Measurement of the radial matrix elements for the $6s{}^{2}S_{1/2}\to 7p{}^{2}P_J$ transitions in cesium

We report measurements of the electric dipole matrix elements of the ${}^{133}\mathrm{Cs}6s{}^{2}S_{1/2}\to 7p{}^{2}P_{1/2}$ and $6s{}^{2}S_{1/2}\to 7p{}^{2}P_{3/2}$ transitions. Each of these determinations is based on direct, precise comparisons of the absorption coefficients between two absorption lines. For the $\langle 6s{}^{2}S_{1/2}\left|\right|r\left|\right|7p{}^{2}P_{3/2}\rangle$ matrix element, we measure the ratio of the absorption coefficient on this line to that of the $D_1$ transition $6s{}^{2}S_{1/2}\to 6p{}^{2}P_{1/2}$. The matrix element of the $D_1$ line has been determined previously with high precision by many groups. For the $\langle 6s{}^{2}S_{1/2}\left|\right|r\left|\right|7p{}^{2}P_{1/2}\rangle$ matrix element, we measure the ratio of the absorption coefficient on this line to that of the $6s{}^{2}S_{1/2}\to 7p{}^{2}P_{3/2}$ transition. Our results for these matrix elements are $\langle 6s{}^{2}S_{1/2}\left|\right|r\left|\right|7p{}^{2}P_{3/2}\rangle =0.57417\left(57\right)a_0$ and $\langle 6s{}^{2}S_{1/2}\left|\right|r\left|\right|7p{}^{2}P_{1/2}\rangle =0.27810\left(45\right)a_0$. These measurements have implications for the interpretation of parity nonconservation in atoms.

Figure 1

Energy-level diagrams of atomic cesium, showing the states relevant to these measurements. (a) Atoms are excited from the $6s{}^{2}S_{1/2}$ ground state to the $6p{}^{2}P_{1/2}$ ($\lambda =894\mathrm{nm}$) or the $7p{}^{2}P_{3/2}$ ($\lambda =456\mathrm{nm}$) excited state, allowing for a comparison of the absorption coefficients of these two lines. (b) Comparison of the absorption coefficients for the $6s{}^{2}S_{1/2}\to 7p{}^{2}P_{1/2}$ line at 459 nm to that of the $6s{}^{2}S_{1/2}\to 7p{}^{2}P_{3/2}$ line at 456 nm. Wavelengths shown in the figure are vacuum wavelengths.

Figure 2

Experimental setup for the two measurements. The 455.7-nm laser stays the same for both measurement. The 894.6-nm or 459.4-nm laser changes depending on the measurement $R_1$ or $R_2$, respectively, being done. The following abbreviations are used: AOM1 and AOM2, acousto-optic modulators; ECDL, external cavity diode laser; PD1–PD3, photodiodes; FP1 and FP2, Fabry-Pérot cavities; and W, wedged windows. FP2 (in the dashed box) is used only for the measurement of $R_1$.

Figure 3

Examples of absorption spectra recorded at a cold finger temperature of $-2{}^{\circ }\mathrm{C}$. These figures show the photodiode signal versus laser frequency as we scan (a) the 456-nm laser through $F=4\to F^{\prime }=3^{\prime },4^{\prime },5^{\prime }$ components (not resolved) of the $6s{}^{2}S_{1/2}\to 7p{}^{2}P_{3/2}$ transition and (c) the 894-nm laser through $F=3\to F^{\prime }=3^{\prime },4^{\prime }$ components of the $6s{}^{2}S_{1/2}\to 6p{}^{2}P_{1/2}$ transition. The data are shown as the red data points and the result of a least-squares fit is shown by a black dashed line. (b) and (d) Residuals (data minus fit) for (a) and (c), respectively.

Figure 4

Plot of ${\mathrm{{\rm Y}}}^{456}$ against ${\mathrm{{\rm Y}}}^{894}$ showing (a) the data points (circles) and the least-squares fit straight line and (b) the residuals in the ordinate. In (a) the error bars are smaller than the size of the markers. The vertical error bars in (b) represent the combined $1\sigma$ uncertainties in ${\mathrm{{\rm Y}}}^{456}$ and ${\mathrm{{\rm Y}}}^{894}$.

Figure 5

Examples of absorption spectra with the cell of length ${\ell }_{\mathrm{cell}}\sim 6\mathrm{cm}$ at a cold finger temperature of $56{}^{\circ }\mathrm{C}$. These figures show the photodiode signal vs laser frequency as we scan (a) the 459-nm laser through $F=4\to F^{\prime }=3^{\prime },4^{\prime }$ components of the $6s{}^{2}S_{1/2}\to 7p{}^{2}P_{1/2}$ transition and (c) the 456-nm laser through $F=4\to F^{\prime }=3^{\prime },4^{\prime },5^{\prime }$ components of the $6s{}^{2}S_{1/2}\to 7p{}^{2}P_{3/2}$ transition. The data are shown as the red data points and the result of a least-squares fit are shown by a black dashed line. The hyperfine components are not resolved for either transition. (b) and (d) Residuals for (a) and (c), respectively.

Figure 6

Plot of ${\mathrm{{\rm Y}}}^{459}$ vs ${\mathrm{{\rm Y}}}^{456}$ for data set 2 showing (a) the data points (circles) and the line of best fit and (b) residuals in the ordinate. In (a) the error bars are smaller than the size of the markers. The vertical error bars in (b) represent the combined $1\sigma$ uncertainties in ${\mathrm{{\rm Y}}}^{459}$ and ${\mathrm{{\rm Y}}}^{456}$.

Figure 7

Plot of the three sets of $R_2$ results and the weighted mean. We have expanded the error bars of the weighted mean by $\sqrt{{\chi }_r^2}=2.0$ to account for the variation among the individual results.

Figure 8

Plots showing comparisons of various experimental and theoretical determinations of the (a) $R_1\equiv \langle 6s_{1/2}\left|\right|r\left|\right|6p_{1/2}\rangle /\langle 6s_{1/2}\left|\right|r\left|\right|7p_{3/2}\rangle$ and (b) $R_2\equiv \langle 6s_{1/2}\left|\right|r\left|\right|7p_{3/2}\rangle /\langle 6s_{1/2}\left|\right|r\left|\right|7p_{1/2}\rangle$ ratios. See Table 6 for references to these data. For Refs. [7, 39], we plot both the scaled (sc) and single-double (SD) values for $R_2$.

Figure 9

Plots of the experimental and theoretical values of (a) $\langle 6s_{1/2}\left|\right|r\left|\right|7p_{3/2}\rangle$ and (b) $\langle 6s_{1/2}\left|\right|r\left|\right|7p_{1/2}\rangle$, as listed in Table 6. Experimental values are on the left, while theoretical values are shown on the right. See Table 6 for references to these data. For Refs. [7, 39], we have plotted only the scaled (sc) values.