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arXiv:0903.4560 · Chemické listy

Quantum Zeno Effect

Mikhail Lemeshko, Břetislav Friedrich

Published Mar 26, 2009• 0 citations
arXivHTMLPDF

Abstract

We present the physics of the quantum Zeno effect, whose gist is often expressed by invoking the adage "a watched pot never boils". We review aspects of the theoretical and experimental work done on the effect since its inception in 1977, and mention some applications. We dedicate the article - with our very best wishes - to Rudolf Zahradnik at the occasion of his great jubilee. Perhaps Rudolf's lasting youthfulness and freshness are due to that he himself had been frequently observed throughout his life: until the political turn-around in 1989 by those who wished, by their surveillance, to prevent Rudolf from spoiling the youth by his personal culture and his passion for science and things beautiful and useful in general. This attempt had failed. Out of gratitude, the youth has infected Rudolf with its youthfulness. Chronically. Since 1989, Rudolf has been closely watched by the public at large. For the same traits of his as before, but with the opposite goal and for the benefit of all generations. We relish keeping him in sight ...

DOI
10.48550/arxiv.0903.4560

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We present the physics of the quantum Zeno effect, whose gist is often expressed by invoking the adage "a watched pot never boils". We review aspects of the theoretical and experimental work done on the effect since its inception in 1977, and mention some applications. We dedicate the article - with our very best wishes - to Rudolf Zahradnik at the occasion of his great jubilee. Perhaps Rudolf's lasting youthfulness and freshness are due to that he himself had been frequently observed throughout his life: until the political turn-around in 1989 by those who wished, by their surveillance, to prevent Rudolf from spoiling the youth by his personal culture and his passion for science and things beautiful and useful in general. This attempt had failed. Out of gratitude, the youth has infected Rudolf with its youthfulness. Chronically. Since 1989, Rudolf has been closely watched by the public at large. For the same traits of his as before, but with the opposite goal and for the benefit of all generations. We relish keeping him in sight ...
Observe an unstable quantum system frequently enough and its decay slows, and in the limit of continuous observation stops altogether. This is measurement-induced state freezing — the quantum Zeno effect, the physicist's "a watched pot never boils." It was named by Misra and Sudarshan (1977) and measured by Itano, Heinzen, Bollinger and Wineland in a ion trap (1990). It is standard, established quantum mechanics and is not in dispute. This paper does three things. (i) It restates, from first principles and with a numerical runner, why the effect exists at all: it is a statement about the exponent of the short-time survival law, and about nothing else. Frequent projective measurement can suppress a loss that grows quadratically in time (a coherent two-state amplitude, survival ), and cannot suppress a loss that grows linearly in time (a memoryless classical rate, survival ). (ii) It reports the two cases side by side, matched to agree when unwatched and then watched, together with a fitted short-time exponent — 1.9999 for the coherent case, 0.9967 for the classical case — and a "look but do not reset" control. (iii) In a clearly labelled interpretive section it examines the Temporal Dynamics Framework's account of the effect and shows that this account is a fork: the framework's fundamental object [the flip — in standard vocabulary a two-state transition of the underlying oscillation, which may be read either as a coherent amplitude or as a classical rate] must be committed to one reading, and the two readings give opposite answers. Only the coherent reading reproduces Zeno. This record holds one paper on its own and is refreshed every couple of months. The complete deposit, 10.5281/zenodo.21788037, holds every paper with its code and data and is updated first; for the newest version of this paper, go there.
Introduction Quantum theory predicts the striking and paradoxical result that when a system is continuously watched, it does not evolve! Although this effect was noticed much earlier by a number of people [146], [147], [148], [149], [150], it was first formally stated by Misra and Sudarshan [151] and given the appellation ‘Zeno's paradox’ because it evokes the famous paradox of Zeno denying the possibility of motion to a flying arrow. It is as startling as a pot of water on a heater that refuses to boil when continuously watched. This is why it is also called the ‘watched pot effect’. The effect is the result of repeated, frequent measurements on the system, each measurement projecting the system back to its initial state. In other words, the wave function of the system must repeatedly collapse. It is also necessary that the time interval between successive measurements must be much shorter than the critical time of coherent evolution of the system, called the Zeno time [152]. For decays this Zeno time is the time of coherent evolution before the irreversible exponential decay sets in, and is governed by the reciprocal of the range of energies accessible to the decay products. For most decays this is extremely short and hard to detect [153]. In the case of non-exponential time evolution, the relevant Zeno time can be much longer.
In the 5th century B.C.,the philosopher and logician Zeno of Elea posed several paradoxes which remained unresolved for over two thousand five hundred years. The 20th20^{th}20th century saw some resolutions to Zeno's mind boggling problems. This long journey saw many significant milestones in the form of discoveries like the tools of converging series and theories on infinite sets in mathematics. In recent times, the Zeno effect made an intriguing appearance in a rather unlikely place - a situation involving the time evolution of a quantum system, which is subject to "observations" over a period of time. Leonid Khalfin working in the former USSR in the 1960s and ECG Sudarshan and B. Misra at the University of Texas, Austin, first drew attention to this problem. In 1977, ECG Sudarshan and B. Misra published a paper on the quantum Zeno effect, called "The Zeno's paradox in quantum theory". Their fascinating result revealed the bizarre workings of the quantum world. Misra and Sudarshan's 1977 paper activated over two decades of theoretical and experimental explorations into the subject and still continues to evoke a lot of interest. In the following, the quantum Zeno effect is described and a brief outline of some of the work following Misra and Sudarshan's paper is given. The quantum Zeno effect is yet another example of the myriad unimaginable possibilities that lie waiting in the magical world of the quantum.
The term 'quantum Zeno paradox' or 'quantum Zeno effect' refers to the slowing down of the evolution of a quantum system as it is observed more and more frequently.In 1977, Misra and Sudarshan gave a theoretical demonstration of its existence.There has been disagreement regarding the definition of the effect and whether it is really a paradox, requiring new physics, or a consequence of ordinary quantum mechanics.The experiment of Itano, Heinzen, Bollinger and Wineland, published in 1990, is the one most often called a demonstration of the quantum Zeno effect.Some different interpretations are discussed.