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arXiv:1111.5174 · Physical Review A

Hertz-level measurement of the 40 Ca + 4s 2S1/2 – 3d 2D5/2 clock transition frequency with respect to the SI second through the Global Positioning System

Yao Huang, Jian Zhong Cao, P. Liu, Kun Liang, Bao-Quan Ou, H. Guan, Xiaoyang Huang, Tao Li, K. Gao

Published Mar 23, 2012• 61 citations
arXivHTMLPDF

Abstract

We have measured the absolute frequency of a clock transition at the 10${}^{\ensuremath{-}15}$ level with a single, trapped, laser-cooled ${}^{40}$Ca${}^{+}$ ion in a miniature Paul trap. In our measurement, an optical frequency comb is referenced to a hydrogen maser, which is calibrated to the SI second through the Global Positioning System (GPS). By analyzing the experimental data obtained within 32 days of a total averaging time $>$2 $\ifmmode\times\else\texttimes\fi{}$ 10${}^{6}$ s, the absolute frequency of the ${}^{40}$Ca${}^{+}$ 4$s$ ${}^{2}\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}$--3$d$ ${}^{2}\phantom{\rule{-0.16em}{0ex}}{D}_{5/2}$ clock transition is measured as 411 042 129 776 393.0 (1.6) Hz with a fractional uncertainty of 3.9 $\ifmmode\times\else\texttimes\fi{}$ 10${}^{\ensuremath{-}15}$.

DOI
10.1103/physreva.85.030503

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Science•Nov 18, 2004•302 citations
We have measured the absolute frequency of a clock transition at the 10\ensuremath−15{}^{\ensuremath{-}15}\ensuremath−15 level with a single, trapped, laser-cooled 40{}^{40}40Ca+{}^{+}+ ion in a miniature Paul trap. In our measurement, an optical frequency comb is referenced to a hydrogen maser, which is calibrated to the SI second through the Global Positioning System (GPS). By analyzing the experimental data obtained within 32 days of a total averaging time >>>2 \ifmmode×\else\texttimes\fi\ifmmode\times\else\texttimes\fi{}\ifmmode×\else\texttimes\fi 106{}^{6}6 s, the absolute frequency of the 40{}^{40}40Ca+{}^{+}+ 4sss 2S1/2{}^{2}\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}2S1/2​--3ddd 2D5/2{}^{2}\phantom{\rule{-0.16em}{0ex}}{D}_{5/2}2D5/2​ clock transition is measured as 411 042 129 776 393.0 (1.6) Hz with a fractional uncertainty of 3.9 \ifmmode×\else\texttimes\fi\ifmmode\times\else\texttimes\fi{}\ifmmode×\else\texttimes\fi 10\ensuremath−15{}^{\ensuremath{-}15}\ensuremath−15.
Research on the development of the optical frequency standard based on trapped and cold 40 Ca + with the 4s 2 S 1/2 -3d 2 D 5/2 clock transition at 729 nm is reported. A single calcium ion was trapped and laser cooled in the Paul trap and stay in trap for more than 15 days. The linewidth of a 729 nm laser was reduced to less than 10 Hz by locking to a cavity for longer than 50 hours uninterruptedly. The overall systematic uncertainty of the clock transition has been characterized to be better than 6.5×10 −16 . The absolute frequency of the clock transition was measured at 10 −15 level using an optical frequency comb referenced to a Hydrogen maser, which was calibrated to the SI second through the global positioning system (GPS). The frequency value was 411042129776393.0(1.6) Hz after the correction of the systematic shifts.
Absolute frequency measurement of the 40^{40}40Ca+^{+}+ clock transition using a GNSS link to the SI second
We report the absolute frequency measurement of the 4s4s4s $ ^{2}S_{1/2}\leftrightarrow 3d$ 2D5/2^{2}D_{5/2}2D5/2​ 40^{40}40Ca+^{+}+ clock transition with respect to the SI second. To perform this measurement, a link between our laboratory in Innsbruck and the clocks realizing the Coordinated Universal Time at the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig was installed and characterized using the Global Navigation Satellite System GNSS. The comparison between our clock and the ones at PTB was done using the Precise Point Positioning technique. After the evaluation of the systematic shifts, the measured transition frequency is 411 042 129 776 401.2$\pm$0.6 Hz with a fractional uncertainty of 1.5 ×\times× 10−15^{-15}−15. The stability of the clock measurements was also corroborated by comparing two different calcium ion clock experiments, which share the clock laser source at our institute. Furthermore, after careful evaluation of the trap-drive induced ac magnetic fields, we estimate ac Zeeman shifts on the D5/2D_{5/2}D5/2​ sublevels and reevaluate the Landé g-factor of the 3d3d3d 2D5/2^{2}D_{5/2}2D5/2​ level to be g5/2=1.200329(1)_{5/2}= 1.200329(1)5/2​=1.200329(1).
With the development of the technologies in the lasers and the manipulation of cold atoms, the high precision optical frequency standards have been extensively studied and built in recent years. These high precision frequency standards may play an important role in establishing the new time reference, promoting the researches in the fundamental fields, fulfilling the national strategic needs, etc. In this paper, the research progress of high accuracy 40Ca+ optical frequency standard in Wuhan Institute of Physics and Mathematics (WIPM) of Chinese Academy of Sciences is presented. A new ULE super cavity is adopted for stabilizing the frequency of 729 nm clock laser, and the stability of the laser is improved now to 2×10-15 in a duration of 1-100 s. By controlling the external fields and other environmental influences, especially suppressing the micromotion effects of the trapped ion, the uncertainty of the optical frequency standard based on a single 40Ca+ is reduced to 5.5×10-17. The stability of 5×10-17 in a duration of 20000 s is achieved via the comparison between two 40Ca+ optical frequency standards. Several precision measurement experiments are performed, based on the high precision 40Ca+ optical frequency standard. The absolute value of the clock transition frequency of the 40Ca+ optical frequency standard is measured second time, using an optical comb referenced to a hydrogen maser which is calibrated via GPS referenced to UTC (NIM)) using the precise point positioning data-processing technique. The frequency offset of UTC (NIM) relative to the SI second can be evaluated through BIPM circular-T reports, and the newly measured value of m 4s 2S1/2-3m d 2D5/2 transition is adopted by CCTF-20, thus updating the recommended value of 40Ca+ optical clock transition. Besides the absolute frequency measurement, the magic wavelengths of 40Ca+ optical clock transition are measured precisely, and this work is a milestone for establishing all-optical trapped-ion clocks. The lifetime of the m 3 d 2D3/2 and m 3 d 2D5/2 state in 40Ca+ are precisely measured, too. The work mentioned above contributes to the researches of the precision measurements based on cold atomic systems.
The frequency of the 5s 2S(1/2)-4d 2D(5/2) electric quadrupole clock transition in a single, trapped, laser-cooled 88Sr+ ion has been measured by using an optical frequency comb referenced to a cesium fountain primary frequency standard. The frequency of the transition is measured as 444,779,044,095,484.6 (1.5) hertz, with a fractional uncertainty within a factor of 3 of that of the cesium standard. Improvements required to obtain a cesium-limited frequency measurement are described and are expected to lead to a 88Sr+ optical clock with stability and reproducibility exceeding that of the primary cesium standard.