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Physical Review A

Optically induced Faraday effect using three-level atoms

D. Cho, Jai Min Choi, Jang Myun Kim, Q‐Han Park

Published Aug 25, 2005• 31 citations
Publisher

Abstract

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 $nS\text{\ensuremath{-}}nP\text{\ensuremath{-}}nD$ 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 $nS\text{\ensuremath{-}}nP\text{\ensuremath{-}}(n+1)S$ 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.

DOI
10.1103/physreva.72.023821

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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\ensuremath-nP\ensuremath-nDnS\text{\ensuremath{-}}nP\text{\ensuremath{-}}nDnS\ensuremath-nP\ensuremath-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\ensuremath-nP\ensuremath-(n+1)SnS\text{\ensuremath{-}}nP\text{\ensuremath{-}}(n+1)SnS\ensuremath-nP\ensuremath-(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.
Polarization rotation of weak probe light induced by circularly polarized strong coupling light in a $\ensuremath{\Lambda}$ 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.
We demonstrate a type of chiral effect of an atomic medium. Polarization rotation of a probe beam is observed only when both a magnetic field and a linearly polarized coupling beam are present. We compare it with other chiral effects like optical activity, the Faraday effect, and the optically induced Faraday effect from the viewpoint of spatial inversion and time reversal transformations. As a theoretical model we consider a five-level configuration involving the cesium D2D2D2 transition. We use spin-polarized cold cesium atoms trapped in a magneto-optical trap to measure the polarization rotation versus probe detuning. The result shows reasonable agreement with a calculation from the master equation of the five-level configuration.
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 6S1∕2,F=3,mF=06{S}_{1∕2},F=3,{m}_{F}=06S1∕2​,F=3,mF​=0 or 6S1∕2,F=3,mF=36{S}_{1∕2},F=3,{m}_{F}=36S1∕2​,F=3,mF​=3 state by optically pumping atoms trapped in a magneto-optical trap. We use the D1D1D1 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 mF=0{m}_{F}=0mF​=0 and mF=3{m}_{F}=3mF​=3 cases. While dispersion and consequent Faraday rotation play a dominant role when the atoms are in the mF=0{m}_{F}=0mF​=0 state, it is dissipation and circular dichroism that are important when they are in the mF=3{m}_{F}=3mF​=3 state. Similarly, while the size of the Faraday rotation and the circular dichroism for the mF=0{m}_{F}=0mF​=0 case scales linearly with the applied magnetic field, for the mF=3{m}_{F}=3mF​=3 case it is the shift of the probe polarization change versus frequency that is linearly proportional to the magnetic field strength.
We investigate, both theoretically and experimentally, the phenomenon of polarization rotation of a weak, linearly polarized optical (probe) field in an atomic system with multiple three-level electromagnetically induced transparency (EIT) subsystems. The polarization rotation angle can be controlled by a circularly polarized coupling beam, which breaks the symmetry in number of EIT subsystems seen by the left and right circularly polarized components of the weak probe beam. A large polarization rotation angle (up to 45\ifmmode^\circ\else\textdegree\fi{}) has been achieved with a coupling beam power of only 15mW15\phantom{\rule{0.3em}{0ex}}\mathrm{mW}15mW. Detailed theoretical analyses including different transition probabilities in different transitions and Doppler-broadening are presented and the results are in good agreements with the experimentally measured results.
We investigate the nonlinear optical Faraday rotation (OFR) of a probe field passing through a double V–type closed-loop atomic system in the absence of an external static magnetic field. Enhancement OFR is obtained by applying the control fields to establish the closed-loop configuration. It is shown that the scattering of both control fields into the probe field mode via wave mixing induce an OFR enhancement. We find that the rotation of the polarization plane in the nonlinear OFR depends on the intensity and relative phase of applied fields and can be controlled by these parameters. It is demonstrated that applying a microwave field to the system has a constructive role in enhancement of phase-controlled nonlinear OFR.
By using multiple-scale methods, we study analytically the propagation properties of the weak linear polarization probe optical field in a cold lifetime-broadened five-level V type atomic system via electromagnetically induced transparency. It is shown that with the strength of the coupling field increasing, the absorption of the probe optical field decreases rapidly and the group velocity of the probe optical field increases quickly under the consideration of linear effect. However, the velocity is several orders of magnitude slower than the light speed in vacuum. Meanwhile, we find that for the same magnetic field the nonlinear Faraday rotation direction is opposite to linear Faraday rotation, and its rotation angle grows bigger than that of linear Faraday rotation. These results mean that the Faraday rotation of the electromagnetically induced transparency medium can be controlled by the nonlinear effect.