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Communications in Theoretical Physics

Virtual Photon Effects on Chaos in Generalized Lorenz–Haken Equation

R. Ju, Hongbin Huang, Peng Yang, Xia Xie, Huan Zhao

Published Jul 1, 2005• 1 citation
Publisher

Abstract

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.

DOI
10.1088/6102/44/1/65

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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.
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.
Considering the atomic coherences and injected classical field, we derived the n-Onphase-locking Lorenz-Haken equation by using the technique of stochastic differential equations. The effects of detuning, injected field and the atomic coherence on the dynamical characteristics of this equation is then numerically studied. The results show that in laser working situations, the detuning can result in chaotic behaviors of the light phase. Under different conditions, the system can generate four attractors, double attractors and single attractor, and the fractal dimension of the system is larger than that of the locking-phase system. The optical detuning, injected field and atomic coherence can inhibit the chaos of the cavity field. In the optical bistability regions, we obtain symmetric bistability pair, but never find the chaotic attractors.
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.
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.
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.
In this paper, we investigate the time evolution of the atomic operators of a two-level atom interacting with the field via a two-photon process within and without the rotating-wave approximation (RWA) by means of non-relativestic QED. We also verified that the virtual photon field is the cause for quantum chaos embodied by the periodic decay and revival effect of the atom using the numerical and analytic methods, and discussed the reason of neglecting the in-fluence of the virtual photon field on the revival time.