10 -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 3 2 1 0 Pressure [mPa] Center-of-Gravity Frequency Shift [MHz] 0.774 0.773 0.772 f$_{rep}$ - 1000 MHz [MHz] a b c d e f g h i j k l m n o p r q 7 2 P ☛ 6  2 S 1/2 Fluorescence from  6  2 S 1/2 ☞ 6  2 P 1/2  ✌ 7  2 D 3/2 Excitation E xperiment Calculation 3 – F'' 3 – F'' 4 – F'' 4 – F'' The systematic effects were studied by focusing on the six peaks labeled g , h , i , j , k , and l in Fig. 10, corre- sponding to transitions from the F = 3 ground state. The laser intensity on both stages of the transition was varied. For the 6S$_{1}$$_{/}$$_{2}$ → 6P$_{1}$$_{/}$$_{2}$ stage, the change in inten- sity ranged from ≈ 19W/cm 2 to ≈ 3W/cm $^{2}$, spread over ≈ 4000 optical modes within the 10 nm (3.8 THz) filter bandwidth. The slope of the center-of-gravity frequency as a function of light power yields a dependence of 22(27) kHz (Fig. 11), corresponding to an uncertainty of 49 kHz. We find uncertainties due to ac-Stark shifts of 14 kHz for the A constant and 17 kHz for the B constant. FIG. 11: The dependence of the center-of-gravity frequencies f or the 6S 1 / 2 → 6P 1 / 2 → 7D 3 / 2 transition on the power (upper left), the magnetic field (upper right), and the Cs vapor pres- sure (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 . FIG. 10: The calculated spectrum (upper trace) and exper- imental signal (lower trace) of the 7P → 6S fluorescence when the Cs atoms are excited to the 7D 3 / 2 state through the 6P 1 / 2 state. The peaks in the experimental spectrum labeled with letters were used in extracting the transition frequencies as described in the text. ν$_{6S}$$_{1}$$_{/}$$_{2}$$_{:9S}$$_{1}$$_{/}$$_{2}$ = 806 761 363 . 38(19) MHz A$_{9S}$$_{1}$$_{/}$$_{2}$ = 109 . 93(9) MHz . A constant of the 9S$_{1}$$_{/}$$_{2}$ state of This is in good agreement with the previous measure- ments of this transition, summarized with other data in Table II, and improves on the center-of-gravity frequency by two orders of magnitude. The center-of-gravity frequency, magnetic dipole, and electric quadrupole hyperfine coupling constants for the 7D$_{3}$$_{/}$$_{2}$ state were determined from the spectrum in Fig. 10. The filters used in collecting this spectrum were a 890 nm filter with a 10 nm passband for F1 and a 670 nm filter with a 30 nm passband for F2. This spectrum was taken by exciting Cs through the 6P$_{1}$$_{/}$$_{2}$ intermediate state. Use of the 6P$_{1}$$_{/}$$_{2}$ state eliminates possible transi- tions to the 7D$_{5}$$_{/}$$_{2}$ state due to angular momentum se- lection rules. The groups consist of six peaks, corre- sponding to the F → F ′ = 3 → F ′′ = 2 , 3 , 4 and F → F ′ = 4 → F ′′ = 3 , 4 , 5 transitions. The 18 peaks labeled a through r in Fig. 10 were used to extract the frequency and hyperfine coupling constants. No effect of the external magnetic field was observed (Fig. 11), within the measurement uncertainties. Based on the scatter of the data, we assign uncertainties of 17 kHz, 3 kHz, and 17 kHz for the center-of-gravity fre- quency, the hyperfine A constant and the hyperfine B constant, respectively. Spectra were taken at four different temperatures of the vapor cell, corresponding to a Cs vapor pressure of 0.15, 0.2, 0.3, and 2.0 mPa. As with the 9S$_{1}$$_{/}$$_{2}$ state, there appears to be a small dependence of the center-of-gravity frequency as a function of the pressure in the cell, lead- ing to a 28 kHz shift when the pressure is increased by a factor of ≈ 10. However, since we fix the A and B constants, this serves as a maximal shift in the center-of- gravity frequency and we do not attempt to correct for this shift. We take the standard deviation as a conser- vative estimate of the error and assign an uncertainty of 12 kHz to the center-of-gravity frequency due to possi- The 7D state has J > 1 / 2 and, consequently, an elec- tric quadrupole coupling denoted by the hyperfine B con- stant. Minimizing the χ $^{2}$( ν, A, B ) function defined by Eq. (10) with respect to the center-of-gravity frequency and the hyperfine A and B constants, we find a value for the center of gravity of 780 894 762 . 250(28) MHz, a hyperfine A constant value of 7 . 386(6) MHz, and a hy- perfine B constant value of − 0 . 182(50). The χ 2 was 78 for 36 peaks. D. Results for the 7D 3 / 2 state