- Quantum Zeno effect
The

**quantum Zeno effect**is a name coined byGeorge Sudarshan andBaidyanaith Misra of the University of Texas in 1977 in their analysis of the situation in which an unstable particle, if observed continuously, will never decay.Citation | last = Sudarshan | first = E.C.G. | author-link = | last2 = Misra | first2 = B. | author2-link = | title = The Zeno’s paradox in quantum theory | journal = Journal of Mathematical Physics | volume = 18 | issue = 4 | pages = pp. 756–763 | year = 1977 | url =http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JMAPAQ000018000004000756000001&idtype=cvips&gifs=yes | doi = | id = ] One can nearly ”freeze” the evolution of the system by measuring it frequently enough in its (known) initial state. The meaning of the term has since expanded, leading to a more technical definition: time evolution can be suppressed not only by measurement: The quantum Zeno effect is the suppression of unitary time evolution caused byquantum decoherence in quantum systems provided by a variety of sources: measurement, interactions with the environment, stochastic fields, and so on. [*http://arxiv.org/abs/quant-ph/0103034v2 T. Nakanishi, K. Yamane, and M. Kitano: "Absorption-free optical control of spin systems: the quantum Zeno effect in optical pumping" Phys. Rev. A 65, 013404 (2001)*] ] As an outgrowth of study of the quantum Zeno effect, it has become clear that application to a system of sufficiently strong and fast pulses with appropriate symmetry also can "decouple" the system from its decohering environment. [*http://qserver.usc.edu/group/wp-content/uploads/2007/02/pra690323142004.pdf P. Facchi, D. A. Lidar, & S. Pascazio "Unification of dynamical decoupling and the quantum Zeno effect" Physical Review A 69, 032314 (2004)*] ]The name comes from

Zeno's arrow paradox which states that, since an arrow in flight is not seen to move during any single instant, it cannot possibly be moving at all.The idea depends on the "instant of time", a kind of freeze-motion idea that the arrow is "strobed" at each instant and is seemingly stationary, so how can it move in a succession of stationary events?]An earlier theoretical exploration of this effect of measurement was published in 1974 by Degasperis "et al." Citation | author = A. Degasperis, L. Fonda & G.C. Ghirardi | title = Does the lifetime of an unstable system depend on the measuring apparatus? | journal = Il Nuovo Cimento A | volume = 21 | issue = 3 | pages = pp. 471-484 | year = 1974 | url =http://www.springerlink.com/content/4064h6xv57162038/ | doi = | id = ] and

Alan Turing described it in 1954:cite book |title=Alan Turing: Life and Legacy of a Great Thinker |publisher=Springer |year=2004 |author=Christof Teuscher& Douglas Hofstadter |page=p. 54 |isbn=3540200207 |url=http://books.google.com/books?id=th0_ipQKmGMC&pg=PA54&dq=%22Turing+paradox%22&lr=&as_brr=0&sig=ACfU3U0aOoVPNlecFf9n-bOQymEyGFKA5g ] resulting in the earlier name**Turing paradox**. The idea is contained in the early work byJohn von Neumann , sometimes called the "reduction postulate".cite book |author=John von Neumann |title=Mathematische Grundlagen der Quantenmechanik |isbn=3540592075 |publisher=Springer |page=Chapter V.2 |year=1932 (See also: cite book |isbn=0691028931 |author=J. von Neumann |title=Mathematical Foundations of Quantum Mechanics |publisher=Princeton University Press |location=Princeton |year=1955 |page= p. 366); cite book |title=Quantum Measurements and Decoherence |author= Michael B. Mensky |year=2000 |publisher=Springer |url=http://books.google.com/books?id=Bo7jujlMqL8C&pg=PA80&dq=von+Neumann+%22Zeno+effect%22&lr=&as_brr=0&sig=ACfU3U00GYIv_FGyRJ0WbygSahmyKmv55Q

