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arXiv:1111.2446 · Physical Review Letters

High-Accuracy Optical Clock Based on the Octupole Transition in Yb+171

Nils Huntemann, Maksim V. Okhapkin, B. Lipphardt, S. Weyers, Chr. Tamm, E. Peik

Published Feb 29, 2012• 241 citations
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Abstract

We experimentally investigate an optical frequency standard based on the 467 nm (642 THz) electric-octupole reference transition (2)S(1/2)(F=0)→(2)F(7/2)(F=3) in a single trapped (171)Yb(+) ion. The extraordinary features of this transition result from the long natural lifetime and from the 4f(13)6s(2) configuration of the upper state. The electric-quadrupole moment of the (2)F(7/2) state is measured as -0.041(5)ea(0)(2), where e is the elementary charge and a(0) the Bohr radius. We also obtain information on the differential scalar and tensorial components of the static polarizability and of the probe-light-induced ac Stark shift of the octupole transition. With a real-time extrapolation scheme that eliminates this shift, the unperturbed transition frequency is realized with a fractional uncertainty of 7.1×10(-17). The frequency is measured as 642 121 496 772 645.15(52) Hz.

DOI
10.1103/physrevlett.108.090801

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We describe experimental investigations of an optical frequency standard based on a single laser-cooled /sup 171/Yb/sup +/ ion confined in a radiofrequency Paul trap. The electric quadrupole transition from the /sup 2/S/sub 1/2 /(F=0) ground state to the /sup 2/D/sub 3/2/(F=2) state at 435.5 nm is used as the reference transition. The transition was resolved with a Fourier-limited width of approximately 30 Hz. In order to investigate the instability and accuracy of a future frequency standard based on the reference transition, a first experiment was done comparing two laser frequencies stabilized individually to two separate ions in different traps. As a result we found a relative frequency instability /spl sigma//sub y/(640 s)=1.5/spl middot/10/sup -15/ for the difference of the two laser frequencies. We also derived a first estimate /spl Theta/(/sup 2/D/sub 3/2/)=(3.9/spl plusmn/1.9)ea/sub 0//sup 2/ for the electric quadrupole moment of the /sup 2/D/sub 3/2/ state.

