Transition frequencies of the $D$ lines of ${}^{39}\mathrm{K}$, ${}^{40}\mathrm{K}$, and ${}^{41}\mathrm{K}$ measured with a femtosecond laser frequency comb

We report measurements of the transition frequencies $4s{}^{2}S_{1∕2}-4p{}^{2}P_{1∕2}$ and $4s{}^{2}S_{1∕2}-4p{}^{2}P_{3∕2}$ of the potassium isotopes 39, 40, and 41 through an atomic beam experiment with a fractional uncertainty of about $2\times {10}^{-10}$. For frequency calibration, a fs-laser comb referenced to a Cs atomic clock was used. Compared to previous results, hyperfine constants for the states $4p{}^{2}P_{1∕2}$ and $4p{}^{2}P_{3∕2}$ and isotope shifts are given with a considerably reduced uncertainty. This paper also resolves the discrepancy of transition frequencies measured by Banerjee et al. [Phys. Rev. A 70, 052505 (2004)] and Scherf et al. [Z. Phys. D 36, 31 (1996)] and the hyperfine constant $A({}^{39}\mathrm{K},{}^{2}P_{1∕2})$ reported by Banerjee et al. [Europhys. Lett. 65, 172 (2004)] and Bendali et al. [J. Phys. B 14, 4231 (1981)].

Figure 1

(Color online) Laser system used for the frequency measurement. OD, optical diode; BS, beam splitter; 50%, 50% beam splitter; PBS, polarizing beam splitter; PZT, piezoelectric actuator; $\lambda ∕4$, $\lambda ∕4$ retarder.

Figure 2

Record of the $D_1$ transitions $F=2\to F^{\prime }=1,2$ in ${}^{39}\mathrm{K}$. The lower trace shows the residuals of the fit, which was used to determine the line center. Note the zoom factor of about 50.

Figure 3

The $D_1$ transitions $F=9∕2\to F^{\prime }=9∕2,7∕2$ in ${}^{40}\mathrm{K}$. The frequency dependent background stems from the wings of the transitions in ${}^{39}\mathrm{K}$. The lower trace shows the residuals of the fit magnified by a factor of about 40.

Figure 4

Spectrum of the transitions belonging to the $D_2$ line of ${}^{39}\mathrm{K}$. On the left-hand side, the lower hyperfine state is $F=2$, the right-hand side depicts the spectrum from $F=1$. The residuals are enlarged by a factor 30.

Figure 5

The $F=2\to F^{\prime }=1,2,3$ component of the ${}^{41}\mathrm{K}$ $D_2$ line (left-hand side), and the spectrum of $F=1\to F^{\prime }=0,1,2$ (right-hand side) is shown. In both parts, two curves with residuals are shown. The upper one is obtained when the hyperfine constants of the ${}^{2}P_{3∕2}$ state are fitted. For the lower case, they were fixed to literature values [27] (see text).

Figure 6

Hyperfine constants determined from our work and by other authors. Left-hand side, $A{}^{2}P_{1∕2}$; center, $A{}^{2}P_{3∕2}$; right-hand side, $B{}^{2}P_{3∕2}$.