page=§4.1.1, pp. 315 ff |isbn=0792362276 ; cite book |isbn=0120038498 |year=2003 |publisher= Academic Press |author=Ch. Wunderlich & Ch. Balzer (Benjamin Bederson & H Walther, editors) |title=Advances in Atomic, Molecular, and Optical Physics: Vol. 49 |url=http://books.google.com/books?id=mmhJ37o8fdwC&pg=PA315&dq=von+Neumann+%22Zeno+effect%22&lr=&as_brr=0&sig=ACfU3U1eXn5NebR83_wew8ZXal34E9fguQ]According to the reduction postulate, each measurement causes the

wavefunction to "collapse" to a pureeigenstate of the measurement basis. In the context of this effect, an "observation" can simply be the absorption of a particle, without an observer in any conventional sense. However, there is controversy over the interpretation of the effect, sometimes referred to as the "measurement problem " in traversing the interface between microscopic and macroscopic.cite book |title=The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics |author=George Greenstein & Arthur Zajonc |isbn=076372470X |year=2005 |publisher=Jones & Bartlett Publishers |page= p. 237 |url=http://books.google.com/books?id=5t0tm0FB1CsC&pg=PA231&dq=%22quantum+Zeno%22&lr=&as_brr=0&sig=ACfU3U0n5c-j5HTI1HpLgc-lk-53L2p0JA#PPA237,M1 ] Citation |title= [*http://arxiv.org/abs/quant-ph/0201115v2 Quantum Zeno subspaces*] |author=P. Facchi and S. Pascazio | journal = Physical Review Letters | volume = 89 | issue= 8 |year = 2002 ]Closely related (and sometimes not distinguished from the quantum Zeno effect) is the

**watchdog effect**, in which the time evolution of a system is affected by its continuous coupling to the environment. citebook |title=Testing Quantum Mechanics on New Ground |page=p. 107 |url=http://books.google.com/books?id=GqRQYEPZRywC&pg=PA114&dq=%22watchdog+effect%22&lr=&as_brr=0&sig=ACfU3U1wJqyLrdtNdcTL5S76ILrTVgWsMg#PPA107,M1

isbn=0521026598 |year=1999 |publisher=Cambridge University Press |author=Partha Ghose ] cite book |title=Foundations and Interpretation of Quantum Mechanics |author=Gennaro Auletta |year=2000 |isbn=9810246145 |publisher=World Scientific |page=p. 341 |url=http://books.google.com/books?id=lSAfY0LEKBMC&pg=RA1-PA341&dq=%22watchdog+effect%22&lr=&as_brr=0&sig=ACfU3U3bBGcVphPl7fkvR4R9u8EIYau9sw#PRA1-PA341,M1 ]**Description**Unstable quantum systems are predicted to exhibit a short time deviation from the exponential decay law.Citation | last = Khalfin | first = L.A. | author-link = | journal = Soviet Phys. JETP | volume = 6 | pages = 1053 | year= 1958 | url =http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=4318804 | doi = | id =| title =Contribution to the decay theory of a quasi-stationary state ] Citation |title= [

*http://www.phytem.ens-cachan.fr/telechargement/Optique_Quantique/Raizen_decay.pdf Experimental evidence for non-exponential decay in quantum tunnelling*] |author=Steven R. Wilkinson, Cyrus F. Bharucha, Martin C. Fischer, Kirk W. Madison, Patrick R. Morrow, Qian Niu, Bala Sundaram & Mark G. Raizen | journal = Nature | volume = 387 | pages = 575 ff |year = 1997 ] This universal phenomenon has led to the prediction that frequent measurements during this nonexponential period could inhibit decay of the system, one form of the**quantum Zeno effect**. Subsequently, it was predicted that an "enhancement" of decay due to frequent measurements could be observed under somewhat more general conditions, leading to the so-called**anti-Zeno effect**.This definition is a paraphrase of the introductory remarks in Raizen "et al." 's paper cited later in this article.]In

quantum mechanics , the interaction mentioned is called ‘‘measurement’’ because its result can be interpreted in terms ofclassical mechanics . Frequent measurement prohibits the transition. It can be a transition of a particle from one half-space to another (which could be used foratomic mirror in anatomic nanoscope ,cite journal

url=http://stacks.iop.org/0953-4075/39/1605

author= D.Kouznetsov

coauthors=H. Oberst, K. Shimizu, A. Neumann, Y. Kuznetsova, J.-F. Bisson, K. Ueda, S. R. J. Brueck

