Virtual Photon Effects on Chaos in Generalized Lorenz-Haken Equation

The dynamics of an ensemble of two-level atoms injected into a single-mode cavity is studied in the exact atom-field interaction situation, in which the counter-rotating terms describing the so-called virtual photon processes neglected in the rotating-wave approximation, are considered. The cavity mode is driven by the injected classical field,and the atom is prepared in a coherent superposition of the two levels. We first derive the generalized Lorenz-Haken equation by using the technique of quantum Langevin equation, and then numerically study the dynamics of this equation.We find that the virtual photon processes have strong effects on the dynamics, which can cause the trajectory in phase space of strange attractor spiral around four focus points, and the trajectory is modulated by virtual photon processes.The chaos region in parameter space is now enlarged. It should be stressed that the strange attractor can exist in optical bistability, and whether the atomic coherences and classical field can inhibit chaos depends on the laser frequency.     

非锁相Lorenz-Haken方程动力学研究

考虑原子的相干性和经典注入光场，利用随机微分方程给出非锁相条件下的Lorenz-Haken方程，研究失谐量、注入经典光场和原子相干性对非锁相Lorenz-Haken方程动力学特性的影响．在激光运转情形，失谐量造成光场位相的混沌，系统在不同条件下，出现四吸引子、双吸引子及单吸引子混沌状态，且体系的分数维维数较锁相条件下增加．光场失谐量、注入光场和原子相干性可抑制混沌．在双稳态运转下，光场位相为π的偶数倍或奇数倍，使光场稳定于正值和负值，故体系出现对称双稳态对，但无混沌状态． 关键词： 非锁相Lorenz-Haken方程 混沌 原子相干性 注入光场     

Chaotic Phenomena in a Two-Photon Laser with Injected Signal

The instability and the chaotic phenomena in a two-photon laser with injected signal are discussed for the homogeneously broadened single mode ring cavity. The structure of the system's attractors is considered by using the Lyapunov exponents and the Lyapunov dimension. The strange attractors of chaos and superchaos are found. The strange attractor displaying superchaos is not observed in one-photon laser with injected signal.     

Dynamic Equations and Nonlinear Dynamics of Cascade Two-Photon Laser

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.     

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

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.     

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

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.     

Freezing coherent field growth in a cavity by the quantum zeno effect

We have frozen the coherent evolution of a field in a cavity by repeated measurements of its photon number. We use circular Rydberg atoms dispersively coupled to the cavity mode for an absorption-free photon counting. These measurements inhibit the growth of a field injected in the cavity by a classical source. This manifestation of the quantum Zeno effect illustrates the backaction of the photon number determination onto the field phase. The residual growth of the field can be seen as a random walk of its amplitude in the two-dimensional phase space. This experiment sheds light onto the measurement process and opens perspectives for active quantum feedback.     

A METHOD OF CONTROLLING SPATIOTEMPORAL CHAOS IN COUPLED MAP LATTICES

We propose a method that allows one to control spatiotemporal chaos by applying pulses proportional to the system variables and compressing the phase space of strange attractor in nonlinear system. The method is illustrated by the coupled map lattices at different strengths of coupling. Various numerical results are given. The advantage of this method is that it does not need to know any previous knowledge of the system dynamics.     

Soliton as strange attractor: nonlinear synchronization and chaos

We show that dissipative solitons can have dynamics similar to that of a strange attractor in low-dimensional systems. Using a model of a passively mode-locked fiber laser as an example, we show that soliton pulsations with periods equal to several round-trips of the cavity can be chaotic, even though they are synchronized with the round-trip time. The chaotic part of this motion is quantified using a two-dimensional map and estimating the Lyapunov exponent. We found a specific route to chaotic motion that occurs through the creation, increase, and overlap of "islands" of chaos rather than through multiplication of frequencies.     

Virtual photon effects on classical chaos in a periodically kicked Rydberg atom system

We study classical chaos in the system of a two-level Rydberg atom interacting with a pulsed standing microwave. This model approaches the form of an atom optics realization of a usual delta-kicked rotor under the rotating-wave approximation (RWA). We find that the non-energy-conserving processes or virtual photon processes neglected in the RWA have a strong effect on the classical chaos, which can enhance, reduce and even completely suppress the chaos under certain kicked conditions. The system displays non-KAM dynamical behavior for rational and irrational kicks.     

Strange attractor simulated on a quantum computer

We show that dissipative classical dynamics converging to a strange attractor can be simulated on a quantum computer. Such quantum computations allow to investigate efficiently the small scale structure of strange attractors, yielding new information inaccessible to classical computers. This opens new possibilities for quantum simulations of various dissipative processes in nature. Received 10 August 2002 Published online 29 October 2002 RID="a" ID="a"e-mail: dima@irsamc.ups-tlse.fr RID="b" ID="b"UMR 5626 du CNRS     

Generic singularity studies revisited

Intermittency and chaos are shown to occur in a single-mode laser driven on resonance by an external constant amplitude electric field and a periodically modulated inversion. Numerically the strange attractor of the system is found to be approximately a two-dimensional manifold in an appropriate three-dimensional phase space.     

