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Physical Review A

Evaluation of the systematic shifts of a single- 40 Ca + -ion frequency standard

Yao Huang, Qu Liu, Jian Zhong Cao, Bao-Quan Ou, Peiliang Liu, Hua Guan, Xue-Ren Huang, Kelin Gao

Published Nov 21, 2011• 34 citations
Publisher

Abstract

Progress on the evaluation of systematic frequency shifts is described in the development of the optical frequency standard based on single-trapped ${}^{40}$Ca${}^{+}$ with a ``clock'' transition at 729 nm. The overall systematic uncertainty of the 4$s$ ${}^{2}$$\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}$-3$d$ ${}^{2}$$\phantom{\rule{-0.16em}{0ex}}{D}_{5/2}$ clock resonance has been characterized to be 7.8 \ifmmode\times\else\texttimes\fi{} 10${}^{\ensuremath{-}16}$. This uncertainty is at a level similar to the Cs fountain primary standard, while the potential stability for the ${}^{40}$Ca${}^{+}$ clock exceeds that of Cs.

DOI
10.1103/physreva.84.053841

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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.

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Aug 29, 2007•8 citations
Progress on the evaluation of systematic frequency shifts is described in the development of the optical frequency standard based on single-trapped 40{}^{40}40Ca+{}^{+}+ with a ``clock'' transition at 729 nm. The overall systematic uncertainty of the 4sss {}^{2}$$\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}-3ddd {}^{2}$$\phantom{\rule{-0.16em}{0ex}}{D}_{5/2} clock resonance has been characterized to be 7.8 \ifmmode\times\else\texttimes\fi{} 10\ensuremath−16{}^{\ensuremath{-}16}\ensuremath−16. This uncertainty is at a level similar to the Cs fountain primary standard, while the potential stability for the 40{}^{40}40Ca+{}^{+}+ clock exceeds that of Cs.
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.
Abstract —We are proceeding with a development of an optical frequency standard using a 2 S 1/2 – 2 D 5/2 electric quadrupole transition of Ca + ions in a small radio-frequency trap. We have theoretically confirmed that an uncertainty of <1 x 10 -15 is attainable in measurement of the 2 S 1/2 – 2 D 5/2 transition frequency. Experimentally, we have developed stable laser-diode systems and observed the quantum jump of single 40 Ca + ions to the 2 D 5/2 state. I. I NTRODUCTION The uncertainty of primary frequency standards using Cs atoms reaches around 10 -15 and the inherent limits involved in them are discussed. On the other hand, frequency standards using new materials and methods are proposed for developing more accurate frequency standards. Recently, several groups have measured frequencies of the ionic forbidden transitions in the optical region to apply them to the clock transitions of optical frequency standards [1]. We now proceeds with study on an optical frequency standard using single Ca
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.
Optical frequency standards based on narrow absorptions in laser-cooled single trapped ions have recently begun to demonstrate stabilities that are competitive with cold atom fountain microwave standards. This paper presents a short review of the wider state-of-the-art development of these single cold trapped ion frequency standards, coupled with a more detailed account of recent results achieved at National Physical Laboratory in respect of single ion systems based on 88Sr+, 87Sr+ and 171Yb+. Narrow linewidth data for the optical clock quadrupole and octupole transitions respectively at 674 nm in 88Sr+ and 467 nm in 171Yb+, are presented, together with a discussion of current systematics and future projections. The potential for optical clock operation is outlined.
The present decade has seen great advances in optical frequency standards following the development of femtosecond laser frequency combs. With this technology, combined with a stable and narrow probe laser source (50-100 Hz linewidth), we made a systematic study of the 5s 2S1/2-4d 2D5/2 (S-D) transition frequency of the 88Sr+ ion as a function of the quantization axis in the trap. This study revealed the presence of systematic shifts caused by residual micromotion in our rf Paul trap and led to an evaluation of those shifts. Also, a method was developed based on the measurement of the Zeeman spectrum of the clock transition to cancel the electric quadrupole shift caused by patch potentials on the trap electrodes. From these results, we also determined the absolute frequency of the S-D clock transition frequency at 674 nm with a fractional frequency uncertainty of 3.4 × 10-14. We have since made improvements to our probe laser system and have observed 5 Hz Fourier transform limited linewidths on a Zeeman component of the S-D transition of the 88Sr+ ion. To observe such a narrow transition it is essential to have a known and well behaved drift of the laser frequency during the few minutes it takes to measure the ion resonance using the quantum jump signal. Our approach to minimize the drift rate and its sensitivity to temperature fluctuations has been to stabilize the cavity at the temperature where its coefficient of thermal expansion is zero. We will present an overview of our recent progress made on the frequency standard based on the laser-cooled and trapped single ion of 88Sr+.