Continuous measurements in quantum theory

Eberle, E.G.

doi:10.1007/bf02785177

Cited by 5 publications

(4 citation statements)

References 5 publications

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“…The QZE and this experiment have not only aroused considerable interest in the literature [8,9], but the very relevance of the above experimental results for the QZE has given rise to controversies. In particular the projection postulate and its applicability in this experiment have been cast into doubt, and it was pointed out that the experiment could be understood without recourse to the QZE by simply including the probe laser in the dynamics, e.g.…”

Section: Introductionmentioning

confidence: 99%

Quantum Zeno effect and light - dark periods for a single atom

Beige¹,

Hegerfeldt²

1997

J. Phys. A: Math. Gen.

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The quantum Zeno effect (QZE) predicts a slow-down of the time development of a system under rapidly repeated ideal measurements, and experimentally this was tested for an ensemble of atoms using short laser pulses for non-selective state measurements. Here we consider such pulses for selective measurements on a single system. Each probe pulse will cause a burst of fluorescence or no fluorescence. If the probe pulses were strictly ideal measurements, the QZE would predict periods of fluorescence bursts alternating with periods of no fluorescence (light and dark periods) which would become longer and longer with increasing frequency of the measurements. The non-ideal character of the measurements is taken into account by incorporating the laser pulses in the interaction, and this is used to determine the corrections to the ideal case. In the limit, when the time ∆t between the laser pulses goes to zero, no freezing occurs but instead we show convergence to the familiar macroscopic light and dark periods of the continuously driven Dehmelt system. An experiment of this type should be feasible for a single atom or ion in a trap.

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Section: Introductionmentioning

confidence: 99%

Quantum Zeno effect and light - dark periods for a single atom

Beige¹,

Hegerfeldt²

1997

J. Phys. A: Math. Gen.

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“…In particular the use of the projection postulate and reduction of the wavefunction have been criticized, and the very existence of the QZE has been cast into doubt. It is no exaggeration to say that the QZE has aroused tremendous interest in the literature [18,19,20].…”

Section: Introductionmentioning

confidence: 99%

Projection postulate and atomic quantum Zeno effect

1996

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The projection postulate has been used to predict a slow-down of the time evolution of the state of a system under rapidly repeated measurements, and ultimately a freezing of the state. To test this so-called quantum Zeno effect an experiment was performed by Itano et al. (Phys. Rev. A 41, 2295) in which an atomic-level measurement was realized by means of a short laser pulse. The relevance of the results has given rise to controversies in the literature. In particular the projection postulate and its applicability in this experiment have been cast into doubt. In this paper we show analytically that for a wide range of parameters such a short laser pulse acts as an effective level measurement to which the usual projection postulate applies with high accuracy. The corrections to the ideal reductions and their accumulation over n pulses are calculated. Our conclusion is that the projection postulate is an excellent pragmatic tool for a quick and simple understanding of the slow-down of time evolution in experiments of this type. However, corrections have to be included, and an actual freezing does not seem possible because of the finite duration of measurements.

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“…The quantum Zeno effect and the experiment of Ref. [7] have given rise to a large number of publications [17].…”

Section: Introductionmentioning

confidence: 99%

Atomic quantum zeno effect for ensembles and single systems

1997

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The so-called quantum Zeno effect is essentially a consequence of the projection postulate for ideal measurements. To test the effect Itano et al. have performed an experiment on an ensemble of atoms where rapidly repeated level measurements were realized by means of short laser pulses. Using dynamical considerations we give an explanation why the projection postulate can be applied in good approximation to such measurements. Corrections to ideal measurements are determined explicitly. This is used to discuss in how far the experiment of Itano et al. can be considered as a test of the quantum Zeno effect. We also analyze a new possible experiment on a single atom where stochastic light and dark periods can be interpreted as manifestation of the quantum Zeno effect. We show that the measurement point of view gives a quick and intuitive understanding of experiments of the above type, although a finer analysis has to take the corrections into account. 1

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Continuous measurements in quantum theory

Cited by 5 publications

References 5 publications

Quantum Zeno effect and light - dark periods for a single atom

Quantum Zeno effect and light - dark periods for a single atom

Projection postulate and atomic quantum Zeno effect

Atomic quantum zeno effect for ensembles and single systems

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