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arXiv:quant-ph/0101044

Quantum Zeno effects with "pulsed" and "continuous" measurements

Paolo Facchi A, Saverio Pascazio

Published Jan 11, 2001• 8 citations
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Abstract

The dynamics of a quantum system undergoing measurements is investigated. Depending on the features of the interaction Hamiltonian, the decay can be slowed (quantum Zeno effect) or accelerated (inverse quantum Zeno effect), by changing the time interval between successive (pulsed) measurements or, alternatively, by varying the "strength" of the (continuous) measurement.

DOI
10.48550/arxiv.quant-ph/0101044

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The dynamics of a quantum system undergoing measurements is investigated. Depending on the features of the interaction Hamiltonian, the decay can be slowed (quantum Zeno effect) or accelerated (inverse quantum Zeno effect), by changing the time interval between successive (pulsed) measurements or, alternatively, by varying the "strength" of the (continuous) measurement.
We analyze the Zeno phenomenon in quantum field theory. The decay of an unstable system can be modified by changing the time interval between successive measurements (or by varying the coupling to an external system that plays the role of measuring apparatus). We speak of quantum Zeno effect if the decay is slowed and of inverse quantum Zeno (or Heraclitus) effect if it is accelerated. The analysis of the transition between these two regimes requires close scrutiny of the features of the interaction Hamiltonian. We look in detail at quantum field theoretical models of the Lee type.
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.
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.