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

Dynamical features of a classically chaotic quantum system: Symmetry breaking and the disappearance of the squeezing effect

Rui-hua Xie, Gong-ou Xu

Published Aug 1, 1996• 14 citations
Publisher

Abstract

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.

DOI
10.1103/physreve.54.1402

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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 demonstrate the dependence of the entanglement dynamics on the global classical regime of regular, mixed and chaotic dynamics with initial squeezed coherent states.By squeezing the initial states, we are able to enhance or suppress the entanglement entropy of the dynamically generated quantum states relative to those produced via initial coherent states.This suggests the possibility of exploiting a judicious selection of initial squeezed states to create quantum states with enhanced entanglement entropy dynamically for the purpose of robust quantum information processing.
Quantum entanglement in the Hénon–Heiles system is analyzed using the squeezed coherent state. Enhancement of quantum entanglement via squeezing is explored in connection with chaotic and regular dynamics of the system. It is found that the entanglement enhancement via squeezing is implicitly linked to the local structure of the classical phase-space and it shows a clear quantum-classical correspondence. In particular, the entanglement enhancement via squeezing is found to be negligible for a highly chaotic orbit compared to the regular and weakly chaotic orbits, and shows a clear correspondence to the degree of chaos present in the classical initial condition. We believe that these results might be useful to develop efficient strategies to enhance entanglement in quantum systems.
Based on the dynamical symmetry group characterizing the integrability of classical as well as quantum mechanics, quantum dynamics with proper initial conditions was genuinely formulated, and analytical solutions in the form of soliton-like state evolving around a certain invariant torus were obtained. It has been shown that, in case the intrinsic size of the evolving quantum state is significantly smaller than the extent of its evolving orbit, the motion can be satisfactorily treated with classical approximation. Having demonstrated the quantum-classical correspondence of regular motion, the possibility to study quantum chaos on the basis dynamical symmetry breaking was briefly discussed.