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We experimentally investigate an optical frequency standard based on the 467 nm (642 THz) electric-octupole reference transition (2)S(1/2)(F=0)→(2)F(7/2)(F=3) in a single trapped (171)Yb(+) ion. The extraordinary features of this transition result from the long natural lifetime and from the 4f(13)6s(2) configuration of the upper state. The electric-quadrupole moment of the (2)F(7/2) state is measured as -0.041(5)ea(0)(2), where e is the elementary charge and a(0) the Bohr radius. We also obtain information on the differential scalar and tensorial components of the static polarizability and of the probe-light-induced ac Stark shift of the octupole transition. With a real-time extrapolation scheme that eliminates this shift, the unperturbed transition frequency is realized with a fractional uncertainty of 7.1×10(-17). The frequency is measured as 642 121 496 772 645.15(52) Hz.
We experimentally investigate an optical frequency standard based on the (2)S1/2(F=0)→(2)F7/2(F=3) electric octupole (E3) transition of a single trapped (171)Yb+ ion. For the spectroscopy of this strongly forbidden transition, we utilize a Ramsey-type excitation scheme that provides immunity to probe-induced frequency shifts. The cancellation of these shifts is controlled by interleaved single-pulse Rabi spectroscopy, which reduces the related relative frequency uncertainty to 1.1×10(-18). To determine the frequency shift due to thermal radiation emitted by the ion's environment, we measure the static scalar differential polarizability of the E3 transition as 0.888(16)×10(-40) J m(2)/V(2) and a dynamic correction η(300 K)=-0.0015(7). This reduces the uncertainty due to thermal radiation to 1.8×10(-18). The residual motion of the ion yields the largest contribution (2.1×10(-18)) to the total systematic relative uncertainty of the clock of 3.2×10(-18).
We report experimental investigations of a single-ion optical frequency standard based on 171Yb+{^{171}\text{Y}\text{b}}^{+}171Yb+. The ion is confined in a cylindrically symmetric radiofrequency Paul trap. The reference transition is the ${^{2}S}_{1/2}(F=0)--{^{2}D}_{3/2}({F}^{\ensuremath{'}}=2)$ electric quadrupole transition at 688 THz. Using a differential measurement scheme, we determine the shift of the reference transition frequency that occurs due to the interaction of the electric quadrupole moment of the 2D3/2{^{2}D}_{3/2}2D3/2​ state with the gradient of the electrostatic stray field in the trap. We determine an upper limit for the instability of the quadrupole shift over times between 100 s to 20 h. We also observe the variations in the shift and in the applied stray-field compensation voltages that result from loading a new ion into the trap and during a subsequent storage period of 74 days. This information is utilized to measure the absolute frequency of the reference transition with an uncertainty that is a factor of 3 smaller than that of the previous measurement. Using a fiber laser based optical frequency comb generator and the cesium fountain clock CSF1 of PTB (Physikalisch-Technische Bundesanstalt), the frequency at 300 K temperature is determined as $688\text{ }358\text{ }979\text{ }309\text{ }306.62\ifmmode\pm\else\textpm\fi{}0.73\text{ }\text{Hz}$.
Forbidden transitions in single trapped ion systems are being considered as references for future optical frequency standards. These standards are expected to have application as highly stable and reproducible optical clocks, realizations of the metre and as optical frequency standards in their own right. This paper prescribes the work carried out at the National Physical Laboratory over recent years to use a highly forbidden 2S1/2 - 2F7/2 467 nm electric octupole transition in a single ion of 171Yb+ as a frequency reference. A review of the previous measurements needed to the locate octupole transition in this 171-isotope is given and a more detailed discussion of recent work is presented. This includes spectroscopy of the octupole transition with kilohertz resolution and a direct measurement of its optical frequency. Measurements of the dynamic Stark and the quadratic Zeeman shifts on the octupole frequency are also discussed.
The171Yb+ion possesses two transitions that are applicable as references for optical frequency standards and several general features make this ion attractive: All relevant radiations for cooling and excitation can be generated from diode lasers. A nuclear spin of 1/2 ensures a simple sublevel structure. Long storage times of Yb+in ion traps are easily obtained. The2S1/2(F = 0) →2D3/2(F = 2, mF= 0) electric quadrupole transition at 436 nm with a natural linewidth of 3.1 Hz provides a quantum noise limited instability of a single-ion frequency standard of about 2 × 10-15in 1 s. The electric octupole transition2S1/2(F = 0)→2F7/2(F = 3, mF= 0) at 467 nm with a natural linewidth in the nHz range will allow to surpass that instability level. It also possesses a lower sensitivity to field-induced frequency shifts. In this system the Fourier-limited interrogation linewidth can be adapted to that of the best available laser sources, which are presently at the level below 1 Hz. Both transitions have been recommended as secondary representations of the SI second.
The 2S1/2(F=0)2F7/2(F=3,mF=0){}^{2}{S}_{1/2}{(F=0)}^{2}{F}_{7/2}{(F=3,m}_{F}=0)2S1/2​(F=0)2F7/2​(F=3,mF​=0) transition at 467 nm in a single trapped, laser-cooled ion of 171Yb+{}^{171}{\mathrm{Yb}}^{+}171Yb+ has been measured to be fYb+=642121496771.26(23)kHz{f}_{{\mathrm{Yb}}^{+}}=642121496771.26(23)\mathrm{kHz}fYb+​=642121496771.26(23)kHz using a femtosecond laser frequency comb generator. The measurement is limited by measurement statistics and by the ac Stark shift, both related to the 4.5 kHz linewidth of the probe laser at the time. The systematic shifts of the transition, including ac Stark, second-order Zeeman, quadrupole, and blackbody shifts, have been evaluated.
We describe experimental investigations of an optical frequency standard based on a single laser-cooled /sup 171/Yb/sup +/ ion confined in a radiofrequency Paul trap. The electric quadrupole transition from the /sup 2/S/sub 1/2 /(F=0) ground state to the /sup 2/D/sub 3/2/(F=2) state at 435.5 nm is used as the reference transition. The transition was resolved with a Fourier-limited width of approximately 30 Hz. In order to investigate the instability and accuracy of a future frequency standard based on the reference transition, a first experiment was done comparing two laser frequencies stabilized individually to two separate ions in different traps. As a result we found a relative frequency instability /spl sigma//sub y/(640 s)=1.5/spl middot/10/sup -15/ for the difference of the two laser frequencies. We also derived a first estimate /spl Theta/(/sup 2/D/sub 3/2/)=(3.9/spl plusmn/1.9)ea/sub 0//sup 2/ for the electric quadrupole moment of the /sup 2/D/sub 3/2/ state.