title=Ridged atomic mirrors and atomic nanoscope

journal=JOPB

volume=39

pages=1605–1623

year=2006

doi=10.1088/0953-4075/39/7/005] ) a transition of a photon in a waveguide from one mode to another, and it can be a transition of an atom from one quantum state to another.It can be a transition from the subspace without decoherent loss of a q-bit to a state with a q-bit lost in aquantum computer .cite book |title=Quantum computing: a short course from theory to experiment |author=Joachim Stolze & Dieter Suter |page=§7.3.7 p.99 |url=http://books.google.com/books?id=VkPGN1z15bcC&printsec=frontcover&dq=intitle:Quantum+intitle:Computing+inauthor:Stolze&lr=&as_brr=0&sig=ACfU3U0Z5EOIsWAGa11fj1TdmrtKdNQeBg#PPA99,M1

isbn=3527407871 |publisher=Wiley-VCH |year=2008 |edition=2nd Edition ] [*Quantum computer: URL: http://www.physorg.com/news11087.html*] In this sense, for the q-bit correction, it is sufficient to determine whether the decoherence has already occurred or not.All these can be considered as applications of the Zeno effect.cite journal

url=http://userpages.umbc.edu/~pittmtb1/pdf%20publications/PRA%20Zeno%20Gates.pdf

author=JD Franson

coauthors=B. C. Jacobs, and T. B. Pittman

title=Quantum computing using single photons and the Zeno effect

journal=PRA

volume=70

year=2006

doi=10.1103/PhysRevA.70.062302] By its nature, the effect appears only in systems with distinguishable quantum states, and hence is inapplicable to classical phenomena and macroscopic bodies.**Various realizations and general definition**The treatment of the Zeno effect as paradox is not limited by the pre-historic time of Zenon, and not limited tothe processes of quantum decay. In general, the term

**Zeno effect**is applied to various transitions;and sometimes these transitions may be very different from just a "decay" (whether exponential ornon-exponential). One of realizations refers to the observation of an object (the Zenon's arrow, or any quantum particle)as it leaves some region of space. In XX century, the trapping (confinement) of a particle in some region by itsobservation outside the region was considered as total nonsense,indicating some non-completeness ofquantum mechanics cite journal

title=The screen problem

author=B.Mielnik

journal=Foundations of physics

volume=24

issue=8

pages=1113-1129

year=1994] .Even in 2001, the confinement by absorption was considered as a paradoxcite journal

title=Quantum Zeno effect in optical fibers

author=K.Yamane, M.Ito, M.Kitano

journal=Optics Communications

volume=192

issue=3-6

pages=299-307

year=2001] . Later, similar effects of suppression of Raman Scattering is considered expected "effect" cite journal

journal=Physics Letters A

title=Quantum Zeno effect in Raman scattering

author=K.Thun, J.Perina, J.Krepelka.

volume=299

issue=1

pages=19-30

year=2002

issn=0375-9601] [*cite journal*] cite journal

title=Quantum Zeno effect in cascaded parametric down-conversion with losses

author: J.Perina

journal=Physics Letters A

volume=325

issue=1

pages=16-20

year=2004

comment=7

url=http://annex.jsap.or.jp/OSJ/opticalreview/TOC-Lists/vol12/12e0363tx.htm

author= D.Kouznetsov

coauthors= H.Oberst

title=Reflection of Waves from a Ridged Surface and the Zeno Effect

journal=Optical Review

volume=12

pages=1605-1623

year=2005] , not aparadox at all.The absorption of light at some wavelength, releasing a light, escaped from some mode of a fiber, or evenrelaxation of a particle, as it enters some region, all these processes can be interpreted as measurement.Such a measurement suppresses the transition, and is called**Zeno effect**in the scientific literature.In order to cover all this phenomena (including the original effect of suppression of the quantum decay), theZeno effect can be defined as Class of phenomena when some transition is suppressed by the interaction, thatallows the interpretation of the resulting state in terms "transition did not yet happen" and "transition already occurs", or "The proposition that evolution of a quantum system is stopped ifthe state of the system is continuously measured by a macroscopic device to check whether the system isstill in its initial state" cite journal

