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Applied Physics Express

Frequency Measurement of the Optical Clock Transition of40Ca+Ions with an Uncertainty of 10-14Level

Kensuke Matsubara, Kazuhiro Hayasaka, Ying Li, Hiroyuki Ito, Shigeo Nagano, Masatoshi Kajita, Mizuhiko Hosokawa

Published Jun 6, 2008• 65 citations
Publisher

Abstract

The absolute frequency of the 4 2 S 1/2 –3 2 D 5/2 optical clock transition of 40 Ca + ions has been measured for the first time with respect to the Système International (SI) second. A single 40 Ca + ion is laser-cooled in a small ion trap and the transition frequency is measured as the average of two symmetrical Zeeman components. The frequency is determined to be 411 042 129 776 385 (±18) Hz from 48 measurements.

DOI
10.1143/apex.1.067011

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Physical Review Letters•Dec 22, 2025•13 citations
The absolute frequency of the 4 2 S 1/2 –3 2 D 5/2 optical clock transition of 40 Ca + ions has been measured for the first time with respect to the Système International (SI) second. A single 40 Ca + ion is laser-cooled in a small ion trap and the transition frequency is measured as the average of two symmetrical Zeeman components. The frequency is determined to be 411 042 129 776 385 (±18) Hz from 48 measurements.
We have measured the absolute frequency of a clock transition at the 10${}^{\ensuremath{-}15}$ 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 $\ifmmode\times\else\texttimes\fi{}$ 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 $\ifmmode\times\else\texttimes\fi{}$ 10${}^{\ensuremath{-}15}$.
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).
We developed an optical frequency standard using40Ca+with the 42S1/2-32D5/2electric quadrupole transition. Its absolute transition frequency is 411 042 129 776 390(7) Hz. The uncertainty is limited by the electric quadrupole shift and ambient magnetic field fluctuation. To determine the absolute transition frequency with a better uncertainty, we have observed two pairs of the symmetrically-splitting Zeeman components and measured the transition frequency which is corrected for the electric quadrupole shift. It will be used to determine the absolute transition frequency with respect to the SI base units of time and length. In addition, we are developing a magnetic-shielded ion-trap chamber to reduce the transition-line broadening caused by the magnetic field fluctuation.
We developed an optical frequency standard with the 4 2S1/2-3 2D5/2 electric quadrupole transition of 40Ca+ ions. Its absolute transition frequency is 411 042 129 776 390(±7) Hz. The accuracy is limited by the electric quadrupole shift and the ambient magnetic field fluctuation. To determine the absolute transition frequency with a better accuracy, we have observed two pairs of the symmetrically-splitting Zeeman components and measured the transition frequency corrected for the electric quadrupole shift. In addition, we are developing a magnetic-shielded ion-trap chamber to suppress the transition-line broadening caused by the magnetic field fluctuation.
We report a single-ion optical clock based on the 4S_{1/2}→3D_{5/2} transition of the ^{40}Ca^{+} ion, operated in a liquid nitrogen cryogenic environment, achieving a total systematic uncertainty of 4.4×10^{-19}. We employ a refined temperature evaluation scheme to reduce the frequency uncertainty due to blackbody radiation, and 3D sideband cooling to minimize the second-order Doppler shift. We have precisely determined the average Zeeman coefficient of the ^{40}Ca^{+} clock transition to be 14.345(15) Hz/mT^{2}, thereby significantly reducing the quadratic Zeeman shift uncertainty. Moreover, the cryogenic environment enables the lowest reported heating rate due to ambient electric field noise in trapped-ion optical clocks.