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Journal of Physics B Atomic Molecular and Optical Physics

Optimum measurement strategies for trapped ion optical frequency standards

Erling Riis, Alastair G. Sinclair

Published Dec 7, 2004• 28 citations
Publisher

Abstract

The experimental parameters required in order to maximize the stability of a single-ion based optical clock are analysed. This stability is a trade-off between on the one hand the steepness of the discriminant signal derived from the laser excitation of the ion and on the other the binomial noise associated with the excitation of a single particle. Optimum conditions are found for both Rabi and Ramsey excitation of the clock transition.

DOI
10.1088/0953-4075/37/24/001

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The experimental parameters required in order to maximize the stability of a single-ion based optical clock are analysed. This stability is a trade-off between on the one hand the steepness of the discriminant signal derived from the laser excitation of the ion and on the other the binomial noise associated with the excitation of a single particle. Optimum conditions are found for both Rabi and Ramsey excitation of the clock transition.
A fundamental limit to the stability of a single-ion optical frequency standard is set by quantum noise in the measurement of the internal state of the ion. We discuss how the interrogation sequence and the processing of the atomic resonance signal can be optimized in order to obtain the highest possible stability under realistic experimental conditions. A servo algorithm is presented that stabilizes a laser frequency to the single-ion signal and that eliminates errors due to laser frequency drift. Numerical simulations of the servo characteristics are compared to experimental data from a frequency comparison of two single-ion standards based on a transition at 688 THz in 171 Yb + . Experimentally, an instability σ y (100 s) = 9 × 10 −16 is obtained in the frequency difference between both standards.
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).
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.
Summary form only given. A single laser-cooled indium ion, stored in a radio-frequency trap, is expected to be one of the most promising candidates for the creation of a new generation of optical frequency standards with an anticipated accuracy of up to 10/sup -18/. On the way to achieving such a high level of accuracy, one of the main limitations is the short-term frequency instability of the laser system, used to excite the narrow /sup 1/S/sub 0/-/sup 3/P/sub 0/ In/sup +/ clock transition. Since the signal from the single ion is small, the laser system should posses extremely high frequency stability (on the level of /spl Delta/v/v=10/sup -14//spl divide/10/sup -15/) for averaging times of about one second in order to reduce statistical uncertainties and to minimize the time of experiment. In this paper, we report our recent results on the improvement of the short-term frequency stability of the laser system.
A single laser cooled ion in a radiofrequency trap can serve as the basis for a highly stable optical frequency standard. We present recent results of our work on single indium ions, using the /sup 1/S/sub 0/ to /sup 3/P/sub 0/ transition at 236.5 nm wave-length as the clock transition. This resonance has a linewidth of only 0.82 Hz where systematic shifts should be controllable on the mHz level. A single In/sup +/ ion is stored in a miniature Paul-Straubel trap and laser cooled to a temperature of about 100 /spl mu/K. The clock transition is excited using a frequency quadrupled Nd:YAG laser. A fractional resolution of 1.3/spl middot/10/sup -13/ has been achieved so far (linewidth of 170 Hz at 1267 THz). The absolute frequency of the clock transition clock transition has been measured with an uncertainty of 2/spl middot/10/sup -13/ using a frequency chain and a methane-stabilized HeNe laser as a reference, that was calibrated with a cesium clock.
For the past 15 years, tremendous progress within the fields of laser stabilization, optical frequency combs and atom cooling and trapping have allowed the realization of optical atomic clocks with unrivaled performances. These instruments can perform frequency comparisons with fractional uncertainties well below 10-17, finding applications in fundamental physics tests, relativistic geodesy and time and frequency metrology. Even though most optical clocks are currently laboratory setups, several proposals for using these clocks for field measurements or within an optical clock network have been published, and most of time and frequency metrology institutes have started to develop transportable optical clocks. For the purpose of this special issue, we chose to focus on trapped-ion optical clocks. Even though their short-term fractional frequency stability is impaired by a lower signal-to-noise ratio, they offer a high potential for compactness: trapped ions demand low optical powers and simple loading schemes, and can be trapped in small vacuum chambers. We review recent advances on the clock key components, including ion trap and ultra-stable optical cavity, as well as existing projects and experiments which draw the picture of what future transportable, single-ion optical clocks may resemble.