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Physical Review A

Quantum Zeno effect

Wayne M. Itano, Daniel J. Heinzen, J. J. Bollinger, David J. Wineland

Published Mar 1, 1990• 1,185 citations
Publisher

Abstract

The quantum Zero effect is the inhibition of transitions between quantum states by frequent measurements of the state. The inhibition arises because the measurement causes a collapse (reduction) of the wave function. If the time between measurements is short enough, the wave function usually collapses back to the initial state. We have observed this effect in an rf transition between two $^{9}$${\mathrm{Be}}^{+}$ ground-state hyperfine levels. The ions were confined in a Penning trap and laser cooled. Short pulses of light, applied at the same time as the rf field, made the measurements. If an ion was in one state, it scattered a few photons; if it was in the other, it scattered no photons. In the latter case the wave-function collapse was due to a null measurement. Good agreement was found with calculations.

DOI
10.1103/physreva.41.2295

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Laser-cooled ions stored in Penning traps are essentially free from collisions and other perturbations that could cause relaxations. This, and the fact that their energy levels can easily be manipulated with rf and laser radiation, makes them well suited for demonstrating certain aspects of quantum measurement theory. The quantum Zeno effect is the inhibition of transitions between states by frequent measurements.1 We have observed this effect in a 9Be+ ground-state rf transition. The measurements are short pulses of light. If the ion is in one state, it scatters a few photons; if it is in the other, it scatters no photons. In the latter case the wavefunction collapse is due to a null measurement.2 The dynamics of this system are similar to those which are predicted to lead to nonexponential spontaneous decay at short times.

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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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Comment on ‘‘Quantum Zeno effect’’

L. E. Ballentine

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.''

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The quantum Zero effect is the inhibition of transitions between quantum states by frequent measurements of the state. The inhibition arises because the measurement causes a collapse (reduction) of the wave function. If the time between measurements is short enough, the wave function usually collapses back to the initial state. We have observed this effect in an rf transition between two ^{9}$${\mathrm{Be}}^{+} ground-state hyperfine levels. The ions were confined in a Penning trap and laser cooled. Short pulses of light, applied at the same time as the rf field, made the measurements. If an ion was in one state, it scattered a few photons; if it was in the other, it scattered no photons. In the latter case the wave-function collapse was due to a null measurement. Good agreement was found with calculations.
Laser-cooled ions stored in Penning traps are essentially free from collisions and other perturbations that could cause relaxations. This, and the fact that their energy levels can easily be manipulated with rf and laser radiation, makes them well suited for demonstrating certain aspects of quantum measurement theory. The quantum Zeno effect is the inhibition of transitions between states by frequent measurements.1 We have observed this effect in a 9Be+ ground-state rf transition. The measurements are short pulses of light. If the ion is in one state, it scatters a few photons; if it is in the other, it scatters no photons. In the latter case the wavefunction collapse is due to a null measurement.2 The dynamics of this system are similar to those which are predicted to lead to nonexponential spontaneous decay at short times.
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 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.''
Continuous and pulsed quantum Zeno effects were observed using a 87Rb Bose-Einstein condensate. Oscillations between two ground hyperfine states of a magnetically trapped condensate, externally driven at a transition rate omega(R), were suppressed by destructively measuring the population in one of the states with resonant light. The suppression of the transition rate in the two-level system was quantified for pulsed measurements with a time interval deltat between pulses and continuous measurements with a scattering rate gamma. We observe that the continuous measurements exhibit the same suppression in the transition rate as the pulsed measurements when gammadeltat=3.60(0.43), in agreement with the predicted value of 4. Increasing the measurement rate suppressed the transition rate down to 0.005 omega(R).
The evolution of a quantum system is supposed to be impeded by measurement of an involved observable. This effect has been proven indistinguishable from the effect of dephasing the system's wave function, except in an individual quantum system. The coherent dynamics, on an optical E2 line, of a single trapped ion driven by light of negligible phase drift has been alternated with interrogations of the internal ion state. Retardation of the ion's nutation, equivalent to the quantum Zeno effect, is demonstrated in the statistics of sequences of probe-light scattering ''on'' and ''off'' detections, the latter representing back-action-free measurement.
The quantum Zeno effect (QZE) is not only interesting as a manifestation of the counterintuitive behavior of quantum mechanics, but may also have practical applications. When a spectroscopy laser is applied to target atoms or ions prepared in an initial state, the Rabi flopping of an auxiliary transition sharing one common level can be inhibited. This effect is found to be strongly dependent on the detuning of the spectroscopy laser and offers a sensitive spectroscopy signal which allows for high precision spectroscopy of transitions with a small excitation rate. We demonstrate this method with direct frequency comb spectroscopy using the minute power of a single mode to drive a dipole allowed transition in a single trapped ion. Resolving the individual modes of the frequency comb demonstrates that the simple instantaneous quantum collapse description of the QZE can not be applied here, as these modes need several pulses to build up.