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Physical Review A

Continuous and pulsed observations in the quantum Zeno effect

Lawrence S. Schulman

Published Mar 1, 1998• 141 citations
Publisher

Abstract

The usual formulation of the quantum Zeno effect (QZE) uses a sequence of rapid observations to prevent change. The same effect can be achieved with continuous observation. For partial inhibition of change we provide a quantitative relation between pulsed (at intervals $\ensuremath{\delta}t$) and continuous (with response time ${\ensuremath{\tau}}_{O}$) observations: the slowdown is the same for $\ensuremath{\delta}t=4{\ensuremath{\tau}}_{O}.$ Including the continuous observer in the Hamiltonian gives an alternative view of the QZE, showing the appropriateness of the name ``dominated time evolution.'' Finally, the variation on the QZE in which a nonconstant sequence of projections can force change is also shown to be achievable by time-varying continuous observation.

DOI
10.1103/physreva.57.1509

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The usual formulation of the quantum Zeno effect (QZE) uses a sequence of rapid observations to prevent change. The same effect can be achieved with continuous observation. For partial inhibition of change we provide a quantitative relation between pulsed (at intervals \ensuremathδt\ensuremath{\delta}t\ensuremathδt) and continuous (with response time \ensuremathτO{\ensuremath{\tau}}_{O}\ensuremathτO​) observations: the slowdown is the same for \ensuremathδt=4\ensuremathτO.\ensuremath{\delta}t=4{\ensuremath{\tau}}_{O}.\ensuremathδt=4\ensuremathτO​. Including the continuous observer in the Hamiltonian gives an alternative view of the QZE, showing the appropriateness of the name ``dominated time evolution.'' Finally, the variation on the QZE in which a nonconstant sequence of projections can force change is also shown to be achievable by time-varying continuous observation.
The quantum Zeno effect (QZE) is the striking prediction that the decay of any unstable quantum state can be inhibited by sufficiently frequent observations (measurements). The consensus opinion has upheld the QZE as a general feature of quantum mechanics, which should lead to the inhibition of any decay. The claim of QZE generality hinges on the assumption that successive observations can in principle be made at time intervals too short for the system to change appreciably. However, this assumption and the generality of the QZE have scarcely been investigated thus far. We have addressed these issues by showing that (i) the QZE is principally unattainable in radiative or radioactive decay, because the required measurement rates would cause the system to disintegrate; (ii) decay acceleration by frequent measurements (the anti-Zeno effect -- AZE) is much more ubiquitous than its inhibition. The AZE is shown to be observable as the enhancement of tunneling rates (e.g., for atoms trapped in ramped-up potentials or in current-swept Josephson junctions), fluorescence rates (e.g., for Rydberg atoms perturbed by noisy optical fields) and photon depolarization rates (in randomly modulated Pockels cells).
The quantum Zeno effect (QZE) introduced by Misra and Sudarshan consists in the ability of repeated measurements to inhibit or slow down unitary evolution. Its fundamental status in quantum mechanics has long been firmly established, but its much broader context, in-depth understanding and its applications are growing at a faster pace than ever before. Over the years, there have been several pivotal developments that have made the QZE and related effects the basic paradigms underlying the control of evolution in quantum systems:
Summary form only given. The quantum Zeno effect (QZE) is the striking possibility of inhibiting the decay of an unstable quantum state by sufficiently frequent measurements. This effect is currently believed to be universal, even though it has only been observed for oscillations between discrete states. Recently we showed that both the QZE and the inverse (anti-) Zeno effect (AZE) can be observed on spontaneous decay in cavities. We develop a general theory of evolution of quantum systems in the presence of frequent measurements. We consider both the ideal case of instantaneous projections of the wave function to the initial state and some possible measurement schemes. The considerations imply the impossibility of the continuous-observation limit necessary to stop quantum evolution (the quantum Zeno paradox). Indeed, this limit leads to an unbounded increase of the energy fluctuations of the system, which would cause the system to disintegrate. The present theory describes different measurement effects, including the QZE and AZE, and allows us to obtain the general criteria of their validity. In particular, we show that the AZE, rather than the QZE, is achievable for spontaneous decay of atoms in free space.