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理论物理通讯：英文版

Dynamics of Two-Photon Lasers with A Atomic Level Configuration

Yang, Peng, Qian Qian, Feng, Huang, Hongbin, Xie Xie, Xia, Zhang, Yajun

Published Jan 1, 2006• 0 citations
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Abstract

我们少些导出尺寸有Λ a tomic 的二光子的激光的动态方程由与原子连贯和注射的古典地的考虑使用量 Langevin 方程方法铺平配置。然后，我们由计算分叉图和最大的 Lyapunovexponent (MLE ) 分析稳定性和二光子的激光的混乱动力学。我们的结果证明 Lorenz 奇怪的引起注意的人和一个焦点奇怪的引起注意的人能在这个系统存在，并且当原子连贯经由危机导致混乱时，混乱能经由 Hopf 分叉或危机由注射的古典地被导致或禁止，并且经由 Hopf 分叉或危机禁止混乱。

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[1]C.O.Weiss and R.Vilaseca,Dynamics of Lasers,VCH,Weinheim (1991); Instabilities and Chaos in Quantum Optics,eds.F.T.Arecchi and R.G.Harrison,Springer-Verlag,Berlin (1987). [2]H.Haken,Phys.Lett.A 53 (1975) 77. [3]Ju Rui,Huang Hong-Bin,Yang Peng,Xie Xia,and Zhao Huan,Commun.Theor.Phys.(Beijing,China) 44 (2005) 65; Ju Rui,Zhang Ya-Jun,Huang Hong-Bin,and Zhao Huan,Acta Phys.Sin.53 (2004) 2191 (in Chinese). [4]C.Z.Ning and H.Haken,Z.Phys.B 77 (1989) 247; B 77 (1989) 157; B 77 (1989) 163; J.Zakrenwski and M.Lewenstein,Phys.Rev.A 45 (1992) 2057. [5]G.J.deValearcel,E.Roldan,and R.Vilaseca,Phys.Rev.A 45 (1992) R2674; Phys.Rev.A 49 (1994) 1243. [6]X.Xie,H.B.Huang,F.Qian,Y.J.Zhang,P.Yang,and G.X.Qi,Commun.Theor.Phys.(Beijing,China) 46 (2006) 1042. [7]X.L.Deng,H.Q.Ma,B.D.Chen,and H.B.Huang,Phys.Lett.A 290 (2001) 77. [8]C.Benkert,and M.O.Scully,Phys.Rev.A 42 (1990) 2817. [9]M.O.Scully and M.S.Zubairy,Quantum Optics,Cambridge University Press,Cambridge (1997).

理论物理通讯：英文版•Jan 1, 2006•0 citations
我们少些导出尺寸有Λ a tomic 的二光子的激光的动态方程由与原子连贯和注射的古典地的考虑使用量 Langevin 方程方法铺平配置。然后，我们由计算分叉图和最大的 Lyapunovexponent (MLE ) 分析稳定性和二光子的激光的混乱动力学。我们的结果证明 Lorenz 奇怪的引起注意的人和一个焦点奇怪的引起注意的人能在这个系统存在，并且当原子连贯经由危机导致混乱时，混乱能经由 Hopf 分叉或危机由注射的古典地被导致或禁止，并且经由 Hopf 分叉或危机禁止混乱。
We derive the dimensionless dynamic equations of two-photon lasers with Λ atomic level configuration by using the quantum Langevin equation method with the considerations of atomic coherence and injected classical fields. Then we analyze the stability and the chaotic dynamics of the two-photon laser by calculating the bifurcation diagram and the maximum Lyapunov exponent (MLE). Our results show that the Lorenz strange attractors and one-focus strange attractors can exist in this system, and the chaos can be induced or inhibited by the injected classical fields via Hopf-bifurcations or crises, while the atomic coherence induces chaos via crises, and inhibit chaos via Hopf bifurcation or crises.
我们导出方程并且学习二光子的激光，在洞的电磁的地被协调地准备的三水平的原子和古典地在驾驶注入了洞的串联的非线性的动力学。如此的一个系统的动态方程被使用量 Langevin 操作员的技术导出，然后在不同开车条件下面数字地被学习。结果在某些条件下面显示出那二光子的激光能产生的串联混乱，加倍的时期，周期、稳定、双稳态的状态。混乱能被原子人口，原子连贯，和注射的古典地禁止。另外，没有混乱发生在光双性人稳定性。
Based on the cascade two-photon laser dynamic equation derived with the technique of quantum Langevin operators with the considerations of coherently prepared three-level atoms and the classical field injected into the cavity, we numerically study the effects of atomic coherence and classical field on the chaotic dynamics of a two-photon laser. Lyapunov exponent and bifurcation diagram calculations show that the Lorenz chaos and hyperchaos can be induced or inhibited by the atomic coherence and the classical field via crisis or Hopf bifurcations.
[1]C.O.Weiss and R.Vilaseca,Dynamics of Lasers,VCH,Weinheim (1991); Instabilities and Chaos in Quantum Optics,eds.F.T.Arecchi and R.G.Harrison,Springer-Verlag,Berlin (1987). [2]H.Haken,Phys.Lett.A 53 (1975) 77. [3]Ju Rui,Huang Hong-Bin,Yang Peng,Xie Xia,and Zhao Huan,Commun.Theor.Phys.(Beijing,China) 44 (2005) 65; Ju Rui,Zhang Ya-Jun,Huang Hong-Bin,and Zhao Huan,Acta Phys.Sin.53 (2004) 2191 (in Chinese). [4]C.Z.Ning and H.Haken,Z.Phys.B 77 (1989) 247; B 77 (1989) 157; B 77 (1989) 163; J.Zakrenwski and M.Lewenstein,Phys.Rev.A 45 (1992) 2057. [5]G.J.deValearcel,E.Roldan,and R.Vilaseca,Phys.Rev.A 45 (1992) R2674; Phys.Rev.A 49 (1994) 1243. [6]X.Xie,H.B.Huang,F.Qian,Y.J.Zhang,P.Yang,and G.X.Qi,Commun.Theor.Phys.(Beijing,China) 46 (2006) 1042. [7]X.L.Deng,H.Q.Ma,B.D.Chen,and H.B.Huang,Phys.Lett.A 290 (2001) 77. [8]C.Benkert,and M.O.Scully,Phys.Rev.A 42 (1990) 2817. [9]M.O.Scully and M.S.Zubairy,Quantum Optics,Cambridge University Press,Cambridge (1997).