Quantum Zeno effect

The breakthrough Zeno aftereffect is a name coined by George Sudarshan and Baidyanath Misra of the University of Texas in 1977 in their assay of the bearings in which an ambiguous particle, if empiric continuously, will never decay.1 One can about "freeze" the change of the arrangement by barometer it frequently abundant in its (known) antecedent state. The acceptation of the appellation has back expanded, arch to a added abstruse analogue in which time change can be suppressed not alone by measurement: the breakthrough Zeno aftereffect is the abolishment of unitary time change acquired by breakthrough decoherence in breakthrough systems provided by a array of sources: measurement, interactions with the environment, academic fields, and so on.2 As an bulge of abstraction of the breakthrough Zeno effect, it has become bright that applying a alternation of abundantly able and fast pulses with adapted agreement can aswell decouple a arrangement from its decohering environment.3

The name comes from Zeno's arrow absurdity which states that, back an arrow in flight is not apparent to move during any individual instant, it cannot possibly be affective at all.4

An beforehand abstract analysis of this aftereffect of altitude was appear in 1974 by Degasperis et al. 5 and Alan Turing declared it in 1954:6

resulting in the beforehand name Turing paradox. The abstraction is independent in the aboriginal plan by John von Neumann, sometimes alleged the abridgement postulate.7

According to the abridgement postulate, anniversary altitude causes the wavefunction to "collapse" to a authentic eigenstate of the altitude basis. In the ambience of this effect, an "observation" can artlessly be the assimilation of a particle, after an eyewitness in any accepted sense. However, there is altercation over the estimation of the effect, sometimes referred to as the "measurement problem" in traversing the interface amid diminutive and macroscopic.89

Closely accompanying (and sometimes not acclaimed from the breakthrough Zeno effect) is the babysitter effect, in which the time change of a arrangement is afflicted by its connected coupling to the environment.1011

Description

Unstable breakthrough systems are predicted to display a abbreviate time aberration from the exponential adulteration law.1213 This accepted abnormality has led to the anticipation that common abstracts during this nonexponential aeon could arrest adulteration of the system, one anatomy of the breakthrough Zeno effect. Subsequently, it was predicted that an accessory of adulteration due to common abstracts could be empiric beneath somewhat added accepted conditions, arch to the alleged anti-Zeno effect.14

In breakthrough mechanics, the alternation mentioned is alleged "measurement" because its aftereffect can be interpreted in agreement of classical mechanics. Common altitude prohibits the transition. It can be a alteration of a atom from one half-space to addition (which could be acclimated for diminutive mirror in an diminutive nanoscope15) as in the time of accession botheration 16 17, a alteration of a photon in a waveguide from one approach to another, and it can be a alteration of an atom from one breakthrough accompaniment to another. It can be a alteration from the subspace after decoherent accident of a q-bit to a accompaniment with a q-bit absent in a breakthrough computer.1819 In this sense, for the q-bit correction, it is acceptable to actuate whether the decoherence has already occurred or not. All these can be advised as applications of the Zeno effect.20 By its nature, the aftereffect appears alone in systems with apparent breakthrough states, and appropriately is extraneous to classical phenomena and arresting bodies.

Various realizations and general definition

The analysis of the Zeno aftereffect as a absurdity is not bound to the processes of breakthrough decay. In general, the appellation Zeno aftereffect is activated to assorted transitions, and sometimes these transitions may be actual altered from a simple "decay" (whether exponential or non-exponential).

One ability refers to the ascertainment of an article (Zeno's arrow, or any breakthrough particle) as it leaves some arena of space. In the 20th century, the accoutrement (confinement) of a atom in some arena by its ascertainment alfresco the arena was advised as nonsensical, advertence some non-completeness of breakthrough mechanics.21 Even as backward as 2001, bonds by assimilation was advised as a paradox.22 Later, agnate furnishings of the abolishment of Raman drop was advised an accepted effect,232425 not a absurdity at all. The assimilation of a photon at some wavelength, the absolution of a photon (for archetype one that has able from some approach of a fiber), or even the alleviation of a atom as it enters some region, are all processes that can be interpreted as measurement. Such a altitude suppresses the transition, and is alleged the Zeno aftereffect in the accurate literature.

In adjustment to awning all of these phenomena (including the aboriginal aftereffect of abolishment of breakthrough decay), the Zeno aftereffect can be authentic as a chic of phenomena in which some alteration is suppressed by an alternation — one that allows the estimation of the consistent accompaniment in the agreement alteration did not yet appear and alteration has already occurred, or The hypothesis that the change of a breakthrough arrangement is apoplectic if the accompaniment of the arrangement is continuously abstinent by a arresting accessory to analysis whether the arrangement is still in its antecedent state.26

Periodic measurement of a quantum system

Consider a arrangement in a accompaniment A, which is the eigenstate of some altitude operator. Say the arrangement beneath chargeless time change will adulteration with a assertive anticipation into accompaniment B. If abstracts are fabricated periodically, with some bound breach amid anniversary one, at anniversary measurement, the beachcomber action collapses to an eigenstate of the altitude operator. Amid the measurements, the arrangement evolves abroad from this eigenstate into a superposition accompaniment of the states A and B. If the superposition accompaniment is measured, it will afresh collapse, either aback into accompaniment A as in the aboriginal measurement, or abroad into accompaniment B. However, its anticipation of annoyed into accompaniment B, afterwards a actual abbreviate bulk of time t, is proportional to t², back probabilities are proportional to boxlike amplitudes, and amplitudes behave linearly. Thus, in the absolute of a ample amount of abbreviate intervals, with a altitude at the end of every interval, the anticipation of authoritative the alteration to B goes to zero.

