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We present a theoretical and experimental study of polarization spectroscopy of rubidium atoms. All of the populations of the magnetic sublevels were calculated from the rate equations and used in the calculation of the polarization spectroscopy spectra. Using this model, we could generate theoretical line shapes of the polarization spectra on the $D_2$ transitions of rubidium atoms. The experimental results demonstrated that our model accurately reproduced spectra for all transitions in hyperfine structures.

We theoretically and experimentally investigate double-electromagnetically-induced transparency (double-EIT) cooling of two-dimensional ion crystals confined in a Paul trap. The double-EIT ground-state cooling is observed for ${{}^{171}\mathrm{Yb}}^{+}$ ions with a clock state, for which EIT cooling has not been realized like many other ions with a simple $\mathrm{\Lambda }$ scheme. A cooling rate of $\dot{\overline{n}}=34(\pm 1.8){\mathrm{ms}}^{-1}$ and a cooling limit of $\overline{n}=0.06(\pm 0.059)$ are observed for a single ion. The measured cooling rate and limit are consistent with theoretical predictions. We apply double-EIT cooling to the transverse modes of two-dimensional (2D) crystals with up to 12 ions. In our 2D crystals, the micromotion and the transverse mode directions are perpendicular, which makes them decoupled. Therefore, the cooling on transverse modes is not disturbed by micromotion, which is confirmed in our experiment. For the center of mass mode of a 12-ion crystal, we observe a cooling rate and a cooling limit that are consistent with those of a single ion, including heating rates proportional to the number of ions. This method can be extended to other hyperfine qubits, and near ground-state cooling of stationary 2D crystals with large numbers of ions may advance the field of quantum information sciences.

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We present discrimination of the effect of one-photon and two-photon coherences in electromagnetically induced transparency for a three-level ladder-type atomic system. After the optical Bloch equations for a three-level atom, with either cycling or non-cycling transitions, were solved numerically, the solutions were averaged over the velocity distribution and finite transit time. Through this we were able to discriminate one-photon and two-photon coherence parts of the calculated spectra. We also found that the spectra showed peaks as the branching ratio of the intermediate (excited) state increased (decreased). The experimental results of previous reports [H. S. Moon, et al., Opt. Express 16, 12163 (2008); H. S. Moon and H. R. Noh, J. Phys. B 44, 055004 (2011)] could well be accounted for by this discrimination of one-photon and two-photon coherences in the transmittance signals for the simplified three-level atomic system.

We clarify an interpretation of transmittance signals in ladder-type atomic systems by discriminating the contributions of one-photon resonance, two-photon resonance, and a mixed term of both in the calculated spectra for these ladder-type multilevel atoms. When the two-photon-resonance effect is distinguished from an accurate spectrum calculated by modeling ladder-type electromagnetically-induced transparency for the $5S_{1/2}-5P_{3/2}-5D_{5/2}$ transitions of ${}^{87}$Rb atoms, we find that the transmittance signals for the $5D_{5/2}(F^{\prime \prime }=2,3)$ states are mainly composed of the mixed term related not to pure-two-photon atomic coherence but to the optical-pumping effect whereas the transmittance signal for the $5D_{5/2}(F^{\prime \prime }=4)$ state originates from both the pure-two-photon-resonance term and the mixed term. DOI: http://dx.doi.org/10.1103/PhysRevA.85.033817 ©2012 American Physical Society