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Journal of Physics Conference Series

Hamiltonian flows, short-time propagators and the quantum Zeno effect

Maurice A. de Gosson, Basil J. Hiley

Published Apr 14, 2014• 1 citation
Publisher

Abstract

In a recent paper we have examined the short-time propagator for the Schrödinger equation of a point source. An accurate expression modulo Δ t 2 for the propagator showed that it was independent of the quantum potential implying that the quantum motion is classical for very short times. In this paper we apply these results to the experiment of Itano, Heinzen, Bollinger and Wineland which demonstrates the quantum Zeno effect in beryllium. We show that the transition is inhibited because the applied continuous wave radiation suppresses the quantum potential necessary for the transition to occur. This shows there is no need to appeal to wave function collapse.

DOI
10.1088/1742-6596/504/1/012027

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In a recent paper we have examined the short-time propagator for the Schrödinger equation of a point source. An accurate expression modulo Δ t 2 for the propagator showed that it was independent of the quantum potential implying that the quantum motion is classical for very short times. In this paper we apply these results to the experiment of Itano, Heinzen, Bollinger and Wineland which demonstrates the quantum Zeno effect in beryllium. We show that the transition is inhibited because the applied continuous wave radiation suppresses the quantum potential necessary for the transition to occur. This shows there is no need to appeal to wave function collapse.
Itano and co-workers [Wayne M. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, Phys. Rev. A 41, 2295 (1990)] have recently reported the experimental verification of the quantum Zeno effect, which is the inhibition of a quantum transition by frequent measurements. In this article, we offer an alternative interpretation of the quantum Zeno effect. We show that an analysis of the dynamics of the full three-level system gives the same result. There is no need to assume explicitly that the wave function has collapsed, nor even to assume that an ideal measurement has been made. In addition, we differentiate between what has been referred to as the quantum Zeno effect and what has been termed the quantum Zeno paradox. The former is the inhibition of induced transitions, and the latter is the, as yet experimentally unobserved, inhibition of spontaneous decay. Our interpretation, which emphasizes the ``measurement''-induced interruption of atomic-state coherences as the cause of inhibited quantum transitions, suggests a resolution to the quantum Zeno paradox. The theoretical limit of continuous observation is discussed.
As of October 2006, there were approximately 535 citations to the seminal 1977 paper of Misra and Sudarshan that pointed out the quantum Zeno paradox (more often called the quantum Zeno effect). In simple terms, the quantum Zeno effect refers to a slowing down of the evolution of a quantum state in the limit that the state is observed continuously. There has been much disagreement as to how the quantum Zeno effect should be defined and as to whether it is really a paradox, requiring new physics, or merely a consequence of "ordinary" quantum mechanics. The experiment of Itano, Heinzen, Bollinger, and Wineland, published in 1990, has been cited around 347 times and seems to be the one most often called a demonstration of the quantum Zeno effect. Given that there is disagreement as to what the quantum Zeno effect is , there naturally is disagreement as to whether that experiment demonstrated the quantum Zeno effect. Some differing perspectives regarding the quantum Zeno effect and what would constitute an experimental demonstration are discussed.
The term 'quantum Zeno paradox' or 'quantum Zeno effect' refers to the slowing down of the evolution of a quantum system as it is observed more and more frequently.In 1977, Misra and Sudarshan gave a theoretical demonstration of its existence.There has been disagreement regarding the definition of the effect and whether it is really a paradox, requiring new physics, or a consequence of ordinary quantum mechanics.The experiment of Itano, Heinzen, Bollinger and Wineland, published in 1990, is the one most often called a demonstration of the quantum Zeno effect.Some different interpretations are discussed.