author=A.D.Panov

journal=Physics Letters A

volume= 281

year=2001

page=9] .**Periodic measurement of a quantum system**Given a system in a state A, which is the

eigenstate of some measurement operator. Say the system under free time evolution will decay with a certain probability into state B. If measurements are made periodically, with some finite interval between each one, at each measurement, the wave function collapses to an eigenstate of the measurement operator. Between the measurements, the system evolves away from this eigenstate into asuperposition state of the states A and B. When the superposition state is measured, it will again collapse, either back into state A as in the first measurement, or away into state B. However, its probability of collapsing into state B, after a very short amount of time "t", is proportional to "t"², since probabilities are proportional to squared amplitudes, and amplitudes behave linearly. Thus, in the limit of a large number of short intervals, with a measurement at the end of every interval, the probability of making the transition to B goes to zero.According to decoherence theory, the collapse of the wave function is not a discrete, instantaneous event. A "measurement" is equivalent to strongly coupling the quantum system to the noisy thermal environment for a brief period of time, and continuous strong coupling is equivalent to frequent "measurement". The time it takes for the wave function to "collapse" is related to the decoherence time of the system when coupled to the environment. The stronger the coupling is, and the shorter the decoherence time, the faster it will collapse. So in the decoherence picture, a perfect implementation of the quantum Zeno effect corresponds to the limit where a quantum system is continuously coupled to the environment, and where that coupling is infinitely strong, and where the "environment" is an infinitely large source of thermal randomness.

**Experiments and discussion**Experimentally, strong suppression of the evolution of a quantum system due to environmental coupling has been observed in a number of microscopic systems.

In 1989, David Wineland and his group at

NIST cite journal

url=http://www.boulder.nist.gov/timefreq/general/pdf/858.pdf

author=W.M.Itano

coauthors=D.J.Heinsen, J.J.Bokkinger, D.J.Wineland

title=Quantum Zeno effect

journal=PRA

volume=41

pages=2295–2300

year=1990

doi=10.1103/PhysRevA.41.2295] observed the quantum Zeno effect for a two-level atomic system that is interrogated during its evolution. Approximately 5000^{9}Be^{+}ions were stored in a cylindricalPenning trap and laser cooled to below 250 mK. A resonant RF pulse was applied which, if applied alone, would cause the entire ground state population to migrate into an excited state. After the pulse was applied, the ions were monitored for photons emitted due to relaxation. The ion trap was then regularly "measured" by applying a sequence ofultraviolet pulses, during the RF pulse. As expected, the ultraviolet pulses suppressed the evolution of the system into the excited state. The results were in good agreement with theoretical models. A recent review describes subsequent work in this arena.D. Leibfried, R. Blatt, C. Monroe & D. Wineland: "Quantum dynamics of single trapped ions" [*http://cua.mit.edu/8.422_old/PHYSICS-leibfried-blatt-monroe-wineland-quantum-dynamics-of-single-trapped-ions-rmp75-p281-2003.pdf Reviews of Modern Physics, Vol. 75, January 2003 p. 281 ff*] ] In 2001,Mark G. Raizen and his group at theUniversity of Texas at Austin , observed the quantum Zeno and anti-Zeno effects for an unstable quantum system,M. C. Fischer, B. Gutiérrez-Medina, and M. G. Raizen "Observation of the Quantum Zeno and Anti-Zeno Effects in an Unstable System" [*http://arxiv.org/abs/quant-ph/0104035v1 Phys. Rev. Lett. 87, 040402 (2001)*] ] as originally proposed by Sudarshan and Misra. Ultracold sodium atoms were trapped in an accelerating optical lattice and the loss due to tunneling was measured. The evolution was interrupted by reducing the acceleration, thereby stoppingquantum tunneling . The group observed suppression or enhancement of the decay rate, depending on the regime of measurement.It is still an open question how close one can approach the limit of an infinite number of interrogations due to the Heisenberg uncertainty involved in shorter measurement times. In 2006, Streed "et al." at MIT observed the dependence of the Zeno effect on measurement pulse characteristics.Erik W. Streed, Jongchul Mun, Micah Boyd, Gretchen K. Campbell, Patrick Medley, Wolfgang Ketterle & David E. Pritchard: "Continuous and Pulsed Quantum Zeno Effect" [

