Optically induced Faraday effect in a $\Lambda$ configuration of spin-polarized cold cesium atoms

Polarization rotation of weak probe light induced by circularly polarized strong coupling light in a $\Lambda$ configuration is studied. We use spin-polarized cold cesium atoms trapped in a magneto-optical trap to remove complications from Zeeman distribution, Doppler broadening, and collisional decoherence. By using a very low probe intensity and short illumination period we work in a strictly linear regime. The probe and the coupling fields are optically phase locked to eliminate phase fluctuation and consequent atomic decoherence. Using this idealized situation we clarify the roles of optically induced Faraday rotation, circular dichroism, and electromagnetically induced transparency (EIT) in determining the final state of the probe light. In particular, we identify an experimental situation where the roles of atomic coherence and EIT are important.

Figure 1

(Color online) Level scheme of cesium atoms used in the experiment. Dotted lines are probe transitions and thick lines are coupling transitions. ①: $\mid 6S_{1∕2},F=3,m_F=0⟩$; ②: $\mid 6S_{1∕2},F=4,m_F=-2⟩$; ③: $\mid 6S_{1∕2},F=4,m_F=0⟩$; ④: $\mid 6P_{3∕2},F=3,m_F=-1⟩$; ⑤: $\mid 6P_{3∕2},F=3,m_F=+1⟩$.

Figure 2

(Color online) Schematic diagram for the optical Faraday rotation apparatus. ML: master laser; CL: coupling laser; PL: probe laser; OPLL: optical phase lock loop; PD: fast photodiode; AOM: acousto-optic modulator; SE: solid etalon; WP: waveplate, PBS: polarizing beam splitter; INT: gated integrators; DAQ: data acquisition system.

Figure 3

(a) Normalized transmitted probe beam powers for the ${\sigma }^{+}$ (●) and ${\sigma }^{-}$ (엯) components and (b) for the $+45°$ (●) and $-45°$ (엯) components versus ${\Delta }_P∕{\Gamma }_P$ when ${\Delta }_C=0$. Solid lines represent theoretical curves for corresponding components.

Figure 4

Rotation angle $\psi$ (●) and degree of circular dichroism $\sin 2\chi$ (엯) (a) with and (b) without the optical pumping. Dotted and solid lines represent theoretical curves.

Figure 5

Change in the sign of the rotational angle $\psi$ under the polarization reversal of the coupling field: When the coupling polarization is ${\sigma }^{+}$ (●) and when it is ${\sigma }^{-}$ (엯). The solid lines are to guide the eye.

Figure 6

Calculated maximum rotation angle ${\psi }_{\max }$ for spin-polarized cold cesium atoms at ${\Delta }_P={\Delta }_P^0$ versus coupling intensity when the atomic coherence is considered (●) and when it is not considered (◇).