Precision measurement of the oscillator strength of the cesium $6{}^{2}S_{1∕2}\to 5{}^{2}D_{5∕2}$ electric quadrupole transition in propagating and evanescent wave fields

Hyperfine-structure-resolved absorption spectra of the $6{}^{2}S_{1∕2}\to 5{}^{2}D_{5∕2}$ of cesium atoms have been observed with a temperature-controlled cell and a diode laser. From a comparison with the absorption of the $D_2$ transition at the same atom density range, the oscillator strength of the electric quadrupole transition was determined to be $(4.69\pm 0.05)\times {10}^{-7}$. Reflection spectra of the same transition have also been observed in the partial and total reflection regimes with a reflection cell. An increase in the apparent oscillator strength was observed for total reflection with an increase in the angle of incidence, by a factor up to 1.5 at ${\theta }_c+83.8\mathrm{mrad}$ and 2.4 at ${\theta }_c+107.5\mathrm{mrad}$ for $s$ and $p$ polarizations, respectively, where ${\theta }_c$ is the critical angle. The observed enhancement is ascribed to the incidence-angle-dependent wave vector and polarization vector of the evanescent wave.

Figure 1

(a) The experimental setup. LD, laser diode; FPI, Fabry-Pérot interferometer; PD, photodiode; GTP, Glan-Thompson prism; FG, function generator; DAC, digital-analog converter; W-lamp, tungsten filament lamp; CCD, CCD camera. (b) Energy-level diagrams of the Cs $6{}^{2}S_{1∕2}\to 6{}^{2}P_{3∕2}$ (left) and $6{}^{2}S_{1∕2}\to 5{}^{2}D_{5∕2}$ (right) transitions with the HFS splitting.

Figure 2

(a) Transmission spectra of the $6{}^{2}S_{1∕2}\to 6{}^{2}P_{3∕2}$ electric dipole transition at several temperatures of the coldest point. (b) The dependence of the equivalent width on the atom density; the experiment (open circles) and the calculation (solid line).

Figure 3

An example of raw data for the transmission spectra measurement of the $6{}^{2}S_{1∕2}\to 5{}^{2}D_{5∕2}$ electric quadrupole transition. The temperatures of the coldest point and the main body of the cell are 470.7 and 477.5 K, respectively. (i) The lock-in amplified signal of the laser light intensity transmitted through the cell, (ii) the transmitted light intensity, (iii) the light intensity reference, and (iv) the frequency marker. (i), (ii), (iii), and (iv) correspond to those in Fig. 1a.

Figure 4

The absorption spectra (the first derivative) for (a) $6{}^{2}S_{1∕2}(F=4)\to 5{}^{2}D_{5∕2}(F^{\prime }=2\text{–}6)$ and (b) $6{}^{2}S_{1∕2}(F=3)\to 5{}^{2}D_{5∕2}(F^{\prime }=1\text{–}5)$ transitions. The temperatures of the coldest point and the main body are 445.5 and 462.3 K, respectively. The density is $5.319\times {10}^{20}{\mathrm{m}}^{-3}$. The solid and dashed curves show the experimental and calculated results, respectively.

Figure 5

The oscillator strength determined at several atom densities. For the $6{}^{2}S_{1∕2}(F=4)\to 5{}^{2}D_{5∕2}(F^{\prime }=2\text{–}6)$ transition, the experimental values are shown by the closed circles and the fitted value is shown by the solid line. For the $6{}^{2}S_{1∕2}(F=3)\to 5{}^{2}D_{5∕2}(F^{\prime }=1\text{–}5)$ transition, the experimental values are shown by the closed triangles The experimental value by Glab (open square) [8] is also shown.

Figure 6

(a) The experimental setup. LD, laser diode; FPI, Fabry-Pérot interferometer; GTP, Glan-Thompson prism; PD, photodiode; FG, function generator; DAC, digital-analog converter; BS, beam splitter. (b) The geometry of the reflection cell which includes the prism cell and the cover cell.

Figure 7

An example of raw data of the ATR spectroscopy on the $6{}^{2}S_{1∕2}\to 5{}^{2}D_{5∕2}$ transition. (i) The lock-in amplified signal of the transmitted light through the reference cell, (ii) that of the reflected light by the prism cell, (iii) the laser light intensity, and (iv) the frequency marker. ${\theta }_i$ is 0.7571 rad (43.38°).

Figure 8

Comparison of the experimental spectrum (solid line) with the calculated one (dotted line) in which the oscillator strength is assumed to be constant; (a),(c),(e) for $p$ polarization and (b),(d),(f) for $s$ polarization. The angular detuning is shown in each figure.

Figure 9

The ratio of $A_{s;p}\left({\theta }_i\right)$ between experiment and calculation, as a function of the angular detuning $\delta$ from ${\theta }_c$. In the calculation the oscillator strength is assumed to be constant. The solid and dotted lines show the enhancement factors for $p$ and $s$ polarization [11, 27].