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netic field in the region of the vapor cell. The field wa s reduced to a level of < 1 µ T over the interaction reg ion inside the vapor cell. 

Two-photon resonance signals were monitored by mea - suring the 7P$_{J}$ → 6S$_{1}$$_{/}$$_{2}$ ( J = 1 / 2, 3 / 2) cascade fl uo- rescence at 459 nm and 455 nm. The fluorescence wa s collected at a right angle to the two counter-propagatin g beams and was detected by a photomultiplier tube. Th e detector was shielded from background light and the scat - tered light from the excitation laser beams by a 457 .9 nm filter with a 10 nm pass band (F3). The detec tor output was amplified and filtered (low-pass at 1 kHz, 6 dB/octave) before being sampled and recorded with a computer-controlled data acquisition board (DAQ). 

The DAQ used in these measurements is similar t o that used in Refs. [16, 17, 25]. The computer controlle d the scan of the repetition rate by stepping the frequenc y of the signal generator to which the repetition rate wa s phase locked. Data scans were collected by changing th e frequency of the signal generator from 1000 . 771 725 M H z to 1000 . 774 725 MHz in 1 Hz steps. This 3 kHz ra n g e in the repetition rate results in a 2-3 GHz variation in the two-photon frequency, depending on the transition . At each 1 Hz step the fluorescence was digitized wit h multiple samples and averaged for 1 s. The statist ic a l mean and the uncertainty in the mean were evaluated a t each repetition rate frequency. Spectra were collected fo r both increasing and decreasing frequency scans, resultin g in 6002 data points. 

Figure 3 shows the spectrum collected as the repeti- tion rate of the frequency comb was scanned without using the filters marked as F1 and F2 in Fig. 2. T h e spectrum consists of a multitude of narrow Doppler-free peaks and a Doppler-broadened background. The narrow peaks are due to excitation to the 8S, 9S and 7D states by two counter-propagating photons, while the Doppler- broadened background is due to excitation from two co- propagating photons. The observed spectrum is quite complicated because of the numerous discrete frequencies present in the comb combined with the multiple atomic energy levels and transition pathways accessible. 

The spectrum is greatly simplified and the Doppler background is eliminated by introducing filters F1 and F2, as shown in Fig. 2. The presence of the filters re- stricts the transitions and enables the selection of indi- vidual excitation pathways. Figure 4 shows the spec- trum observed when one of the counter-propagating laser beams is restricted to be between 845 nm to 855 nm and the other between 780nm to 800 nm. With this combi- nation, the first beam can excite the atoms on only the 6S$_{1}$$_{/}$$_{2}$ → 6P$_{3}$$_{/}$$_{2}$ transition at 852 nm (the D$_{2}$ transition) and the second beam can only excite the atoms on the 6P$_{3}$$_{/}$$_{2}$ → 8S$_{1}$$_{/}$$_{2}$ transition at 795 nm. This eliminates ex- 

## III. OBSERVED SPECTRA AND THEORETICAL CONSIDERATIONS 

<img src='content_image/391823.jpg'>

citations to the 9S$_{1}$$_{/}$$_{2}$ , 7D$_{3}$$_{/}$$_{2}$ , and 7D$_{5}$$_{/}$$_{2}$ states, as well as the excitation to the 8S$_{1}$$_{/}$$_{2}$ state through the 6P$_{1}$$_{/}$$_{2}$ state and removes the Doppler-broadened background. The re- sulting spectrum consists of groups of two or three peaks. The peaks labeled d , e , and f form one such spectral group and are shown in more detail in Fig. 5. Each spec- tral group is the result of excitation from a given ground- state hyperfine level to a given excited-state hyperfine level, and the individual peaks in the group correspond to specific transition pathways through every allowable 

