Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Decoherence and the quantum-classical limit in phase space (Invited Paper)

L. Davidovich, Fabricio Toscano, R. L. de Matos Filho

Published May 23, 2005• 0 citations

Abstract

We discuss the emergence of the classical description from quantum mechanics for chaotic systems. We consider a specific model, which corresponds to an ion trapped in a harmonic potential and submitted to a sequence of laser pulses: the kicked harmonic oscillator, under conditions that lead to chaotic behavior for the classical system. We show that noise plays an essential role in the transition from quantum to classical behavior. This transition is described in terms of the separation between the classical phase space distribution and the Wigner function corresponding to the quantum system, obtained by integrating over the whole phase space the magnitude of the difference between the two distributions. It is shown that, in the semiclassical limit, this separation is governed by a single parameter, which depends on the diffusion coefficient, the Lamb-Dicke parameter, and the kick strength. The Lamb-Dicke parameter plays the role of a dimensioneless Planck constant. As this parameter goes to zero, we show that both distributions remain close together for all times.

DOI: 10.1117/12.609100

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