*http://arxiv.org/abs/cond-mat/0606430v1 Physical Phys. Rev. Lett. 97, 260402 (2006)*] ]The interpretation of experiments in terms of the "Zeno effect" helps describe the origin of a phenomenon. Nevertheless, such an interpretation does not bring any principally new features not described with the

Schrödinger equation of the quantum system. Even more, the detailed description of experiments with the "Zeno effect", especially at the limit of high frequency of measurements (high efficiency of suppression of transition, or high reflectivity of aridged mirror ) usually do not behave as expected for an idealized measurement,cite journal

url=http://stacks.iop.org/0953-4075/39/1605

author= D.Kouznetsov

coauthors=H. Oberst, K. Shimizu, A. Neumann, Y. Kuznetsova, J.-F. Bisson, K. Ueda, S. R. J. Brueck

title=Ridged atomic mirrors and atomic nanoscope

journal=JOPB

volume=39It should be noted that the Qauntum Zeno affect is dependent upon the reductionist postulate for reconciling the measurement problem. Thus, the Quantum Zeno effect does not apply to all interpretations of quantum theory; in particular, the Many-Worlds Interpretation (a.k.a. the Multiverse Interpretation) and the Quantum Logic Interpretation. Also, the Quantum Zeno affect may only hold for directly observed quantum systems, meaning that statistically observed systems (i.e. macromolecular systems of approximately 30 or more atoms) might not be affected by the Zeno effect. These qualifications mean that the Zeno effect may possibly be a useful experimental design for testing the Many-Worlds Hypothesis, the Quantum Logic Hypothesis, and various hypotheses related to Quantum Computing.

pages=1605–1623

year=2006

doi=10.1088/0953-4075/39/7/005] and require analysis of the mechanism of the interaction.K. Koshino and A Shimizu (2005) "Quantum Zeno effect by general measurements" [*http://arxiv.org/abs/quant-ph/0411145v2 Physics Reports, Volume 412, Issue 4, p. 191-275*] ]Lastly, it should be noted that the Quantum Zeno effect is dependent upon the reductionist postulate for reconciling the measurement problem. Thus, the Quantum Zeno effect does not apply to all interpretations of quantum theory; in particular, the Many-Worlds Interpretation (a.k.a. the Multiverse Interpretation) and the Quantum Logic Interpretation. Also, the Quantum Zeno affect may only hold for directly observed quantum systems, meaning that statistically observed systems (i.e. macromolecular systems of approximately 30 or more atoms) may possibly not exhibit system decoupling, despite constituent systems showing that behavior. (More simply, just because a single atom or a few atoms display the Zeno effect, doesn't mean that larger groups of atoms will display the Zeno effect. This is directly related to decoherence and the measurement problem.). These qualifications mean that the Zeno effect may possibly be a useful experimental design for testing the Many-Worlds Hypothesis, the Quantum Logic Hypothesis, and various hypotheses related to Quantum Computing.

**ignificance to cognitive science**The quantum Zeno effect (with its own controversies related to measurement) is becoming a central concept in the exploration of controversial and unproven theories of

quantum mind consciousness within the discipline ofcognitive science . In his book, "Mindful Universe" (2007)Henry Stapp , professor of quantum physics at UC Berkeley, claims that the quantum Zeno effect is the main method by which the mind holds a superposition of the state of the brain in theattention . He advances that this phenomenon is the principal method by which the conscious will effects change, a possible solution to themind-body dichotomy . Stapp and co-workers do not claim finality of their theory, but only:J.M. Schwartz, H.P. Stapp & M. Beauregard (2005) "Quantum physics in neuroscience and psychology: a neurophysical model of mind-brain interaction", [*http://journals.royalsociety.org/content/fl8g2b86ykbxht3m/ Philosophical Transactions of the Royal Society of London B Volume 360, Number 1458 / June 29, 2005 Pages 1309-1327 DOI 10.1098/rstb.2004.1598*] ]:The new framework, unlike its classic-physics-based predecessor, is erected directly upon, and is compatible with, the prevailing principles of physics.

