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理论物理通讯：英文版

Dynamic Equations and Nonlinear Dynamics of Cascade Two-Photon Laser

Xie Xie, Xia, Huang, Hongbin, Qian Qian, Feng, Zhang, Yajun, Yang, Peng, Qi, Guan-Xiao

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

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。

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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

Effects of Atomic Coherence and Injected Classical Field on Chaotic Dynamics of Non-degenerate Cascade Two-Photon Lasers

Yajun Zhang, Huang Hong-Bin, Peng Yang +1 more

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.

Communications in Theoretical Physics•Aug 1, 2007•0 citations
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。
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 equations and study nonlinear dynamics of cascade two-photon laser, in which the electromagnetic field in the cavity is driven by coherently prepared three-level atoms and classical field injected into the cavity. The dynamic equations of such a system are derived by using the technique of quantum Langevin operators, and then are studied numerically under different driving conditions. The results show that under certain conditions the cascade two-photon laser can generate chaotic, period doubling, periodic, stable and bistable states. Chaos can be inhibited by atomic populations, atomic coherences, and injected classical field. In addition, no chaos occurs in optical bistability.
[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).
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.