Decoherence and Measurement in Open Quantum Systems

Abstract

We review results of a recently developed model of a microscopic quantum system interacting with the macroscopic world components which are modeled by collections of bosonic modes. The interaction is via a general operator $Λ$ of the system, coupled to the creation and annihilation operators of the environment modes. We assume that in the process of a nearly instantaneous quantum measurement, the function of the environment involves two distinct parts: the pointer and the bath. Interaction of the system with the bath leads to decoherence such that the system and the pointer both evolve into a statistical mixture state described by the density matrix such that the system is in one of the eigenstates of $Λ$ with the correct quantum mechanical probability, whereas the expectation values of pointer operators retain amplified information on that eigenstate. We argue that this process represents the initial step of a quantum measurement. Calculation of the elements of the reduced density matrix of the system and pointer is carried out exactly, and time dependence of decoherence is identified. We discuss general implications of our model of energy-conserving coupling to a heat bath for processes of adiabatic quantum decoherence. We also evaluate changes in the expectation values of certain pointer operators and suggest that these can be interpreted as macroscopic indicators of the measurement outcome.