According to decoherence theory, the collapse of the beachcomber action is not a discrete, direct event. A "measurement" is agnate to acerb coupling the breakthrough arrangement to the blatant thermal ambiance for a abrupt aeon of time, and connected able coupling is agnate to common "measurement". The time it takes for the beachcomber action to "collapse" is accompanying to the decoherence time of the arrangement if accompanying to the environment. The stronger the coupling is, and the beneath the decoherence time, the faster it will collapse. So in the decoherence picture, a absolute accomplishing of the breakthrough Zeno aftereffect corresponds to the absolute area a breakthrough arrangement is continuously accompanying to the environment, and area that coupling is always strong, and area the "environment" is an always ample antecedent of thermal randomness.

Experiments and discussion

Experimentally, able abolishment of the change of a breakthrough arrangement due to ecology coupling has been empiric in a amount of diminutive systems.

In 1989, David Wineland and his accumulation at NIST27 empiric the breakthrough Zeno aftereffect for a two-level diminutive arrangement that is interrogated during its evolution. Approximately 5000 9Be+ ions were stored in a annular Penning allurement and laser cooled to beneath 250 mK. A beating RF beating was activated which, if activated alone, would could cause the absolute amphitheatre accompaniment citizenry to drift into an aflame state. After the beating was applied, the ions were monitored for photons emitted due to relaxation. The ion allurement was again consistently "measured" by applying a arrangement of ultraviolet pulses, during the RF pulse. As expected, the ultraviolet pulses suppressed the change of the arrangement into the aflame state. The after-effects were in acceptable acceding with abstract models. A contempo analysis describes consecutive plan in this arena.28

Mark G. Raizen

The Breakthrough Zeno Aftereffect is acclimated in bartering diminutive magnetometers and by itself by bird's alluring ambit acoustic apparatus (magnetoreception).30

It is still an accessible catechism how carefully one can access the absolute of an absolute amount of interrogations due to the Heisenberg ambiguity complex in beneath altitude times. In 2006, Streed et al. at MIT empiric the assurance of the Zeno aftereffect on altitude beating characteristics.31

The estimation of abstracts in agreement of the "Zeno effect" helps call the agent of a phenomenon. Nevertheless, such an estimation does not accompany any principally new appearance not declared with the Schrödinger blueprint of the breakthrough system.3233

Even more, the abundant description of abstracts with the "Zeno effect", abnormally at the absolute of top abundance of abstracts (high ability of abolishment of transition, or top reflectivity of a asperous mirror) usually do not behave as accepted for an arcadian measurement,15 and crave assay of the apparatus of the interaction.34

It was apparent that the Breakthrough Zeno aftereffect persists in the many-worlds and about states interpretations of breakthrough mechanics.35

Significance to cognitive science

The breakthrough Zeno aftereffect (with its own controversies accompanying to the botheration of measurement) is acceptable a axial abstraction in the analysis of arguable theories of breakthrough apperception alertness aural the conduct of cerebral science. In his book Mindful Universe (2007), Henry Stapp claims that the apperception holds the academician in a superposition of states application the breakthrough Zeno effect. He advances that this abnormality is the arch adjustment by which the acquainted can aftereffect change, a accessible band-aid to the mind-body dichotomy. Stapp and co-workers do not affirmation certitude of their theory, but only:36

The new framework, clashing its classic-physics-based predecessor, is erected anon upon, and is accordant with, the prevailing attempt of physics.

conjectures

Needless to say, such conjectures accept their opponents, confined conceivably to actualize added furor, rather than less, for example, see Bourget.37 A arbitrary of the bearings is provided by Davies:38

There accept been abounding claims that breakthrough mechanics plays a key role in the agent and/or operation of biological organisms, above alone accouterment the base for the shapes and sizes of biological molecules and their actinic affinities.…The case for breakthrough analysis charcoal one of “not proven.” There are abounding evocative abstracts and curve of altercation advertence that some biological functions accomplish abutting to, or within, the breakthrough regime, but as yet no assured archetype has been presented of non-trivial breakthrough furnishings at plan in a key biological process.

While this endure argument may no best be valid,39 the acceptation of the Zeno aftereffect in free the amount of breakthrough decoherence in biological systems charcoal unknown.