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arXiv:1409.2576 · Physical Review Letters

Measurement of Magic Wavelengths for the Ca+40 Clock Transition

Peiliang Liu, Yao Huang, Bian Wu, H. Shao, Hua Guan, Yong-Bo Tang, Chengbin Li, Jim Mitroy, Kelin Gao

Published Jun 2, 2015• 48 citations
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Abstract

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.

DOI
10.1103/physrevlett.114.223001

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The progress of the precision spectroscopy with single trapped and laser cooled 40Ca+ ion

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The experimental study at Wuhan Institute of Physics and Mathematics (WIPM), Chinese Academy of Scienses (CAS) on the precision spetroscopy based on single trapped Ca+ ion is described in this paper. A single Ca+ ion is trapped in a miniature Paul trap and laser cooled to Lamb-Dicke regime, and the ion can be trapped more than 2 months. The linewidth of the 729 nm laser for probing the Ca+ 4s2S1/2-3d2D5/2 clock transition is reduced to lessthan 1 Hz by locked to a super cavity, and the 729 nm laser can be locked more than 1 month continuously. Two similar Ca + ion optical frequency standards are set up for frequency comparison. The systematic uncertainty is evaluated to be <6 ´ 10−17 for both ftrquency standards. The frequency difference of two frequency standards is measured to be 3.0 (5.5) ´ 10−17 within 42 d. The Allan deviation for a single clock is measured to be 1×10−14τ−1/2 with a 3-d-continuous comparison, the stability for a reaches 7 ´ 10−17 at an averaging time of 20000 s. Meanwhile, the absolute frequency of the Ca+ 4s2S1/2-3d2D5/2 clock transition is measured to be 411042129776401.7(1.1) Hz with respect to the SI second through the Global Positioning System (GPSx). The precision spectroscopy experiments are carried out based on the single Ca+ ion system. The magic wavelengths for the Ca+ optical frequency standardare measured to be λ|mj|=1/2=395.7992(7) nm and λ|mj|=3/2=395.7990(7) nm, which agrees with theoretical calculation made by Tang et al. The lifetime of the 3d2D5/2 is measured to be 1174(10) ms, which is agree with the experimental measurement made by University of Oxford and University of Innsbruck and the recent theoretical calculation made by Sahoo.

Zhongguo kexue. Wulixue Lixue Tianwenxue•Jun 17, 2016•0 citations
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.
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 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.
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.
The experimental study at Wuhan Institute of Physics and Mathematics (WIPM), Chinese Academy of Scienses (CAS) on the precision spetroscopy based on single trapped Ca+ ion is described in this paper. A single Ca+ ion is trapped in a miniature Paul trap and laser cooled to Lamb-Dicke regime, and the ion can be trapped more than 2 months. The linewidth of the 729 nm laser for probing the Ca+ 4s2S1/2-3d2D5/2 clock transition is reduced to lessthan 1 Hz by locked to a super cavity, and the 729 nm laser can be locked more than 1 month continuously. Two similar Ca + ion optical frequency standards are set up for frequency comparison. The systematic uncertainty is evaluated to be <6 ´ 10−17 for both ftrquency standards. The frequency difference of two frequency standards is measured to be 3.0 (5.5) ´ 10−17 within 42 d. The Allan deviation for a single clock is measured to be 1×10−14τ−1/2 with a 3-d-continuous comparison, the stability for a reaches 7 ´ 10−17 at an averaging time of 20000 s. Meanwhile, the absolute frequency of the Ca+ 4s2S1/2-3d2D5/2 clock transition is measured to be 411042129776401.7(1.1) Hz with respect to the SI second through the Global Positioning System (GPSx). The precision spectroscopy experiments are carried out based on the single Ca+ ion system. The magic wavelengths for the Ca+ optical frequency standardare measured to be λ|mj|=1/2=395.7992(7) nm and λ|mj|=3/2=395.7990(7) nm, which agrees with theoretical calculation made by Tang et al. The lifetime of the 3d2D5/2 is measured to be 1174(10) ms, which is agree with the experimental measurement made by University of Oxford and University of Innsbruck and the recent theoretical calculation made by Sahoo.