Needless to say, such conjectures have their opponents, serving perhaps to create more furor, rather than less, for example, see Bourget.Bourget, David: " Quantum Leaps in Philosophy of Mind: A Critique of Stapp's Theory" [

*http://www.newdualism.org/papers/D.Bourget/QLPM.htm Journal of Consciousness Studies, Volume 11, Number 12, 2004 , pp. 17-42(26)*] ] A summary of the situation is provided by Davies:PCW Davies: "Does quantum mechanics play a non-trivial role in life?" [*http://aca.mq.edu.au/PaulDavies/publications/papers/'Does%20quantum%20mechanics%20play%20a%20non%20trivial%20role%20in%20life'%20BioSystems%20paper.pdf BioSystems 78 (2004) 69–79*] ] :There have been many claims that quantum mechanics plays a key role in the origin and/or operation of biological organisms, beyond merely providing the basis for the shapes and sizes of biological molecules and their chemical affinities.…The case for quantum biology remains one of “not proven.” There are many suggestive experiments and lines of argument indicating that some biological functions operate close to, or within, the quantum regime, but as yet no clear-cut example has been presented of non-trivial quantum effects at work in a key biological process.**ee also***

Interference

*Zeno's paradoxes

*Wavefunction collapse

*Measurement problem

*Quantum decoherence

*Quantum Darwinism

*Einselection **External links*** [

*http://www.lysator.liu.se/~jc/zeno.qcl.html Zeno.qcl*] A computer program written in QCL which demonstrates the Quantum Zeno effect**References*** [

*http://xstructure.inr.ac.ru/x-bin/theme3.py?level=1&index1=-209310 Quantum Zeno effect on arxiv.org*]

*Wikimedia Foundation.
2010.*

### См. также в других словарях:

**Zeno**— is a Greek name derived from the more ancient variant Zenon. The word may refer to any of the following:PeoplePhilosophers* Zeno of Elea (c.490–c.430 BC), philosopher, follower of Parmenides, famed for his paradoxes . * Zeno of Citium (333 BC 264 … Wikipedia**Quantum decoherence**— Quantum mechanics Uncertainty principle … Wikipedia**Zeno's paradoxes**— Achilles and the Tortoise redirects here. For other uses, see Achilles and the Tortoise (disambiguation). Arrow paradox redirects here. For other uses, see Arrow paradox (disambiguation). Zeno s paradoxes are a set of problems generally thought… … Wikipedia**Zeno-Effekt**— Der Quanten Zeno Effekt ist ein Effekt aus der Quantenmechanik, bei dem ein Übergang eines quantenmechanischen Systems von einem Zustand in einen anderen, z. B. der Zerfall eines radioaktiven Atomkernes oder die Lichtaussendung eines angeregten… … Deutsch Wikipedia**Quantum mind–body problem**— The quantum mind–body problem refers to the philosophical discussions of the mind–body problem in the context of quantum mechanics. Since quantum mechanics involves quantum superpositions, which are not perceived by observers, some… … Wikipedia**Quantum reflection**— is a physical phenomenon involving the reflection of a matter wave from an attractive potential. In classical physics, such a phenomenon is not possible; for instance when one magnet is pulled toward another, you do not expect one of the magnets… … Wikipedia**Measurement in quantum mechanics**— Quantum mechanics Uncertainty principle … Wikipedia**Quanten-Zeno-Paradoxon**— Der Quanten Zeno Effekt ist ein Effekt aus der Quantenmechanik, bei dem ein Übergang eines quantenmechanischen Systems von einem Zustand in einen anderen, z. B. der Zerfall eines radioaktiven Atomkernes oder die Lichtaussendung eines angeregten… … Deutsch Wikipedia**Quanten-Zeno-Effekt**— Der Quanten Zeno Effekt ist ein Effekt aus der Quantenmechanik, bei dem ein Übergang eines quantenmechanischen Systems von einem Zustand in einen anderen, z. B. die Lichtaussendung eines angeregten Atoms, durch wiederholt ausgeführte… … Deutsch Wikipedia**Introduction to quantum mechanics**— This article is an accessible, non technical introduction to the subject. For the main encyclopedia article, see Quantum mechanics. Quantum mechanics … Wikipedia