Chaos in an Ar+ Composite Resonator Laser Using KNSBN;Cu Crystal Self-Pumped Phase-Conjugator

Observation of the dynamics in a single-mode Ar⁺ composite resonator laser using KNSBN;Cu crystal self-pumped phase-conjugator is reported. The sequence of instabilities occurring on gain change corresponds to the transition the chaos of the logistic equation. Period-doubling route to chaos, and period-5, -3,-3×2, and -2 together with -3 windows in the chaotic range were observed. The strange attractor which is similar to that of the forced Duffing equation is obtained by reconstructing phase-space pictures of the system.     

偏振态移位键控光混沌通信系统的保密性

为了评判偏振态移位键控(PolSK)光混沌通信系统的保密性强弱,先要验证它的混沌特性,因此对该系统的信号进行了分析。利用三种方法判定该信号是否具有混沌特性:在三维相空间观察奇异吸引子;分别从最大李氏(Lyapunov)指数满足的方程出发以及wolf法计算其最大李氏指数;并计算其自功率谱密度函数。结果明显观察到奇异吸引子,算得最大李氏指数分别为0.0364和0.0106,都大于零,自功率谱为噪声背景、宽峰的连续谱;从而判定该系统传输的信号确实是混沌信号。另一方面,用最小伪邻点算法计算该系统信号的嵌入维数,结果达到6维,说明该系统具有中高维度混沌特性;结合系统的抗攻击性分析,得出结论:相比于一般的混沌掩盖方案,该系统具有较强的保密性和安全性。     

准周期外力驱动下Lorenz系统的动力学行为

本文研究了准周期外力驱动下Lorenz系统的动力学行为，发现当外强迫的振幅达到某一个临界值时，系统的动力学行为将会发生根本性的变化，由此揭示了产生非混沌奇怪吸引子(Strange Nonchaotic Attractor, SNA)的一个新机制：准周期外强迫振幅的加大导致系统由奇怪的混沌吸引子转变为SNA，系统的相空间最终被压缩至一个准周期环上.并且本文的结果表明，外强迫的临界振幅与Lorenz系统Rayleigh数的大小成正比，而其受外强迫频率变化的影响并不大. 关键词： 准周期 Lorenz系统 非混沌奇怪吸引子     

Chaotic dynamics of superconductor vortices in the plastic phase

We present numerical simulation results of driven vortex lattices in the presence of random disorder at zero temperature. We show that the plastic dynamics is readily understood in the framework of chaos theory. Intermittency "routes to chaos" have been clearly identified, and positive Lyapunov exponents and broadband noise, both characteristic of chaos, are found to coincide with the differential resistance peak. Furthermore, the fractal dimension of the strange attractor reveals that the chaotic dynamics of vortices is low dimensional.     

Evolution of a two-parameter chaotic dynamics from universal attractors

We observed endlessly repeating sequences of the period-doubling universal route to chaos followed by ordered states in the dynamics of a two-parameter 1-D system. The coalescence of these sequences are reported together with measurements of a strange attractor which evolves from this overlap.     

Strange Nonchaotic Attractors in a Time-Delay System

A nonchaotic attractor is observed in an infinite-dimensional system which is related to optical bistability and described by a nonlinear time-delay differential equation. The observed nonchaotic attractor is characterized by the strange trajectory of attractor but with negative value for the largest Lyapunov exponent, as well as the Fourier power spectra.     

基于小波变换的混沌信号相空间重构研究

应用小波变换和非线性动力学方法研究了混沌信号在相空间中的行为，指出混沌时间序 列的小波变换实质上是在重构的相空间中，混沌吸引子向小波滤波器向量所张的空间中的投 影，与Packard等人提出的相空间重构方法本质上是一致的.实验结果表明，混沌信号经过 小波变换后，吸引子轨迹与原有轨迹具有相似的结构，同时，系统的关联维数、Kolmogorov 熵等非线性不变量仍然得到保留.这些结果表明，利用小波变换研究混沌信号是有效的. 关键词： 小波变换 相空间重构 混沌信号 脑电信号     

Structure and evolution of strange attractors in non-elastic triangular billiards

We study non-elastic billiard dynamics in an equilateral triangular table. In such dynamics, collisions with the walls of the table are not elastic, as in standard billiards; rather, the outgoing angle of the trajectory with the normal vector to the boundary at the point of collision is a uniform factor λ < 1 smaller than the incoming angle. This leads to contraction in phase space for the discrete-time dynamics between consecutive collisions, and hence to attractors of zero Lebesgue measure, which are almost always fractal strange attractors with chaotic dynamics, due to the presence of an expansion mechanism. We study the structure of these strange attractors and their evolution as the contraction parameter λ is varied. For λ∈(0,1/3), we prove rigorously that the attractor has the structure of a Cantor set times an interval, whereas for larger values of λ gaps arise in the Cantor structure. For λ close to 1, the attractor splits into three transitive components, whose basins of attraction have fractal boundaries.