zhang, Baolin Zhang, Miao Wang, Liyan Tang, Ting-Yun Shi, Kelin Gao

Published Feb 16, 2022• 1 citation
arXivHTMLPDF

Abstract

For the first time, we experimentally determine the infrared magic wavelength for the $^{40}$Ca$^{+}$ $4s\, ^{2}\!S_{1/2} \rightarrow 3d\,^{2}\!D_{5/2}$ electric quadrupole transition by observation of the light shift canceling in $^{40}$Ca$^{+}$ optical clock. A "magic" magnetic field direction is chosen to make the magic wavelength insensitive to both the linear polarization purity and the polarization direction of the laser. The determined magic wavelength for this transition is 1056.37(9)~nm, which is not only in good agreement with theoretical predictions but also more precise by a factor of about 300. Using this measured magic wavelength we also derive the differential static polarizability to be $-44.32(32)$~a.u., which will be an important input for the evaluation of the blackbody radiation shift at room temperatures. Our work paves a way for all-optical-trapping of $^{40}$Ca$^{+}$ optical clock.

DOI
10.48550/arxiv.2202.07828

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Measurement of infrared magic wavelength for an all-optical trapping of 40^{40}40Ca+^{+}+ ion clock
For the first time, we experimentally determine the infrared magic wavelength for the 40^{40}40Ca+^{+}+ 4s 2 ⁣S1/2→3d 2 ⁣D5/24s\, ^{2}\!S_{1/2} \rightarrow 3d\,^{2}\!D_{5/2}4s2S1/2​→3d2D5/2​ electric quadrupole transition by observation of the light shift canceling in 40^{40}40Ca+^{+}+ optical clock. A "magic" magnetic field direction is chosen to make the magic wavelength insensitive to both the linear polarization purity and the polarization direction of the laser. The determined magic wavelength for this transition is 1056.37(9)~nm, which is not only in good agreement with theoretical predictions but also more precise by a factor of about 300. Using this measured magic wavelength we also derive the differential static polarizability to be −44.32(32)-44.32(32)−44.32(32)~a.u., which will be an important input for the evaluation of the blackbody radiation shift at room temperatures. Our work paves a way for all-optical-trapping of 40^{40}40Ca+^{+}+ optical clock.
Abstract For the first time, we experimentally determine the infrared magic wavelength for the 40Ca+ 4 s 2 S 1 / 2 → 3 d 2 D 5 / 2 electric quadrupole transition by observation of the light shift canceling in 40Ca+ optical clock. A ‘magic’ magnetic field direction is chosen to make the magic wavelength insensitive to both the linear polarization purity and the polarization direction of the laser. The determined magic wavelength for this transition is 1056.37(9) nm, which is not only in good agreement with theoretical predictions (‘Dirac–Fock plus core polarization’ method) but also more precise by a factor of about 300. Using this measured magic wavelength, we also derive the differential static polarizability to be −44.32(32) a.u., which will be an important input for the evaluation of the blackbody radiation shift at room temperatures. Our work paves a way for all-optical-trapping of 40Ca+ optical clock.
We demonstrate experimentally the existence of magic wavelengths and determine the ratio of oscillator strengths for a single trapped ion. For the first time, two magic wavelengths near 396 nm for the ^{40}Ca^{+} clock transition are measured simultaneously with high precision. By tuning the applied laser to an intermediate wavelength between transitions 4s_{1/2}→4p_{1/2} and 4s_{1/2}→4p_{3/2}, the sensitivity of the clock transition Stark shift to the oscillator strengths is greatly enhanced. Furthermore, with the measured magic wavelengths, we determine the ratio of the oscillator strengths with a deviation of less than 0.5%. Our experimental method may be applied to measure magic wavelengths for other ion clock transitions. Promisingly, the measurement of these magic wavelengths paves the way to building all-optical trapped ion clocks.
The dynamic polarizabilities of the atomic states with angular momentum j>1/2j>1/2j>1/2 are sensitive to the angle between the quantization axis ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{e}}_{z}$ and the polarization vector $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\epsilon}}$ owing to the contribution of anisotropic tensor polarizabilities. The magic wavelength at which the differential Stark shift of an atomic transition nullifies depends on this angle. We identified the magic wavelengths for the $4{s}_{1/2}\ensuremath{\rightarrow}3{d}_{3/2,5/2}$ transitions of Ca+{\mathrm{Ca}}^{+}Ca+ ions at different angles between ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{e}}_{z}$ and $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\epsilon}}$ in the case of linearly polarized light. The magic wavelengths near 395.79 nm, which lie between the $4{s}_{1/2}\ensuremath{\rightarrow}4{p}_{1/2}$ and $4{s}_{1/2}\ensuremath{\rightarrow}4{p}_{3/2}$ transition wavelengths, remain insensitive to the angle, while the longest magic wavelength, which is around 1000 nm, for each of the magnetic sublevel transitions is very sensitive to the angle. We suggest that accurate measurements on the longest magic wavelengths for the $4{s}_{1/2}\ensuremath{\rightarrow}3{d}_{5/2}$ and $4{s}_{1/2}\ensuremath{\rightarrow}3{d}_{3/2}$ transitions can be used to determine the oscillator strengths for the $4{s}_{1/2}\ensuremath{\rightarrow}4{p}_{1/2,3/2}, 3{d}_{5/2}\ensuremath{\rightarrow}4{p}_{3/2}$, and $3{d}_{3/2}\ensuremath{\rightarrow}4{p}_{1/2,3/2}$ transitions, and the difference of the static polarizabilities of the 4s1/24{s}_{1/2}4s1/2​ and 3d5/23{d}_{5/2}3d5/2​ states, and the tensor polarizability of the 3d5/23{d}_{5/2}3d5/2​ state.
Abstract In present work, we have investigated the roles of dynamic quadrupole polarizabilities and the effect of electric field gradient in the accurate determination of magic wavelengths of the clock transitions for Ca + , Sr + and Ba + ions for linearly polarized light. We have employed relativistic all-order method for the evaluation of matrix elements for accurate determination of polarizability. The effect of gradient of electric field on magic wavelengths is analyzed with reference to small and large values of applied electric field-gradients in context to the experiments. Additional magic wavelengths have been revealed when the ratio of the electric field-gradient to electric field strength ( η = ‖ ( ∇ ε ∗ ⊗ ∇ ε ) ( k ) ‖ ‖ ( ε ∗ ⊗ ε ) ( k ) ‖ ) exceeds 0.1 a.u.. It is also observed that the characteristics of the trap can be switched with alteration in η . We have also estimated additional parameters such as trap depths, photon scattering rates and sensitivity to laser linewidths for these newly emerged magic wavelengths. Therefore, we believe that it is crucial to consider the spatial variation of any electric field while determining magic wavelengths for better understanding and implementation of laser trapping techniques.
The zero crossing of the dynamic differential scalar polarizability of the ${S}_{1/2}\ensuremath{-}{D}_{5/2}$ clock transition in 138Ba+^{138}\mathrm{Ba}^{+}138Ba+ has been determined to be 459.1614(28)THz459.1614(28)\phantom{\rule{0.28em}{0ex}}\mathrm{THz}459.1614(28)THz. Together with previously determined matrix elements and branching ratios, this tightly constrains the dynamic differential scalar polarizability of the clock transition over a large wavelength range ($\ensuremath{\gtrsim}700\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$). In particular, it allows an estimate of the blackbody radiation shift of the clock transition at room temperature.
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.