Measurement of the $5D$-level polarizability in laser-cooled Rb atoms

We report on accurate measurements of the scalar ${\alpha }_S$ and tensor ${\alpha }_T$ polarizabilities of the $5D$ fine structure levels $5D_{3/2}$ and $5D_{5/2}$ in Rb. The measured values (in atomic units) ${\alpha }_S\left({5D}_{3/2}\right)=18400\left(75\right)$, ${\alpha }_T\left({5D}_{3/2}\right)=-750\left(30\right)$, ${\alpha }_S\left({5D}_{5/2}\right)=18600\left(76\right)$ and ${\alpha }_T\left({5D}_{5/2}\right)=-1440\left(60\right)$ show reasonable correspondence to previously published theoretical predictions, but are more accurate. We implemented laser excitation of the $5D$ level in a laser-cooled cloud of optically polarized Rb-87 atoms placed in a constant electric field.

Figure 1

Capacitor assembly and laser beam orientation. The MOT is formed close to the center of a flat capacitor consisting of two 80%-transparent meshes glued to parallel glass plates with a mesh separation of 1 cm. The circularly ${\sigma }^{+}$-polarized pump beam at 780 nm is parallel to the electric field ($z$ axis), while the probe beam is directed at an angle of ${11}^{\circ }$ in the $z$-$y$ plane to the pump beam and is also circularly polarized (either ${\sigma }^{+}$ or ${\sigma }^{-}$) with respect to its wave vector ${\mathit{k}}_{\mathrm{probe}}$.

Figure 2

Numerical calculations of the electric field distribution with 1 kV applied to the capacitor depicted in Fig. 1. Top: Field distribution at the central plane ($x$-$y$) of the capacitor.

Bottom: Zoom in of the central volume. The origin is positioned at the geometric center of the capacitor.

Figure 3

Relevant energy levels in Rb-87 (not to scale) and excitation laser fields. Radiation at 780-nm coupling 5$S$${}_{1/2}$ and 5$P$${}_{3/2}$ levels was used for laser cooling and for optical pumping of Rb atoms. The pump beam was ${\sigma }^{+}$ polarized and directed along the $z$ axis (see Fig. 1), transferring population to the $5P_{3/2}(F=3,m_F=+3)$ level. The polarized probe laser beam at 776 nm was tuned in resonance to one of the hyperfine transitions $5P_{3/2}\to 5D_{3/2,5/2}$. Excitation of the $5D$ level was measured by spontaneous emission of 410-nm photons via the 6$P$ level.

Figure 4

Pulse sequence in our experiment. After laser cooling for 19 $\mu$s, the cooling laser was switched off for 1 $\mu$s for optical pumping (780 nm, 500 ns) and probing the 5$P$$\to$$5D$ transition (776 nm, 100 ns). To avoid the ac Stark shift from strong 780-nm pumping radiation while obtaining enough signal, the probe pulse was switched on 10 ns after the pump was switched off. Detection starts simultaneously with the probe beam and lasts for $1\mu$s. The whole cycle was repeated every 20 $\mu$s, and the MOT magnetic field was continuously on.

Figure 5

Top: Spectral line profiles of the $5P_{3/2}\to 5D_{5/2}$ transition with the probe beam ${\sigma }^{+}$ polarized along ${\mathit{k}}_{\mathrm{probe}}$. The dashed line corresponds to zero electric field, $\mathcal{E}=0$ kV/cm, and the solid line to $\mathcal{E}=2.5$ kV/cm. The hyperfine component $F=3$ is excited because the probe beam possesses a fraction of linear polarization if projected onto the $z$ axis. Bottom: The same experiment, but for the probe beam ${\sigma }^{-}$ polarized along its wave vector. The amplitude of $F=3$ significantly increases because the transition to the sublevel $5D(F=3,m_F=2)$ becomes allowed (see also Fig. 3). Fits are done by the model function (c) described in the text.

Figure 6

Top: Spectral line profiles of the $5P_{3/2}\to 5D_{3/2}$ transition with the probe beam ${\sigma }^{+}$ polarized with respect to ${\mathit{k}}_{\mathrm{probe}}$. The dashed line corresponds to zero electric field, $\mathcal{E}=0$ kV/cm, and the solid line to $\mathcal{E}=2.5$ kV/cm. The hyperfine component $F=3$ is clearly visible due to the component of linear polarization, but $F=2$ is not distinguishable from the noise. The spectrum proves the high efficiency of optical pumping and the absence of ${\sigma }^{-}$ component. Bottom: Same experiment, but for the probe beam ${\sigma }^{-}$ polarized with respect to ${\mathit{k}}_{\mathrm{probe}}$. Now the component with $F=2$ is efficiently excited according to Fig. 3. Fits are done by the model function (c) described in the text.

Figure 7

Frequency shift of transitions to the $5D_{5/2}(F=4)$ and $5D_{5/2}(F=3)$ hyperfine sublevels at different values of electric field ${\mathcal{E}}_z$. The polarization of the probe beam along ${\mathit{k}}_{\mathrm{probe}}$ was ${\sigma }^{+}$ and ${\sigma }^{-}$, respectively. A parabolic fit according to (4) is used.

Figure 8

An atom in a pumping beam and an external magnetic field. The pumping beam is propagating along the $z$ axis, which is selected as a quantization axis in the initial basis. Maximum influence of the magnetic field on the optical pumping process will take place when the magnetic field is perpendicular to the $z$ axis.

Figure 9

Top: Numerical calculations of the population of the magnetic level of $5P_{3/2}$ with $m=3$ during the optical pumping and after that. The population of the magnetic sublevel is normalized to the total population on the $5P_{3/2}$ level. Bottom: Total population of the $5P_{3/2}$ level.