Polarization spectroscopy in rubidium and cesium

We develop a theoretical treatment of polarization spectroscopy and use it to make predictions about the general form of polarization spectra in the alkali-metal atoms. Using our model, we generate theoretical spectra for the $D2$ transitions in ${}^{87}\mathrm{Rb}$, ${}^{85}\mathrm{Rb}$, and ${}^{133}\mathrm{Cs}$. Experiments demonstrate that the model accurately reproduces spectra of transitions from the upper hyperfine level of the ground state only. Among these, the closed transition $F\to F^{\prime }=F+1$ dominates, with a steep gradient through line center ideally suited for use as a reference in laser locking.

Figure 1

Time evolution of population. The population of the eight ground-state sublevels of ${}^{87}\mathrm{Rb}$ are plotted as a function of time after the pump beam is turned on. The pump drives ${\sigma }^{+}$ transitions and has an intensity of 0.1$I_{\mathrm{sat}}$. Vertical axes are identical to emphasize differences in population behavior. (a) Laser tuned to $F=2\to F^{\prime }=3$ transition. Within a few $\mathrm{\mu }\mathrm{s}$ the initial isotropic population distribution becomes highly anisotropic, as atoms are optically pumped into the $\mid 2,2⟩$ state. As this transition is closed, no change occurs in the population of the $F=1$ manifold. (b) When the laser is tuned to the $F=2\to F^{\prime }=2$ transition the atoms are again optically pumped towards the $\mid 2,2⟩$ state. However, as this is an open transition, a significant fraction of population accumulates in the $F=1$ manifold. These states do not contribute to the medium’s optical anisotropy. (c) For the laser turned to the $F=2\to F^{\prime }=1$ transition even fewer atoms are pumped into the $\mid 2,2⟩$ state.

Figure 2

Sign of anisotropy for closed transitions. (a) For the closed $F=\mathcal{I}+1∕2\to F^{\prime }=F+1$ transition the population is optically pumped into the $\mid F,m_F=F⟩$ state, with a small fraction in the excited state. The line strength ${\alpha }_{F,m_F\to F+1,m_F+1}$ is significantly larger than ${\alpha }_{F,m_F\to F+1,m_F-1}$. (b) For the closed $F=\mathcal{I}-1∕2\to F^{\prime }=F-1$ transition the population is optically pumped into the $\mid F,m_F=F⟩$ and $\mid F,m_F=F-1⟩$ states. There are no allowed ${\sigma }^{+}$ transitions for these states, whereas the line strength for the ${\sigma }^{-}$ transitions are finite. Consequently, the anisotropy of the medium has opposite sign relative to (a). All levels are drawn as for an atom with $\mathcal{I}=5∕2$; the structure of the other alkali-metal atoms is similar.

Figure 3

Experimental layout. A thick glass slide picks off a fraction of the extended cavity diode laser (ECDL) light and splits it into two parallel beams. One beam acts as the probe, and the other as a (nearly) counterpropagating pump. The beams overlap inside a 70-mm (50-mm) Rb (Cs) cell, which rests inside a long solenoid and below a coil that cancels the ambient laboratory field. In the cesium experiment two coils in the Helmholtz configuration replace the solenoid. A half-wave plate rotates the plane of polarization of the probe beam with respect to the polarizing beam splitter (PBS) cube axis; a quarter-wave plate makes the pump circularly polarized.

Figure 4

Experimental (thick line) and theoretical (fine line) polarization spectra of $D2$ line transitions in (a) ${}^{87}\mathrm{Rb}$, (b) ${}^{85}\mathrm{Rb}$, and (c) ${}^{133}\mathrm{Cs}$. Spectra were obtained by tuning the laser frequency to drive transitions from the upper hyperfine level of the atom’s ground state. All three spectra are dominated by the strong dispersion features associated with the closed transition. For the Cs upper hyperfine spectra, solid (dashed) lines represent spectra taken with the vapor cell at $0°$ $(23°)\mathrm{C}$.

Figure 5

Experimental (thick line) and theoretical (fine line) polarization spectra of $D2$ line transitions from the lower hyperfine level of the ground state in ${}^{87}\mathrm{Rb}$.