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arXiv:chao-dyn/9804041 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Light squeezing at the transition to quantum chaos

K. N. Alekseev, Jan Peřina

Published Apr 1, 1998• 9 citations
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Abstract

We investigate theoretically the dynamics of squeezed state generation in nonlinear systems possessing a transition from regular to chaotic dynamics in the limit of a large number of photons. As an example, the model of a kicked Kerr oscillator is considered. We show that at the transition to quantum chaos the maximum possible degree of squeezing increases exponentially in time, in contrast to the regular dynamics, where the degree of squeezing increases only powerwise in time. We demonstrate the one-to-one correspondence of the degree of squeezing and the value of the local Lyapunov instability rate in the corresponding classical chaotic system.

DOI
10.1103/physreve.57.4023

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We examine the dynamics of a wave packet that initially corresponds to a coherent state in the model of a quantum rotator excited by a periodic sequence of kicks. This model is the main model of quantum chaos and allows for a transition from regular behavior to chaotic in the classical limit. By doing a numerical experiment we study the generation of squeezed states in quasiclassical conditions and in a time interval when quantum-classical correspondence is well-defined. We find that the degree of squeezing depends on the degree of local instability in the system and increases with the Chirikov classical stochasticity parameter. We also discuss the dependence of the degree of squeezing on the initial width of the packet, the problem of stability and observability of squeezed states in the transition to quantum chaos, and the dynamics of disintegration of wave packets in quantum chaos.
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.
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.
In this paper we study the dynamics of a nonlinear quantum-optical system subjected to a periodic modulation in the form of kicks. The system consists of a nonabsorbing anharmonic medium related to optical bistability, a degenerate parametric amplifier with a classical pump field that is modulated by a periodic sequence of kicks, and the initial state is taken to be a squeezed vacuum state. Using the related SU(1,1) coherent states (which are squeezed vacuum states), we study and compare the quantum and classical dynamics of the system. The ``classical'' motion in this case means the motion projected onto the phase space defined by the parameter labeling the generalized coherent states. For certain values of the coupling constants, we obtain both regular and chaotic motion in the classical phase space. In the quantum dynamics of the system, the manifestation of the classical chaos turns out to be rather weak, at least in the regime numerically accessible to us. We study the time evolution of the initial-state population probability, the average photon number in the field, and the squeezing of the field. We also briefly discuss the level statistics of the evolution operator.