- Quantum Zeno effect
The quantum Zeno effect is a name coined by
George Sudarshanand Baidyanaith Misraof 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 by quantum decoherencein 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 paradoxwhich 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 Turingdescribed 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 by John 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
wavefunctionto "collapse" to a pure eigenstateof 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 ]
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.]
quantum mechanics, the interaction mentioned is called ‘‘measurement’’ because its result can be interpreted in terms of classical mechanics. Frequent measurement prohibits the transition. It can be a transition of a particle from one half-space to another (which could be used for atomic mirrorin an atomic nanoscope,cite journal
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
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 a
quantum 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
coauthors=B. C. Jacobs, and T. B. Pittman
title=Quantum computing using single photons and the Zeno effect
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 of
quantum mechanicscite journal
title=The screen problem
Foundations of physics
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
year=2001] . Later, similar effects of suppression of Raman Scattering is considered expected "effect" cite journal
Physics Letters A
title=Quantum Zeno effect in Raman scattering
author=K.Thun, J.Perina, J.Krepelka.
issn=0375-9601] [cite journal
title=Quantum Zeno effect in cascaded parametric down-conversion with losses
Physics Letters A
year=2004] cite journal
title=Reflection of Waves from a Ridged Surface and the Zeno Effect
year=2005] , not a
paradoxat 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
Physics Letters A
Periodic measurement of a quantum system
Given a system in a state A, which is the
eigenstateof 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 a superpositionstate 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
coauthors=D.J.Heinsen, J.J.Bokkinger, D.J.Wineland
title=Quantum Zeno effect
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 9Be+ ions were stored in a cylindrical
Penning trapand 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 of ultravioletpulses, 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. Raizenand his group at the University 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 stopping quantum 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 equationof 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 a ridged mirror) usually do not behave as expected for an idealized measurement,cite journal
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
It 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.
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 mindconsciousness within the discipline of cognitive 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 the attention. He advances that this phenomenon is the principal method by which the conscious will effects change, a possible solution to the mind-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.
* [http://www.lysator.liu.se/~jc/zeno.qcl.html Zeno.qcl] A computer program written in QCL which demonstrates the Quantum Zeno effect
* [http://xstructure.inr.ac.ru/x-bin/theme3.py?level=1&index1=-209310 Quantum Zeno effect on arxiv.org]
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