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Frequent observations accelerate decay: The anti-Zeno effect

Kofman, A G, Kurizki, G

Published Jan 1, 2001• 24 citations
OpenAlex

Abstract

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).

Related papers

Frequent Observations Accelerate Decay: The anti-Zeno Effect

A. G. Kofman, G. Kurizki

Abstract The quantum Zeno effect (QZE) is the striking prediction that the decay of any unstable quan­ tum state can be inhibited by sufficiently frequent observations (measurements). The consensus

arXiv:quant-ph/0102002•Zeitschrift für Naturforschung A•Feb 1, 2001•29 citations

When can measurements inhibit decay?

Abraham G. Kofman, Gershon Kurizki

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.

Quantum Electronics and Laser Science Conference•Nov 13, 2002•0 citations

5 Quantum Zeno effect by general measurements

Kazuki Koshino, Akira Shimizu

It was predicted that frequently repeated measurements on an unstable state may alter the decay rate of the state. This is called the quantum Zeno effect (QZE) or the anti-Zeno effect (AZE), depending on whether the decay is suppressed or enhanced. In conventional theories of the QZE and AZE, effects of measurements are simply described by the projection postulate, assuming that each measurement is an instantaneous and ideal one. However, real measurements are not instantaneous and ideal. For the QZE and AZE by such general measurements, interesting and surprising features have recently been revealed, which we review in this article. The results are based on the quantum measurement theory, which is also reviewed briefly. As a typical model, we consider a continuous measurement of the decay of an excited atom by a photodetector that detects a photon emitted from the atom upon decay. This measurement is an indirect negative-result one, for which the curiosity of the QZE and AZE is emphasized. It is shown that the form factor is renormalized as a backaction of the measurement, through which the decay dynamics is modified. In a special case of the flat response, where the detector responds to every photon mode with an identical response time, results of the conventional theories are reproduced qualitatively. However, drastic differences emerge in general cases where the detector responds only to limited photon modes. For example, against predictions of the conventional theories, the QZE or AZE may take place even for states that exactly follow the exponential decay law. We also discuss relation to the cavity quantum electrodynamics.

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Conditions for anti-Zeno-effect observation in free-space atomic radiative decay

Emmanuel Lassalle, C. Champenois, Brian Stout +2 more

Frequent measurements can modify the decay of an unstable quantum state with respect to the free dynamics given by Fermi's golden rule. In a landmark article [A. G. Kofman and G. Kurizki, Nature (London) 405, 546 (2000)], Kofman and Kurizki concluded that in quantum decay processes, acceleration of the decay by frequent measurements, called the quantum anti-Zeno effect (AZE), appears to be ubiquitous, while its counterpart, the quantum Zeno effect, is unattainable. However, up to now there have been no experimental observations of the AZE for atomic radiative decay (spontaneous emission) in free space. In this work, making use of analytical results available for hydrogenlike atoms, we find that in free space, only non-electric-dipole transitions should present an observable AZE, revealing that this effect is consequently much less ubiquitous than first predicted. We then propose an experimental scheme for AZE observation, involving the electric quadrupole transition between ${D}_{5/2}$ and ${S}_{1/2}$ in the alkali-earth ions ${\mathrm{Ca}}^{+}$ and ${\mathrm{Sr}}^{+}$. The proposed protocol is based on the stimulated Raman adiabatic passage technique, which acts like a dephasing quasimeasurement.

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Gershon Kurizki, Goren Gordon

In a strange dream, Henry is coherently transported towards his bride down the aisle. But just as a small portion of him arrives next to her, that portion disappears in a flash of light caused by a snapshot! Henry keeps trying to be united with his bride, but repeated snapshots cause Henry’s collapse to being far away from her. This dream illustrates the quantum Zeno effect (QZE): if a measurement collapses the quantum state with high probability to the initial state, then frequent repeated measurements can almost stop the change of the quantum state. Yet less frequent measurements cause the opposite, anti-Zeno effect (AZE), whereby change or decay increases. Thus, decay is controllable. These effects confirm Zeno’s argument that change is an illusion, as it is up to the observer to prevent or induce it by appropriate observation. The appendix to this chapter explains the QZE for coherent and decay processes.

