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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Dynamical evolution of squeezing and antibunching effects in a quantum chaotic system: The three-level Lipkin model

Rui-hua Xie, Gong-ou Xu

Published Aug 1, 1996• 6 citations
Publisher

Abstract

Time evolution of squeezing and antibunching effects in a nuclear model known as the three-level Lipkin model is analyzed. The two effects occur in the regime of classically regular motion, but disappear in the regime of classically chaotic motion, which is similar to that obtained in a spin-boson model (another quantum chaotic system). \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreve.54.2132

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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jun 1, 1996•5 citations
Time evolution of squeezing and antibunching effects in a nuclear model known as the three-level Lipkin model is analyzed. The two effects occur in the regime of classically regular motion, but disappear in the regime of classically chaotic motion, which is similar to that obtained in a spin-boson model (another quantum chaotic system). \textcopyright{} 1996 The American Physical Society.
Dynamical symmetry and squeezing effect have been investigated in a classically chaotic quantum system [M. Ku\ifmmode \acute{s}\else \'{s}\fi{}, Phys. Rev. Lett. 54, 1343 (1985)] when it is restricted to the following initial condition: the atom in its SU(2) coherent state and the field in the vacuum state. In the regime of classically regular motion, dynamical symmetry and squeezing effects have been exposed under proper choice of the atomic coherent state; but, in that of classically chaotic motion, the symmetry is destroyed thoroughly and the squeezing effect disappears. \textcopyright{} 1996 The American Physical Society.
We study spin squeezing, an intrinsically quantum property, in the quantum kicked top model exhibiting chaotic behaviours in the classical limit. We show that spin squeezing can reveal the underlying chaotic and regular structures in phase space given by a sphere with a unit radius, namely, spin squeezing vanishes after a very short time for an initial spin coherent state centred in a chaotic region of the phase space, whereas spin squeezing occurs over a long period of time for the coherent state centred in an elliptic fixed point. We also study the distribution of the mean spin directions when quantum dynamics take places and give a comparison between the dynamics of spin squeezing and quantum entanglement.
Making use of appropriate quantum-classical correspondence we have examined the differential behavior of regular and chaotic trajectories in terms of quantum decoherence, the evolution of average quantities, and variances and entropy in a driven double-well oscillator in contact with the surroundings. Our numerical analysis has shown that even on a short time scale the decay of the average quantum coherence is multiexponential. While the onset of decoherence is much faster for a regular trajectory, the decay is faster asymptotically for a chaotic trajectory compared to a regular one. The coupling of the system to the environment turns chaotic in a regular evolution. The environment also affects the evolution of quantum variances for a regular trajectory almost from the beginning, while it has an insignificant effect on chaotic evolution up to a time after which, for both trajectories, noise in the quantum variances exhibits remarkable suppression, although fluctuations of the reservoir modes, in general, tend to increase the level of variances. We identify three stages of quantum evolution; a short decoherence regime followed by a Liouville flow, the latter regime being dominated by the classical curvature of the potential. This is the regime at which growth of entropy or quantum variances is exponential, the rate being determined by the classical largest Lyapunov exponent. The last stage is the irreversible flow dominated by diffusion which suppresses noises in the quantum variances. \textcopyright{} 1996 The American Physical Society.