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arXiv:quant-ph/0501097 · IEEE Transactions on Nanotechnology

Decoherence in Quantum Systems

Robert F. O’Connell

Published Jan 1, 2005• 6 citations
arXivHTMLPDF

Abstract

We discuss various definitions of decoherence and how it can be measured. We compare and contrast decoherence in quantum systems with an infinite number of eigenstates (such as the free particle and the oscillator) and spin systems. In the former case, we point out the essential difference between assuming "entanglement at all times" and entanglement with the reservoir occuring at some initial time. We also discuss optimum calculational techniques in both arenas.

DOI
10.1109/tnano.2004.840158

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We discuss various definitions of decoherence and how it can be measured. We compare and contrast decoherence in quantum systems with an infinite number of eigenstates (such as the free particle and the oscillator) and spin systems. In the former case, we point out the essential difference between assuming "entanglement at all times" and entanglement with the reservoir occuring at some initial time. We also discuss optimum calculational techniques in both arenas.
Entanglement is a fundamental concept in quantum mechanics. In this review, we study various aspects of coherence and entanglement, illustrated by several examples. We relate the concepts of loss of coherence and disentanglement, via a model of two two-level atoms in different types of reservoir, including cases of both independent and common baths. Finally, we relate decoherence and disentanglement, by focusing on the sudden death of the entanglement and the dependence of the death time with the distance of our initial condition from the decoherence-free subspace. In particular, we study the sudden death of the entanglement in a two-atom system with a common reservoir.
Throughout this project, the case of a composite system formed by a harmonic oscillator and a two-state atom will be studied; considering both affect each other as \na consequence of a Jaynes-Cummings interaction, and being both coupled to different reservoirs that are assumed to be independent from each other. The effects \nof the decoherence in the evolution of the populations and coherences will be analyzed; specifically the energy dissipation and the coherence loss, as well as the stationary states and the relevance of the Jaynes-Cummings interaction. Finally, the \nsolution of stochastic equations will be analyzed, particularly the evolution of the \nexpectation value of the position operator for the harmonic oscilator; for the case of \nsimultaneous measurements in both subsystems, as well as for a measurement in \nthe harmonic oscillator when the two-state atom undergoes a decoherence process.
Decoherence is the suppression of the interference of quantum states. It plays important roles in the study of the quantum-classical transition. It is also the major obstacle in the implementation of various schemes of quantum computers. Decoherence can be affected by many factors. The interactions between quantum systems of interest and dissipative environments cause the extensively studied environment-induced-decoherence. Decoherence can also occur as the result of a temperature effect. A recent experiment investigated the engineering of decoherence, which involves applying an external field to the quantum system. In this thesis, we study the effect of an external field on decoherence in the case of a harmonic oscillator coupled to a heat bath by calculating its contribution to the attenuation coefficient, which is a measure of decoherence in coordinate space and involves directly observable probability distributions. It is found that, while non-random external force does not result in decoherence, a random external force can lead to intrinsic decoherence that does not require a dissipative environment. The attenuation coefficient for a free harmonic oscillator in a dissipative environment is also calculated using the solution of the initial value quantum Langevin equation. One of the key results obtained is that ”decoherence without dissipation” does not occur in the case of a free harmonic oscillator, in contrast to the case of a free particle.