Comment on “Laser cooling of ${}^{173}\mathrm{Yb}$ for isotope separation and precision hyperfine spectroscopy”

We present measurements of the hyperfine splitting in the ${}^{173}\mathrm{Yb} 6s6p{}^{1}P_{{}_1^{\mathrm{o}}}(F^{\prime }=3/2,7/2)$ states that disagree significantly with those measured previously by Das and Natarajan [Phys. Rev. A 76, 062505 (2007)]. We point out inconsistencies in their measurements and suggest that their error is due to optical pumping and improper determination of the atomic line center. Our measurements are made using an optical frequency comb. We use an optical pumping scheme to improve the signal-to-background ratio for the $F^{\prime }=3/2$ component.

Figure 1

Fluorescence measurements from (a) an isotopically pure, slow ${}^{173}\mathrm{Yb}$ atomic beam and (b) a fast thermal beam. Without the repumper laser tuned to the $F^{\prime }=5/2$ transition (black circles), fluorescence from the $F^{\prime }=3/2$ level is completely absent. The repumper laser makes fluorescence from the $F^{\prime }=3/2$ level easily visible. The solid lines in this plot are fits to line-shape models including one, two, or three Lorentzian peaks, as appropriate.

Figure 2

Simulated data for the ${}^{172}\mathrm{Yb}/{}^{173}\mathrm{Yb}$ complex at 399 nm showing the critical error made in the analysis of Ref. [11]. (a) The computer generates a noisy line shape consisting of two partially resolved Lorentzians with center frequencies at 531 and 589 MHz. The dots are the simulated data; the solid line is a three-Lorentzian fit. The middle panel shows the residuals to the fit. In the model, the peak at 531 MHz is somewhat broader than the peak at 589 MHz. When the center frequencies for peaks “b” and “c” are fixed, a pseudopeak “a” appears in the fit. (b) The frequency difference between peak “c” and the pseudopeak “a” as a function of the “fixed” frequency for peak “b.” Typical $1\sigma$ statistical uncertainties in determining the center frequency in repeated simulations are in the 0.3 MHz range. Dividing this by the square root of, say, 25 measurements reduces the statistical uncertainty in determining the line center to 0.06 MHz.

Figure 3

Measurements of the apparent transition frequency for the $F^{\prime }=7/2$ peak as a function of the polarization angle, ${\theta }_L$. Quantum interference in the excitation and decay pathways shifts the peak. Measurements made at ${\theta }_L=54.7^{\circ }$ eliminate this effect.