Fig. 1. Schematic of the experimental setup. The four spatially separated traveling waves are generated using two cat’s eye reflectors. The ion speed is determined using a retarding field energy analyzer (RFEA). The laser frequency is measured with an optical frequency comb (OFC) referenced to an H-maser.

Fig. 2. (Left) Distribution of data for the absolute frequency of the 23S1(F=5/2)−23P2(F=7/2) transition on a single day. (Right) Histogram illustrating the data distribution, with the blue line representing the Gaussian fit.

Fig. 3. Plot illustrating the ion energy distribution measured via RFEA. Black dots represent variations in ion beam current, measured by the MCP, in response to changes in the retarding field potential voltage. The red dots and line depict the first-order derivative of the black points and its corresponding Gaussian fit curve.

Fig. 4. Measured frequency for the transition from 23S1(F=5/2) to 23P2(F=7/2) in Li7+ on different dates. Each data point represents an average value derived from several hundred measurements conducted within a single day, and the error bars shown encompass both statistical and systematic uncertainties. The gray shading denotes the uncertainty range associated with the final result.

Fig. 5. Ramsey interference fringe spectra obtained according to the scheme shown in Fig. 1.

Fig. 6. Experimental setup for alignment of a cat’s eye retroreflector using interferometry.

Fig. 7. Average frequency of the spectrum, resulting from counter-propagating probe lasers, varies with the frequency difference between them. This average frequency, plotted on the vertical axis, directly corresponds to the absolute frequency. The red line in the graph represents a linear relationship between these variables, with a slope of approximately 34 kHz per MHz.

Fig. 8. Variation of spectroscopy frequency with probe laser power. Only statistical uncertainty is included.

Fig. 9. Dependence of the measured frequency on the probe polarization. Only statistical uncertainty is included.

Fig. 10. Dependence of the measured frequency on the laser linear polarization angle. Only statistical uncertainty is included.

Table 1. Uncertainty Budget for the Determination of the Transition Frequency from 23S1(F=5/2) to 23P2(F=7/2) in ⁷Li⁺ (in kHz)

Table 2. α^ Parameter from Different Sources