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.%利用多重尺度法,解析地研究了Ⅴ型五能级超冷原子电磁感应透明介质中弱的线偏振探测光的传播特性.结果表明,仅考虑系统的线性效应,随着耦合光强度的增加,介质对探测光的吸收迅速减少,而探测光的传播速度逐渐增加,但比真空中的光速要低若干个数量级.同时发现,在相同的外加磁场下探测光的非线性法拉第偏转方向与线性法拉第偏转相反,且偏转角更大.这说明电磁感应透明介质中探测光的法拉第偏转主要是由系统的非线性效应调控.
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