Oxford University Press eBooks•Apr 16, 2020•0 citations

Real measurements and the quantum Zeno effect

Julius Ruseckas, B. Kaulakys

In 1977, Mishra and Sudarshan [J. Math. Phys. 18, 756 (1977)] showed that an unstable particle would never be found decayed while it was continuously observed. They called this effect the quantum Zeno effect (or paradox). Later it was realized that the frequent measurements could also accelerate the decay (quantum anti-Zeno effect). In this paper, we investigate the quantum Zeno effect using the definite model of the measurement. We take into account the finite duration and the finite accuracy of the measurement. A general equation for the jump probability during the measurement is derived. We find that the measurements can cause inhibition (quantum Zeno effect) or acceleration (quantum anti-Zeno effect) of the evolution, depending on the strength of the interaction with the measuring device and on the properties of the system. However, the evolution cannot be fully stopped.

arXiv:quant-ph/0105138•Physical Review A•May 8, 2001•19 citations
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).
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.
It was predicted that frequently repeated measurements on an unstable state may alter the decay rate of the state. This is called the quantum Zeno effect (QZE) or the anti-Zeno effect (AZE), depending on whether the decay is suppressed or enhanced. In conventional theories of the QZE and AZE, effects of measurements are simply described by the projection postulate, assuming that each measurement is an instantaneous and ideal one. However, real measurements are not instantaneous and ideal. For the QZE and AZE by such general measurements, interesting and surprising features have recently been revealed, which we review in this article. The results are based on the quantum measurement theory, which is also reviewed briefly. As a typical model, we consider a continuous measurement of the decay of an excited atom by a photodetector that detects a photon emitted from the atom upon decay. This measurement is an indirect negative-result one, for which the curiosity of the QZE and AZE is emphasized. It is shown that the form factor is renormalized as a backaction of the measurement, through which the decay dynamics is modified. In a special case of the flat response, where the detector responds to every photon mode with an identical response time, results of the conventional theories are reproduced qualitatively. However, drastic differences emerge in general cases where the detector responds only to limited photon modes. For example, against predictions of the conventional theories, the QZE or AZE may take place even for states that exactly follow the exponential decay law. We also discuss relation to the cavity quantum electrodynamics.
Frequent measurements can modify the decay of an unstable quantum state with respect to the free dynamics given by Fermi's golden rule. In a landmark article [A. G. Kofman and G. Kurizki, Nature (London) 405, 546 (2000)], Kofman and Kurizki concluded that in quantum decay processes, acceleration of the decay by frequent measurements, called the quantum anti-Zeno effect (AZE), appears to be ubiquitous, while its counterpart, the quantum Zeno effect, is unattainable. However, up to now there have been no experimental observations of the AZE for atomic radiative decay (spontaneous emission) in free space. In this work, making use of analytical results available for hydrogenlike atoms, we find that in free space, only non-electric-dipole transitions should present an observable AZE, revealing that this effect is consequently much less ubiquitous than first predicted. We then propose an experimental scheme for AZE observation, involving the electric quadrupole transition between D5/2{D}_{5/2}D5/2​ and S1/2{S}_{1/2}S1/2​ in the alkali-earth ions Ca+{\mathrm{Ca}}^{+}Ca+ and Sr+{\mathrm{Sr}}^{+}Sr+. The proposed protocol is based on the stimulated Raman adiabatic passage technique, which acts like a dephasing quasimeasurement.
In a strange dream, Henry is coherently transported towards his bride down the aisle. But just as a small portion of him arrives next to her, that portion disappears in a flash of light caused by a snapshot! Henry keeps trying to be united with his bride, but repeated snapshots cause Henry’s collapse to being far away from her. This dream illustrates the quantum Zeno effect (QZE): if a measurement collapses the quantum state with high probability to the initial state, then frequent repeated measurements can almost stop the change of the quantum state. Yet less frequent measurements cause the opposite, anti-Zeno effect (AZE), whereby change or decay increases. Thus, decay is controllable. These effects confirm Zeno’s argument that change is an illusion, as it is up to the observer to prevent or induce it by appropriate observation. The appendix to this chapter explains the QZE for coherent and decay processes.
In 1977, Mishra and Sudarshan [J. Math. Phys. 18, 756 (1977)] showed that an unstable particle would never be found decayed while it was continuously observed. They called this effect the quantum Zeno effect (or paradox). Later it was realized that the frequent measurements could also accelerate the decay (quantum anti-Zeno effect). In this paper, we investigate the quantum Zeno effect using the definite model of the measurement. We take into account the finite duration and the finite accuracy of the measurement. A general equation for the jump probability during the measurement is derived. We find that the measurements can cause inhibition (quantum Zeno effect) or acceleration (quantum anti-Zeno effect) of the evolution, depending on the strength of the interaction with the measuring device and on the properties of the system. However, the evolution cannot be fully stopped.