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Non-linear Behavior and Quantum Chaos in Laser and Cooperative Atomic Systems

Published Jan 1, 1987• 0 citations
OpenAlex

Abstract

Chaotic behavior of laser oscillation is investigated by numerical calculation of quantum statistical equation of laser field, for the case of single mode and two-level systems. Relaxation-like distribution of laser field is expected from the quantum property of light. Further, coupled spin operators which are the base of atomic two-level system is investigated in expectation of chaotic behavior that might be origin of laser chaos.

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Quantum treatment of laser chaos is very complicated because adiabatic approximation is not applicable for the unstable systems and there exist dissipation and pumping of energy which are not defined as the closed hamiltonian systems. On the other hand, for atomic systems resonantly intreacting with radiation field, it is seen that chaotic atomic motion appears in the case of strong coupling between atoms and radiation or a certain detuning of frequencies.[1] That was investigated in the frame of semiclassical theory, which is based on Maxwel1-Bloch type equations, in which no pumping is introduced. Fully quantum treatment for both atoms and field are now tried for this closed systems, according to distribution function.

•Jul 18, 1988•0 citations
Chaotic behavior of laser oscillation is investigated by numerical calculation of quantum statistical equation of laser field, for the case of single mode and two-level systems. Relaxation-like distribution of laser field is expected from the quantum property of light. Further, coupled spin operators which are the base of atomic two-level system is investigated in expectation of chaotic behavior that might be origin of laser chaos.
Some quantum optical models possessing a transition from regular to chaotic dynamics and influence of 'quantum chaos' to photons statistics are investigated. Particular cases of semiclassical dynamics of a single atom and cooperative system of these atoms with (2j + 1) -- equidistant levels interacting with a quantized photon mode in an ideal cavity were considered. We take into account parametric pumping. Corresponding equations of motion are received without the rotation-wave approximation. It was demonstrated the scenario of transition to chaos, realized by doubling frequencies mechanism with growing of 'atom + field' coupling constant. Chaotic behavior and squeezing degree time dependence were obtained in computer simulations for coupling constant values of order of the atomic frequency, the calculation of the maximal Lyapunov coefficient for the dynamics of many two- level atoms interacting with photon cavity mode as function of 'atoms + field' interaction constant is performed. An influence of possible parametric instabilities of nonlinear media and effects of dissipation for atoms are discussed.
Some quantum optical models possessing a transition from regular to chaotic dynamics and influence of `quantum chaos' to squeezing are investigated. Particular cases of semiclassical dynamics of a single atom and cooperative system of these atoms with (2j + 1)--equidistant levels interacting with a quantized photon mode in an ideal cavity were considered. Corresponding equations of motion are received without the rotation-wave approximation. Chaotic behavior and squeezing degree time dependence were obtained in computer simulations for coupling constant values or order of the atomic frequency.
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 have studied the statistical and squeezing properties of the cavity light generated by a two-level laser. This optical system contains N two-level atoms available in a cavity coupled to a single-mode vacuum reservoir. They are pumped to the top level from the bottom level by means of the electron bombardment. Applying the steady-state solutions of the equations of evolution of the expectation values of the atomic operators and the quantum Langevin equation, we obtained the global and local photon statistics of the single-mode light beam. We have found that, for the two-level laser operating well above the threshold, the uncertainties in the plus and minus quadratures are equal and satisfy the minimum uncertainty relation. In view of this, we have identified the light generated by the laser operating well above threshold to be coherent. On the other hand, the light generated by the laser operating at threshold is found to be chaotic. From the obtained results, we have also observed that a large part of the local mean photon number, the local photon number variance, and the local quadrature variance are confined in a relatively narrow frequency interval.
The behavior of a pumped collection of identical three level atoms in which both the upper pair of levels and the lower pair of levels are coupled to resonant cavity-modes is analyzed. The cases of both incoherent pumping and coherent pumping are considered, and turn out to be qualitatively different. For the case of incoherent pumping, field oscillation can be sustained in only one of the modes, the behavior of the system being that of the familar three-level laser, with oscillation occuring between either the upper pair or lower pair of levels, depending on the relaxation constants. For the case of coherent pumping, however, oscillation can be obtained in both modes. Furthermore, this oscillation is different from that found in a parametric oscillator in the sense that, under certain conditions of operation, the phases of oscillation in the two cavities are independent. The potential application of such behavior is pointed out. (Author)
Quantum treatment of laser chaos is very complicated because adiabatic approximation is not applicable for the unstable systems and there exist dissipation and pumping of energy which are not defined as the closed hamiltonian systems. On the other hand, for atomic systems resonantly intreacting with radiation field, it is seen that chaotic atomic motion appears in the case of strong coupling between atoms and radiation or a certain detuning of frequencies.[1] That was investigated in the frame of semiclassical theory, which is based on Maxwel1-Bloch type equations, in which no pumping is introduced. Fully quantum treatment for both atoms and field are now tried for this closed systems, according to distribution function.