Optically induced Faraday effect using three-level atoms

We investigate an all-optical, pump-probe scheme for the polarization rotation of linearly polarized light in an atomic medium. A circularly polarized control light is shown to play the role of a static magnetic field via a Zeeman-like ac Stark interaction and to induce the optical Faraday rotation (OFR) of the probe light. As a model system, we consider a stationary atom with $nS\text{−}nP\text{−}nD$ level scheme without electronic or nuclear spin. In addition to OFR, we find that electromagnetically induced transparency for the three-level atom and circular dichroism also contribute to the polarization change. We characterize these three effects over different frequency ranges through an explicit calculation of the fractional transmission and the output polarization of the probe light. Our results are compared with the $nS\text{−}nP\text{−}(n+1)S$ scheme, which has been previously studied both theoretically and experimentally. We also compare the optically induced Faraday effect with the Faraday effect from a static magnetic field. We propose an experimental situation to test the theory and address the possibility of producing an atomic medium that is both optically active and transparent.

Figure 1

The three-level atom and the relevant probe and coupling fields. (a) $nS\text{−}nP\text{−}(n+1)S$ scheme. (b) $nS\text{−}nP\text{−}nD$ scheme.

Figure 2

The fractional transmission $T$ (thick line), the degree of circular polarization, $S$ (dotted line), and the optically induced polarization rotation angle $\psi$ (thin line) of the probe light for the cesium $6S\text{−}6S\text{−}7S$ configuration in Fig. 1a. The $x$ axis is the detuning from the $6S\text{−}6P$ resonance, normalized to ${\Gamma }_P$. ${\delta }_{\mathit{AT}}$ is the Autler-Townes splitting of the $\mid 6P,m_l=-1⟩$ state due to the coupling light.

Figure 3

$T$ (thick line), $S$ (dotted line), and $\psi$ (thin line) for the cesium $6S\text{−}6S\text{−}6D$ configuration in Fig. 1b. ${\delta }_{\mathit{AT}}\left({\sigma }^{\pm }\right)$ are the Autler-Townes splittings of the $\mid 6P,m_l=\pm ⟩$ states, respectively, due to the coupling light.

Figure 4

$T$ (thick line) and $\psi$ (thin line) of the probe light near $D2$ transition through a medium of stationary cesium atoms under a $20\text{−}\mathrm{G}$ static magnetic field.

Figure 5

$T$ (thick line), $S$ (dotted line), and $\psi$ (thin line) of the probe light for real cesium atoms with hyperfine structures and Maxwell-Boltzmann distribution. The $6S_{1∕2},F=3\text{−}6P_{1∕2},F=4\text{−}6D_{3∕2},F=3,4,5$ configuration is considered.