Abstract
The quantum Zeno effect (QZE) is often associated with the ironic maxim, “a watched pot never boils”, although the notion of “watching” suggests a continuous activity at odds with the usual (pulsed measurement) presentation of the QZE. We show how continuous watching can provide the same halting of decay as the usual QZE, and, for incomplete hindrance, we provide a precise connection between the interval between projections and the response time of the continuous observer. Thus, watching closely, but not so closely as to halt the “boiling”, is equivalent to—gives the same degree of partial hindrance as—pulsed measurements with a particular pulsing rate. Our demonstration is accomplished by treating the apparatus for the continuous watching as a fully quantum object. This in turn allows us a second perspective on the QZE, in which it is the modified level structure of the combined system/apparatus Hamiltonian that slows the decay. This and other considerations favor the characterization “dominated time evolution” for the QZE.
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References
A. Peres, “Zeno paradox in quantum theory”,Am. J. Phys.,48, 931 (1980).
E. Joos, “Continuous measurement: Watchdog effect versus golden rule”,Phys. Rev. D 29, 1626 (1984).
J. C. Bergquist, R. G. Hulet, W. M. Itano, and D. J. Wineland, “Observation of quantum jumps in a single atom”,Phys. Rev. Lett.,57, 1699 (1986). T. Sauter, W. Neuhauser, R. Blatt, and P. E. Toschek, “Observation of quantum jumps,”Phys. Rev. Lett.,57, 1696 (1986). W. Nagourney, J. Sandberg, and H. Dehmelt, “Shelved optical electron amplifier: Observation of quantum jumps”,Phys. Rev. Lett. 56, 2797 (1986).
L. S. Schulman, “How quick is a quantum jump?” inProceedings of the Adriatico Research Conference: Tunneling and Its Implications, D. Mugnai, A. Ranfagni, and L. S. Schulman, eds. (World Scientific, Singapore, 1997).
L. S. Schulman, “Observational line broadening and the duration of a quantum jump”,J. Phys. A 30, L293 (1997).
L. S. Schulman, A. Ranfagni, and D. Mugnai, “Characteristic scales for dominated time evolution”,Phys. Scr.,49, 536 (1994).
E. Mihokova, S. Pascazio, and L. S. Schulman, “Hindered decay: Quantum Zeno effect through electromagnetic field domination”,Phys. Rev. A,56, 25 (1997).
H. Nakazato, M. Namiki, and S. Pascazio, “Temporal behavior of quantum mechanical systems”,Int. J. Mod. Phys. B 10, 247 (1996).
P. K. Kabir,The CP Puzzle: Strange Decays of the Neutral Kaon, (Academic, New York, 1968).
L. S. Schulman,Time's Arrows and Quantum Measurement (Cambridge University Press, Cambridge, 1997).
J. G. Muga, G. W. Wei, and R. F. Snider, “Survival probability for the Yamaguchi Potential”,Ann. Phys.,252, 336 (1996).
R. B. Griffiths, “Consistent histories and the interpretation of quantum mechanics”,J. Stat. Phys. 36, 219 (1984).
W. H. Zurek, “Decoherence and the transition from quantum to classical”,Phys. Today 36 (October 1991).
L. S. Schulman, “Continuous and pulsed observations in the quantum Zeno effect”,Phys. Rev. A, to appear.
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Schulman, L.S. Watching it boil: Continuous observation for the quantum zeno effect. Found Phys 27, 1623–1636 (1997). https://doi.org/10.1007/BF02551441
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DOI: https://doi.org/10.1007/BF02551441