Frequency measurement of the ${{}^{2}S}_{1/2}\text{−}{{}^{2}F}_{7/2}$ electric octupole transition in a single ${{}^{171}\text{Y}\text{b}}^{+}$ ion

We report on precision laser spectroscopy of the ${{}^{2}S}_{1/2}\left(F=0\right)\text{−}{{}^{2}F}_{7/2}\left(F=3,m_F=0\right)$ clock transition in a single ion of ${{}^{171}\text{Y}\text{b}}^{+}$. A linewidth of $<40\text{Hz}$ 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 $642121496772657\pm 12\text{Hz}$ with a fractional uncertainty of $2\times {10}^{-14}$. This is a factor of 50 better than the previously published value [Hosaka et al., IEEE Trans. Instrum. Meas. 54, 759 (2005)].

Figure 1

Schematic energy-level diagram of ${{}^{171}\text{Y}\text{b}}^{+}$, showing the cooling transition at 369 nm and the ${{}^{2}S}_{1/2}\text{−}{{}^{2}F}_{7/2}$ optical clock transition at 467 nm. The metastable ${{}^{2}D}_{3/2}$ and ${{}^{2}F}_{7/2}$ states are depopulated by laser radiation at 935 and 638 nm, respectively. Microwaves at 12.6 GHz mix the hyperfine levels of the ground state.

Figure 2

(Color online) Experimental setup showing probe-laser system and beam delivery to the ion trap. The frequency of the light at 467 nm, $f_{467}=2\left(f_{\text{cavity}}+2f_{\text{offset}}\right)$, where $f_{\text{cavity}}$ is the cavity frequency and $f_{\text{offset}}$ is the frequency offset to the cavity. ACR, achromatic lens; AO, acousto-optic modulator; EO, electro-optic modulator; $\lambda /4$, quarter-wave plate; PBS, polarizing beam splitter; PD, avalanche photodiode; PMT, photomultiplier tube. The laser systems are represented by boxes showing their wavelength in nanometers.

Figure 3

Spectrum of the heterodyne beat between light locked to two independent cavities at 934 nm (a) after a 1 s acquisition and (b) on averaging for 100 s. The data were taken with a measurement bandwidth of 0.5 Hz.

Figure 4

(a) Plot showing the offset frequency corresponding to individual quantum jumps as a function of time for ten scans of the probe-laser frequency across the 467 nm transition. $f_0=122243000\text{Hz}$ in this figure. A linear fit to the data yields a slope of 33.7 mHz/s, corresponding to a cavity drift rate of 67.4 mHz/s. (b) The drift is removed and the data collated to give the atomic absorption spectrum of the clock transition at 467 nm. The measurement bandwidth is 20 Hz.

Figure 5

(Color online) (a) Frequency of the ULE cavity fringe measured by the optical frequency comb using a counter gate time of 10 s. $f_0=321060503100\text{kHz}$ in this figure. The solid line is a third-order polynomial fit to the data. The linear component of the cavity drift is 0.50 Hz/s. (b) Residuals of the fit. The standard deviation and standard error of the mean are 53 and 1.3 Hz, respectively. (c) Histogram of the residuals. The horizontal lines indicate the values expected for a normal distribution centered on 0 Hz with a width of 53 Hz.

Figure 6

(a) Frequency of the octupole transition as a function of probe-laser power. $f_0=642121496772000\text{Hz}$ in this figure. Each data point corresponds to an individual quantum jump. The solid line is a linear fit to all data points and has a slope of 492 Hz/mW. The data at (b) 0.31 and (c) 2.75 mW are collated and are shown as histograms.

Figure 7

(Color online) Frequency of the octupole transition as a function of probe-laser power for four different focusing conditions. $f_0=642121496772000\text{Hz}$ in this figure. Each data point is the mean of the quantum jump frequencies at a particular power and spot size [for example the data shown in Figs. 6b, 6c], and the standard error is shown. The solid lines are linear fits to the data for each focusing condition.

Figure 8

Comparison of frequencies unperturbed by the ac Stark shift and corrected for maser offsets. $f_0=642121496772600\text{Hz}$ in this figure. Each data point is the zero-power intercept of a fit to individual quantum jumps as shown for example in Fig. 6a. The error bars are those corresponding to the error on the intercept of the fit. Corrections for the deviation of the maser frequency from 10 MHz, as determined by comparison with UTC, are included.

Figure 9

Comparison of measurements of the ${{}^{2}S}_{1/2}\left(F=0\right)\text{−}{{}^{2}F}_{7/2}\left(F=3,m_F=0\right)$ transition frequency over a period of several years. $f_0=642121496770\text{kHz}$ in this figure. Each data point is the mean at the time of measurement and the standard error $\left(1\sigma \right)$ is shown. The solid line is the value for the mean of the measurements made in the period 2001–2003, and the dashed lines are the mean plus and minus one standard errors.