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arXiv:quant-ph/0306002 · Physical Review A

Intrinsic decoherence dynamics in smooth Hamiltonian systems: Quantum-classical correspondence

Jiangbin Gong, Paul W. Brumer

Published Aug 1, 2003• 50 citations
arXivHTMLPDF

Abstract

A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences between the classical and quantum decoherence dynamics of an initial quantum state are exposed using both analytical and computational results. In particular, the classicality of early-time intrinsic decoherence dynamics is explored analytically using a second-order perturbative treatment, and an interesting connection between decoherence rates and the stability nature of classical trajectories is revealed in a simple approximate classical theory of intrinsic decoherence dynamics. The results offer deeper insights into decoherence, dynamics of quantum entanglement, and quantum chaos.

DOI
10.1103/physreva.68.022101

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A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences between the classical and quantum decoherence dynamics of an initial quantum state are exposed using both analytical and computational results. In particular, the classicality of early-time intrinsic decoherence dynamics is explored analytically using a second-order perturbative treatment, and an interesting connection between decoherence rates and the stability nature of classical trajectories is revealed in a simple approximate classical theory of intrinsic decoherence dynamics. The results offer deeper insights into decoherence, dynamics of quantum entanglement, and quantum chaos.
The dynamical properties of quantum entanglement in the Dicke model without rotating-wave approximation are investigated in terms of the reduced-density linear entropy. The characteristic time of decoherence process in the early-time evolution is numerically obtained and it is shown that the characteristic time decreases as the coupling parameter increases. The mean entanglement, which is defined to be averaged over time, is employed to describe the influences of both quantum phase transition and corresponding classical chaos on the behavior of entanglement. For a given energy, initial conditions are taken to be minimum uncertainty wave packets centered at regular and chaotic regions of the classical phase space. It is shown that the entanglement has a distinct change at the quantum phase transition, and that the entanglement for regular initial conditions is smaller than that for chaotic ones in the case of weak coupling, while it fluctuates with small amplitude in strong coupling and for chaotic initial conditions.
We show that the rate of increase of von Neumann entropy computed from the reduced density matrix of an open quantum system is an excellent indicator of the dynamical behavior of its classical hamiltonian counterpart. In decohering quantum analogs of systems which exhibit classical hamiltonian chaos entropy production rate quickly tends to a constant which is given by the sum of the positive Lyapunov exponents, and falls off only as the system approaches equilibrium. By contrast, integrable systems tend to have entropy production rate which decreases as t^{-1} well before equilibrium is attained. Thus, behavior of quantum systems in contact with the environment can be used as a test to determine the nature of their hamiltonian evolution.
Next, quantum-classical correspondence in intrinsic decoherence dynamics is examined via purities and reduced density matrices in both the position and energy representations. Dependence of the correspondence on the nature of the coupling potentials and on the initial conditions are discussed. Decoherence effects on quantum and classical dynamics in reactive scattering problems are investigated. Through the study of dynamics of the isotopic analogues of the collinear H + H2 reaction and transmission over simple one-dimensional barrier potentials, the role of decoherence in improving quantum-classical correspondence is identified with suppressing resonance and tunnelling. Finally, the efficiency of 1+3 photon phase control in the presence of decoherence effects phase is carefully examined in several model cases which include from a population inversion in a two-level bound system to IBr photodissociation. Further, the ways to overcome the control loss caused by dephasing are discussed.