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arXiv:chao-dyn/9803038 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Squeezed state dynamics of kicked quantum systems

Bambi Hu, Baowen Li, Jie Liu, Ji‐Lin Zhou

Published Aug 1, 1998• 18 citations
arXivHTMLPDF

Abstract

We study kicked quantum systems by using the squeezed state approach. Taking the kicked quantum harmonic oscillator as an example, we demonstrate that chaos in an underlying classical system can be enhanced as well as suppressed by quantum fluctuations. Three different energy diffusions are observed in the kicked quantum harmonic oscillator, namely, localization, linear diffusion, and quadratic diffusion.

DOI
10.1103/physreve.58.1743

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We study kicked quantum systems by using the squeezed state approach. Taking the kicked quantum harmonic oscillator as an example, we demonstrate that chaos in an underlying classical system can be enhanced as well as suppressed by quantum fluctuations. Three different energy diffusions are observed in the kicked quantum harmonic oscillator, namely, localization, linear diffusion, and quadratic diffusion.
Control over the quantum dynamics of chaotic kicked rotor systems is demonstrated. Specifically, control over a number of quantum coherent phenomena is achieved by a simple modification of the kicking field. These include the enhancement of the dynamical localization length, the introduction of classical anomalous diffusion assisted control for systems far from the semiclassical regime, and the observation of a variety of strongly nonexponential line shapes for dynamical localization. The results provide excellent examples of controlled quantum dynamics in a system that is classically chaotic and offer opportunities to explore quantum fluctuations and correlations in quantum chaos.
We present a quantum mapping for the kicked harmonic oscillator which relates the probability amplitudes of the undriven oscillator's eigenfunctions over successive kicks.We show how for various kick strengths the wave functions lave a linear energy increase up to the limit imposed b y the finite matrix size of the evolution matrix.We use this linear energy increase to define a quantum diffusion-like coefficient.We also show how this increase in energy causes the wave functions to spread out and become diifuse with fittle or no discernible structure.This model may serve as a paradigm for the study of quantum chaos.
We examine the dynamics of a wave packet that initially corresponds to a coherent state in the model of quantum kicked rotator. This main model of quantum chaos, which allows for a transition from regular to to chaotic behavior in the classical limit, may be realized in experiments with cold atoms. We study the generation of squeezed states in the quasiclassical limit and in a time interval when quantum-classical correspondence is yet well-defined. We find that the degree of squeezing depends on the degree of local instability in the system and increases with the Chirikov parameter of stochasticity. We discuss the dependence of the degree of squeezing on the initial width of the packet, the problems of stability and observability of squeezed states at the transition to quantum chaos, as well as the dynamics of wave packet destruction.
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.