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Physical Review A

Linear and nonlinear Faraday rotations of light polarization in a four-level active-Raman-gain medium

Chengjie Zhu, L. Deng, E. W. Hagley

Published Aug 28, 2013• 9 citations
Publisher

Abstract

We investigate linear and nonlinear Faraday effects in a room-temperature, coherently driven four-level active-Raman-gain (ARG) medium. By using the multiple-scale method, we derive two nonlinear coupled envelope equations governing the dynamics of left- and right-polarized components of a linearly polarized probe field. Under the weak probe field approximation, we demonstrate a factor of four increase of the Faraday rotation angle by the linear and nonlinear response of the ARG scheme without probe field loss. We further compare this ARG system with an $M$-type five-state electromagnetically induced transparency (EIT) scheme and demonstrate the superiority of the ARG scheme over the conventional EIT scheme.

DOI
10.1103/physreva.88.023854

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We study the Faraday rotation of polarization of a probe field in a cold, coherently driven five-level system with an M-type configuration. By means of a method of multiple scales we derive two coupled nonlinear envelope equations, which govern the evolution of two circularly polarized components of the probe field. It is shown that due to the quantum interference effect induced by two control fields, one can obtain a large rotation angle with a very low absorption of the probe field. In addition, an efficient control over the polarization state of the probe field in the system can also be easily realized.
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.
We present a scheme for obtaining entangled photons and quantum phase gates in a room-temperature four-state tripod-type atomic system with two-mode active Raman gain (ARG). We analyze the linear and nonlinear optical responses of this ARG system and show that the scheme is fundamentally different from those based on electromagnetically induced transparency and hence can avoid significant probe-field absorption as well as a temperature-related Doppler effect. We demonstrate that highly entangled photon pairs can be produced and rapidly responding polarization qubit phase gates can be constructed based on the unique features of the enhanced cross-phase-modulation and superluminal probe-field propagation of the system.
A four-level N scheme with a two-mode active Raman gain core is investigated for large and rapidly responding Kerr effect enhancement at room temperature. The new scheme is fundamentally different from the electromagnetically induced transparency (EIT-)based ultraslow-wave Kerr effect enhancement scheme. It eliminates the requirement of group velocity matching and multispecies medium. It also eliminates significant probe field attenuation or distortion associated with weakly driven EIT-based schemes. We show that a probe field can acquire a large, frequency tunable, gain-assisted nonlinear phase shift and yet travel with gain-assisted superluminal propagation velocity. This raises the possibility of rapidly responding, frequency tunable nonlinear phase switching and phase gates for information science.
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.
We study the interaction of a weak probe field, having two orthogonally polarized components, with an optically dense medium of four-level atoms in a tripod configuration. In the presence of a coherent driving laser, electromagnetically induced transparency is attained in the medium, dramatically enhancing its linear as well as nonlinear dispersion while simultaneously suppressing the probe field absorption. We present the semiclassical and fully quantum analysis of the system. We propose an experimentally feasible setup that can induce large Faraday rotation of the probe field polarization and therefore be used for ultrasensitive optical magnetometry. We then study the Kerr nonlinear coupling between the two components of the probe, demonstrating a novel regime of symmetric, extremely efficient cross-phase modulation, capable of fully entangling two single-photon pulses. This scheme may thus pave the way to photon-based quantum information applications, such as deterministic all-optical quantum computation, dense coding, and teleportation.