Measurement of the $4S_{1/2}\to 6S_{1/2}$ transition frequency in atomic potassium via direct frequency-comb spectroscopy

We present an experimental determination of the $4S_{1/2}\to 6S_{1/2}$ transition frequency in atomic potassium ${}^{39}\mathrm{K}$, using direct frequency-comb spectroscopy. The output of a stabilized optical frequency comb was used to excite a thermal atomic vapor. The repetition rate of the frequency comb was scanned and the transitions were excited using stepwise two-photon excitation. The center-of-gravity frequency for the transition was found to be ${\nu }_{\mathrm{cog}}=822951698.09\left(13\right)$ MHz and the measured hyperfine $A$ coefficient of the $6S_{1/2}$ state was $21.93\left(11\right)$ MHz. The measurements are in agreement with previous values and represent an improvement by a factor of 700 in the uncertainty of the center-of-gravity measurement.

Figure 1

Energy level diagram for ${}^{39}\mathrm{K}$ (nuclear spin $I=\frac{3}{2}$) showing the relevant energy levels and hyperfine structure. The excitation wavelengths are indicated for the transitions used. The hyperfine structure of the states involved in the excitation are shown. The $6S_{1/2}$ state is excited via stepwise excitation through the $4P_J$ intermediate states. The excitation is detected via the fluorescence from the $5P_J\to 4S_{1/2}$ decay branch at 405 nm following the $6S_{1/2}\to 5P_J$ decay transition.

Figure 2

Experimental setup. The repetition rate frequency of the frequency comb is monitored and stabilized to a synthesizer that is referenced to a GPS-steered rubidium clock. The frequency of the synthesizer is controlled by a computer. The output of the frequency comb that is not used for the stabilization is split, filtered, counterpropagated, and focused into a vapor cell of potassium. The fluorescence at 405 nm is monitored with a photomultiplier tube (PMT). The current from the PMT is converted to a voltage by use of a transimpedance amplifier and then recorded by the computer.

Figure 3

Experimental and modeled spectra for the $4S_{1/2}\to 6S_{1/2}$ transition. Groups 1 and 3 correspond to excitation from the $4S_{1/2}\left(F=2\right)$ ground state with different total mode numbers. Group 2 corresponds to excitation from the $4S_{1/2}\left(F=1\right)$ ground state. The top trace is the experimental spectra for six scans that are concatenated together. Each scan consists of two overlapping spectra corresponding to increasing and decreasing $f_r$. The calculated spectra are shown below the experimental spectra. The contributions to the signal from the different excitation pathways are shown in the bottom two traces.

Figure 4

Modeled spectra for the $4S_{1/2}\left(F=1\right)\to 6S_{1/2}\left(F^{\prime \prime }\right)$ transitions. The top trace shows the calculation including all relevant mode numbers and intermediate states. The middle two traces (blue) show the excitation through the $4P_{3/2}$ intermediate state. The two traces correspond to excitation with different pairs of mode numbers. The bottom two traces show the excitation through the $4P_{1/2}$ intermediate state with different pairs of mode numbers contributing to the different peaks. Note that in all cases the total mode number, $n_T=892204$, is the same for all of the peaks. For a given transition, the different amplitudes are a result of different resonant velocity classes.