9 C. Results for the 9S 1 / 2 state Figure 8 shows the spectrum obtained for the cascaded two-photon transition 6S$_{1}$$_{/}$$_{2}$ → 6P$_{3}$$_{/}$$_{2}$ → 9S$_{1}$$_{/}$$_{2}$ and the cal- culated spectrum. This spectrum was collected by use of a 850 nm filter with a 10 nm passband for F1 and a 658 nm filter with a 10 nm passband for F2. The measure- ment of the 9S$_{1}$$_{/}$$_{2}$ state through the 6P$_{1}$$_{/}$$_{2}$ intermediate state was not possible because the complementary radia- tion at 635.5 nm was on the edge of the laser bandwidth. The peaks a - p were used to determine the center-of- gravity frequency and the hyperfine A constant as de- scribed above. The extracted center-of-gravity frequency is 806 761 363 . 380(58) MHz and the hyperfine A constant is 109 . 932(30) MHz. The χ 2 was 83 for 32 peaks. The systematic effects due to ac-Stark shifts, Zee- man shifts, pressure shifts, and misalignment effects were investigated in the same way as they were for the 8S$_{1}$$_{/}$$_{2}$ state. The systematic effects were studied by fo- cusing on the three peaks labeled h , i , and j in Fig. 8, corresponding to transitions from the F = 3 ground state hyperfine level to the F ′′ = 3 excited state hyperfine level through the F ′ = 2, 3, and 4 intermediate hyperfine lev- els. The laser intensity for both transitions was varied. For the 6S$_{1}$$_{/}$$_{2}$ → 6P$_{3}$$_{/}$$_{2}$ stage of the transition the variation was from ≈ 40 W/cm 2 to 20 W/cm 2 and was spread over ≈ 4000 optical modes. A linear fit of the center-of-gravity frequency to the power gave a dependence of − 42(127) kHz /P where P is the normalized operating power. We therefore assign a 169 kHz uncertainty to the center-of- gravity frequency due to possible light shifts (Fig. 9). Similarly, for the hyperfine A constant we found a linear dependence consistent with zero slope, 21(58) kHz /P . We take 79 kHz uncertainty to be the uncertainty in the A constant due to possible ac-Stark shifts. As with the 8S$_{1}$$_{/}$$_{2}$ state, no discernable dependence of the frequency on the external magnetic field was observed (Fig. 9). Based on the scatter (standard deviation) of the data we arrive at an uncertainty of 18 kHz for the center-of-gravity frequency and 7 kHz for the hyperfine A constant. Spectra were taken at four different temperatures of the vapor cell corresponding to Cs vapor pressures of 0.15, 1.06, 3.9, and 7.6 mPa. The dependence of the center-of-gravity frequency is shown in Fig. 9. There is evidence of a possible shift in the frequency with pressure. However, even at pressures that are 50 times larger than the nominal operating pressure, we see only a 67 kHz shift. We again use the standard deviation of the data to place a conservative limit on possible uncertainties due to pressure shifts and find a 34 kHz uncertainty in the optical frequency due to temperature dependent effects. A similar analysis for the hyperfine A constant gives an uncertainty due to temperature dependent effects of 15 kHz. a 58 kHz uncertainty for the center-of-gravity frequency and 20 kHz for the hyperfine A constant. The uncertainties to the center-of-gravity frequency and the hyperfine A constant are summarized in Table I. We arrive at a final value for the center-of-gravity fre- quency for the 6S$_{1}$$_{/}$$_{2}$ → 9S$_{1}$$_{/}$$_{2}$ transition and the hyperfine An analysis of the frequency dependence on misalign- ment done in the same way as described above yielded FIG. 8: The calculated spectrum (upper trace) and exper- imental signal (lower trace) of the 7P → 6S fluorescence when the Cs atoms are excited to the 9S 1 / 2 state through the 6P 3 / 2 state. The peaks in the experimental spectrum labeled with letters were used in extracting the transition frequencies, as described in the text. FIG. 9: The dependence of the center-of-gravity frequencies for the 6S 1 / 2 → 6P 3 / 2 → 9S 1 / 2 state on the power (upper left), the magnetic field (upper right), and the Cs vapor pressure (bottom). The straight line for the power dependence is a weighted linear fit to the data. The vertical axis has been offset and centered so that the nominal operating point is at zero for the power-dependence plot. The magnetic field and pressure data are shown scattered about the weighted mean of the data. The power is plotted as a function of the fraction of the maximum power. The magnetic field is plotted as a function of the residual magnetic field, ≈ 50 µT . -0.1 0.0 0.1 1.0 0.5 0.0 Normalized Power Center-of-Gravity Frequency Shift [MHz] -0.1 0.0 0.1 2 1 0 Normalized Magnetic Field Center-of-Gravity Frequency Shift [MHz] -0.1 0.0 0.1 10 5 0 Pressure [mPa] Center-of-Gravity Frequency Shift [MHz] 0.774 0.773 0.772 f$_{rep}$ - 1000 MHz [MHz] a b d c e f g i h j l k m n o p 3 - 3 3 - 3 3 - 3 4 - 4 3 - 4 3 - 4 4 - 3 4 - 3 4 - 4 7 2 P ✟ 6 2 S 1/2 Fluorescence from 6  2 S 1 / 2 ✠ 6  2 P 3/2  ✡ 9  2 S 1/2 Excitation E x periment Calculation