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.
Abstract Multi-ion optical clocks offer the possibility of overcoming the low signal-to-noise ratio of single-ion clocks, while still providing low systematic uncertainties. We present simultaneous spectroscopy of up to four 115 In + clock ions in a linear Coulomb crystal, sympathetically cooled with 172 Yb + ions. In first clock comparisons, we see agreement below 1 × 10 −17 with results obtained using a single In + ion, for which we have evaluated the systematic uncertainty to be 2.5 × 10 −18 . Operation with four clock ions reduces the instability from 1.6 × 10 − 15 / t / ( 1 s ) to 9.2 × 10 − 16 / t / ( 1 s ) . We derive a model for decay-related dead time during state preparation, which matches the observed scaling of instability with clock ion number N , and indicates that 1 / N scaling can be achieved with the addition of a repump laser.
We report on precision laser spectroscopy of the ${^{2}S}_{1/2}(F=0)\text{\ensuremath{-}}{^{2}F}_{7/2}(F=3,{m}_{F}=0)$ clock transition in a single ion of
171Yb+. A linewidth of
<40 Hz is observed and frequency instability due to fluctuation of the ac Stark shift is reduced through improved stability of the beam alignment. The absolute value of the transition frequency, determined using an optical frequency comb, is $642\text{ }121\text{ }496\text{ }772\text{ }657\ifmmode\pm\else\textpm\fi{}12\text{ }\text{Hz}$ with a fractional uncertainty of $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$. This is a factor of 50 better than the previously published value [Hosaka et al., IEEE Trans. Instrum. Meas. 54, 759 (2005)].
Compared to other stable isotopes of
Yb+,
173Yb+ has a richer hyperfine structure, which leads to more favorable clock transitions, spectroscopic techniques for probing new physics, and more sophisticated quantum computing architectures. However, to date, its electronic spectrum remains poorly characterized. Here, we report on efficient laser cooling, state preparation, and detection of a single trapped
173Yb+ ion. The previously unobserved
2S1/2→2D3/2 electric quadrupole transition at 436 nm is coherently excited, and the isotope shift between
171Yb+ and
173Yb+ on this transition is determined with an uncertainty of 1.4 Hz. Using microwave spectroscopy, we resolve the hyperfine structure (HFS) of the
2D3/2 state with a relative uncertainty below
10−8. From the HFS measurement data, we infer for
173Yb a nuclear magnetic octupole moment
Ω=−0.062(8)(b×μN) with uncertainty reduced by more than 2 orders of magnitude compared to previous studies. The data also allow us to determine hyperfine anomalies for the
2S1/2 and
2D3/2 states.
Trapped-ion optical clocks are capable of achieving systematic fractional frequency uncertainties of
10−18 and possibly below. However, the stability of current ion clocks is fundamentally limited by the weak signal of single-ion interrogation. We present an operational, versatile platform for extending clock spectroscopy to arrays of Coulomb crystals consisting of several tens of ions, while allowing systematic shifts as low as
10−19. The concept is applicable to all clock transitions with low differential electric quadrupole moments. We observe 3D excess micromotion amplitudes of all individual ions inside a Coulomb crystal with nm resolution and prove that the related frequency shifts can be controlled simultaneously at the
10−19 level. Using this method, we demonstrate regions of
400 μm and
2 mm length in our trap array with time dilation shifts due to micromotion close to
1×10−19 and below
10−18, respectively. Further measurements of the trapping environment and cooling dynamics calculations for mixed In
+ / Yb
+ crystals show that achievable clock uncertainties due to multi-ion operation in our setup are below
1×10−19. This work will enable clock operation with multiple ions and open up the possibility of new interrogation schemes which allow optical clock stabilities beyond classical limits.
We discuss prospects of precision measurement of the Yb2+ 4f14 1S0–4f13 5d
3P0o transition frequency (1.4 × 1015 Hz). Attainable uncertainty of this precision measurement is theoretically estimated. This transition is free from the electric quadrupole shift, and this specific property allows for precision spectroscopy using a multi-ion string Coulomb crystal and contributes to reduction of the statistical uncertainty. A systematic uncertainty of the order 10−18 is attainable because the Stark and Zeeman shifts are small due to the intrinsic level structure of multiply charged ions. This clock transition can be monitored without quantum logical methods by observing the laser-induced fluorescence from the 1S0–
3P1o transition with a closed optical cycle.