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Physical Review A

Comment on ‘‘Quantum Zeno effect’’

L. E. Ballentine

Published May 1, 1991• 84 citations
Publisher

Abstract

The quantum Zeno effect is not a general characteristic of continuous measurements. In a recently reported experiment [Itano et al., Phys. Rev. A 41, 2295 (1990)], the inhibition of atomic excitation and deexcitation is not due to any ``collapse of the wave function,'' but instead is caused by a very strong perturbation due to the optical pulses and the coupling to the radiation field. The experiment should not be cited as providing empirical evidence in favor of the notion of ``wave-function collapse.''

DOI
10.1103/physreva.43.5165

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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.

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The quantum Zeno effect is the inhibition of the free evolution of a system when that system is subject to a measurement process. The authors of one recent experiment study, W. M. Itano et al., [Phys. Rev. A 41, 2295 (1990)] claimed a demonstration of the quantum Zeno effect. This was done by performing discontinuous atomic-level measurements on a coherently evolving two-level atomic stystem. The measurement was implemented using a pulsed laser strong enough to saturate the two-level atomic system. In this paper, we examine the simpler case where the measurement laser is continuously on and does not saturate the two-level atomic system. In contrast to previous treatments, we show certain parameter regimes wherein an effective state reduction does occur. We ascertain the experimental parameter regimes under which a measurement can be said to have been performed. We show that, in some regimes, fully efficient photon detection does not give good information about the atomic-level populations and hence no measurement has been performed. Throughout, we emphasize that the design of an atomic level-measurement device requires more than the analysis of a mechanism for photon detection or of coherence loss. We gain insight into the operation of a particular measurement process by following the selective evolution of various systems using the quantum-trajectories approach.

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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.

arXiv:quant-ph/0612187•Journal of Physics Conference Series•Nov 1, 2009•30 citations
The quantum Zeno effect is not a general characteristic of continuous measurements. In a recently reported experiment [Itano et al., Phys. Rev. A 41, 2295 (1990)], the inhibition of atomic excitation and deexcitation is not due to any collapse of the wave function,'' but instead is caused by a very strong perturbation due to the optical pulses and the coupling to the radiation field. The experiment should not be cited as providing empirical evidence in favor of the notion of 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.
The quantum Zeno effect is the inhibition of the free evolution of a system when that system is subject to a measurement process. The authors of one recent experiment study, W. M. Itano et al., [Phys. Rev. A 41, 2295 (1990)] claimed a demonstration of the quantum Zeno effect. This was done by performing discontinuous atomic-level measurements on a coherently evolving two-level atomic stystem. The measurement was implemented using a pulsed laser strong enough to saturate the two-level atomic system. In this paper, we examine the simpler case where the measurement laser is continuously on and does not saturate the two-level atomic system. In contrast to previous treatments, we show certain parameter regimes wherein an effective state reduction does occur. We ascertain the experimental parameter regimes under which a measurement can be said to have been performed. We show that, in some regimes, fully efficient photon detection does not give good information about the atomic-level populations and hence no measurement has been performed. Throughout, we emphasize that the design of an atomic level-measurement device requires more than the analysis of a mechanism for photon detection or of coherence loss. We gain insight into the operation of a particular measurement process by following the selective evolution of various systems using the quantum-trajectories approach.
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.