Magneto-optical effect near the $D1$ resonance of spin-polarized cold cesium atoms

We report our study of the magneto-optical effect in a strictly linear regime on spin-polarized cold cesium atoms. Due to the low intensity and the short illumination period of the probe beam, less than 7.5% of the sample atoms change their states by absorbing probe photons. We produce a medium of atoms at rest in either the $6S_{1∕2},F=3,m_F=0$ or $6S_{1∕2},F=3,m_F=3$ state by optically pumping atoms trapped in a magneto-optical trap. We use the $D1$ resonance with large lower and upper state hyperfine splittings as a probe transition to avoid hyperfine mixing from the Zeeman interaction. Under this idealized situation we measure the Stokes parameters in order to find the polarization rotation and circular dichroism experienced by the probe light. We find that there are qualitative differences between the results for the $m_F=0$ and $m_F=3$ cases. While dispersion and consequent Faraday rotation play a dominant role when the atoms are in the $m_F=0$ state, it is dissipation and circular dichroism that are important when they are in the $m_F=3$ state. Similarly, while the size of the Faraday rotation and the circular dichroism for the $m_F=0$ case scales linearly with the applied magnetic field, for the $m_F=3$ case it is the shift of the probe polarization change versus frequency that is linearly proportional to the magnetic field strength.

Figure 1

Output polarization. $\psi$ is the rotation angle determined by ${\beta }_{\pm }$. Ellipticity is characterized by the auxiliary angle $\chi$ with $\tan \chi =b∕a$. A degree of circular dichroism $\sin 2\chi$ is determined by ${\alpha }_{\pm }$.

Figure 2

Relative transition strengths from the $\mid 6S_{1∕2},F=3,m_F⟩$ states to the $\mid 6P_{1∕2},F=4,m_F\pm 1⟩$ states. The numbers in the boxes are $24{\mid ⟨6P_{1∕2},F=4,m_F\pm 1\mid D_{\pm }\mid 6S_{1∕2},F=3,m_F⟩\mid }^2∕{\mid ⟨6P_{1∕2},F=4\parallel D\parallel 6S_{1∕2},F=3⟩\mid }^2$, where $⟨6P_{1∕2},F=4\parallel D\parallel 6S_{1∕2},F=3⟩$ is the reduced matrix element.

Figure 3

Orientation of the quantization field and optical fields. Trapping beams for the MOT, which are also used for the hyperfine pumping, are shown with shaded arrows. $E_{\mathit{OP}}\left(0\right)$ and $E_{\mathit{OP}}(+3)$ are the Zeeman pumping beams for the target states of $m_F=0$ and $m_F=3$, respectively. $E_{\mathit{\text{scan}}}$ is used to monitor the results of the optical pumping and $E_{\mathit{\text{probe}}}$ is the probe field for the Faraday rotation.

Figure 4

Distribution of atoms among the $\mid 6S_{1∕2},F=3,m_F⟩$ sublevles: (a) the sample with only the hyperfine pumping, (b) the sample pumped into the $m_F=0$ sublevel, and (c) the sample pumped into the $m_F=3$ sublevel.

Figure 5

Results of the polarization measurements with the $m_F=0$ sample. (a) $P_{\Vert }\left(●\right)$ $P_{\perp }\left(엯\right)$, (b) $P_{+45}\left(●\right)$, $P_{-45}\left(엯\right)$, and (c) $P_{\sigma +}\left(●\right)$, $P_{\sigma -}\left(엯\right)$. Each component is normalized to the total transmitted power when there are no atoms. (d) the rotation angle $\psi$ in radians (●) and the degree of circular dichroism $\sin 2\chi$ (엯). Theoretical curves are shown with solid and dotted lines.

Figure 6

Results of the polarization measurements with the $m_F=3$ sample.

Figure 7

Measurement results and theoretical curves for the the case of $m_F=0$ state with high and low magnetic fields: (a) the rotation angle $\psi$ in radians and (b) the degree of circular dichroism $\sin 2\chi$ for $B=20\mathrm{G}$ (●) and $B=5\mathrm{G}$ (엯).

Figure 8

Measurement results and theoretical curves for the case of $m_F=3$ state with $B=20\mathrm{G}$ (●) and $B=2\mathrm{G}$ (엯).