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arXiv:1201.2887 · Physical Review Letters

Preferred States of Decoherence under Intermediate System-Environment Coupling

Wen-ge Wang, Lewei He, Jiangbin Gong

Published Feb 17, 2012• 25 citations
arXivHTMLPDF

Abstract

The notion that decoherence rapidly reduces a superposition state to an incoherent mixture implicitly adopts a special representation, namely, the representation of preferred (pointer) states (PS). For weak or strong system-envrionment interaction, the behavior of PS is well known. Via a simple dynamical model that simulates a two-level system interacting with few other degrees of freedom as its environment, it is shown that even for intermediate system-environment coupling, approximate PS may still emerge from the coherent quantum dynamics of the whole system in the absence of any thermal averaging. The found PS can also continuously deform to expected limits for weak or strong system-environment coupling. Computational results are also qualitatively explained. The findings should be useful towards further understanding of decoherence and quantum thermalization processes.

DOI
10.1103/physrevlett.108.070403

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The notion that decoherence rapidly reduces a superposition state to an incoherent mixture implicitly adopts a special representation, namely, the representation of preferred (pointer) states (PS). For weak or strong system-envrionment interaction, the behavior of PS is well known. Via a simple dynamical model that simulates a two-level system interacting with few other degrees of freedom as its environment, it is shown that even for intermediate system-environment coupling, approximate PS may still emerge from the coherent quantum dynamics of the whole system in the absence of any thermal averaging. The found PS can also continuously deform to expected limits for weak or strong system-environment coupling. Computational results are also qualitatively explained. The findings should be useful towards further understanding of decoherence and quantum thermalization processes.
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Dynamics of a two-level system in the superposition of two dephasing environments with Ohmic-like spectral density is studied when considering initial system-environment correlations. The quantum system and one environment are treated as whole thermal equilibrium state, while the other environment is at thermal equilibrium state alone. Which environment the system interacts with is determined by an ancillary two-level system. When the system interacts with mixture of two sub-Ohmic environments, initial correlations can make the mixed dynamics non-Markovian. For two identical sub-Ohmic environments, if performing the projective measurement on the ancillary two-level system at the special time points, whatever the initial state of the system is, the coherence can be enhanced. For two different environments with βħω0/2>>, we get the approximate expression about the coherence of the system when measuring the ancillary two-level system.
Abstract In quantum mechanics, pointer states are eigenstates of the observable of the measurement apparatus that represent the possible positions of the display pointer of the equipment. The origin of this concept lies in attempts to fill the blanks in Everett’s relative-state interpretation, and to make it a fully valid description of physical reality. To achieve this, it was necessary to consider not only the main system interacting with the measurement apparatus (like von Neumann and Everett did) but also the role of the environment in eliminating correlations between different possible measurements when interacting with the measurement apparatus. The interaction of the environment with the main system (and the measurement apparatus) is the core of the decoherence theory, which followed Everett’s thesis. In this article, we review the measurement process according to von Neumann, Everett’s relative state interpretation, the purpose of decoherence and some of its follow-up until Wojciech Zurek’s primordial paper that consolidated the concept of pointer states, previously presented by Heinz Dieter Zeh. Employing a simple physical model consisting of a pair of two-level systems—one representing the main system, the other the measurement apparatus—and a thermal bath—representing the environment—we show how pointer states emerge, explaining its contributions to the question of measurement in quantum mechanics, as well as its limitations. Finally, we briefly show some of its consequences. This paper is accessible to readers with elementary knowledge about quantum mechanics, on the level of graduate courses.
Quantum decoherence is a physical process resulting from a system’s entanglement with an environment. This chapter examines the explanatory wealth of decoherence when brought to bear on foundational issues such as the question of why certain measurement bases seem to be preferred by nature – including the pointer basis of measuring apparatuses – the old familiar measurement problem, and the emergence of classicality. Decoherence satisfactorily explains the behavior of the ammonia molecule. Decoherence introduces no additional nonlinearity but “simply takes real, inevitable, interaction with external degrees of freedom to bear in the Hamiltonian”. The basis-specific nature of decoherence will allow for a satisfying explanation to one of quantum mechanics’ oldest mysteries: that of the pointer basis. The basis-specific nature of decoherence will allow for a satisfying explanation to one of quantum mechanics’ oldest mysteries: that of the pointer basis.
The purpose of the present paper is to derive the pointer states of a macro-object using a simple perturbation method. We study the model Hamiltonian involving the weak interaction between the center of mass and its environment. The main conclusion is that the pointer states emerge as the small part of the total state vector when the interaction Hamiltonian is not dominant: the degrees of freedom being at the center of interaction can be localized. In the weak interaction case, if the disappearance of the energy contribution from the off-diagonal terms is caused by the decoherence, it threatens the conservation law. In this study, however, the energy conservation reasonably holds, since the non-classical (i.e., normal quantum) states give main contribution to it. The emergence of the pointer states also implies the special initial state in which the localized state makes the deep well of the potential. In the result, the unitary time evolution of a pointer state is very different from that of the majority of the original state vector of the total system.