Quantum localization in the periodically kicked Rydberg atom : influence of noise

Abstract

The positively kicked one dimensional Rydberg atom is classically chaotic. One of the most prominent features of classically chaotic systems is the appearence of quantum localization, that is the quantum-mechanical suppression of chaotic diffusion. However, the classical behavior of such a system can be restored by the introduction of noise, that is coupling the system to a stochastic process.<br />In the present work we numerically study quantum localization in the kicked Rydberg atom, and the destruction thereof by noise. The noise model we focus on is pulse-train noise, that is randomizing the amplitudes and the frequency of the kicks. We show that, depending on the strength of the kicks, two distinct regimes exist. In the regime of strong kicks localization only builds up slowly and the contrast between classical and quantum-mechanical results is small. In this regime a small amount of noise is sufficient to destroy quantum localization completely. In the regime of weak kicks quantum localization is stronger and builds up faster. In this regime even large amounts of noise can not drive the system into full quantum-classical convergence. We give an estimation of the localization time, that is the time after which differences in the behavior of the classical and the quantum-mechanical system begin to build up, based on the Lyapunov exponent of the classical system. We show that the results we calculate are in good agreement with the numerical data. Finally we give a perspective on the possibilities of experimentally verifying quantum localization in the kicked Rydberg atom.