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Quantum Zeno effect

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The quantum Zeno effect is a name coined by George Sudarshan and Baidyanaith 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. 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 decoherence in quantum systems provided by a variety of sources: measurement, interactions with the environment, stochastic fields, and so on. 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.

The name comes from Zeno's arrow paradox that, since an arrow in flight is not seen to move during any single instant, it cannot possibly be moving at all.

An earlier theoretical exploration of this effect of measurement was published in 1974 by Degasperis et al. and Alan Turing described it in 1954:

It is easy to show using standard theory that if a system starts in an eigenstate of some observable, and measurements are made of that observable N times a second, then, even if the state is not a stationary one, the probability that the system will be in the same state after, say, one second, tends to one as N tends to infinity; that is, that continual observations will prevent motion …

— Alan Turing as quoted by A. Hodges in Alan Turing: Life and Legacy of a Great Thinker p. 54

resulting in the earlier name Turing paradox. The idea is contained in the early work by John von Neumann, sometimes called the reduction postulate.

According to the reduction postulate, each measurement causes the wavefunction to "collapse" to a pure eigenstate 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.

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.

Description

Unstable quantum systems are predicted to exhibit a short time deviation from the exponential decay law. 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.

In 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 mirror in an atomic nanoscope,) 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. 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. 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 to the 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" (weather exponential or non-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 its observation outside the region was considered as total nonsense, indicating some non-completeness of Quantum Mechanics . Even in 2001, the confinement by absorption was considered as a paradox . Later, similar effects of suppression of Raman Scattering is considered expected effect , not a paradox at all. The absorption of light at some wavelength, releasing a light, escaped from some mode of a fiber, or even relaxation 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), the Zeno effect can be defined as Class of phenomena when some transition is suppressed by the interaction, that allows 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 if the state of the system is continuously measured by a macroscopic device to check whether the system is still in its initial state .

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 a superposition 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 t², 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 observed the quantum Zeno effect for a two-level atomic system that is interrogated during its evolution. Approximately 5000 Be ions were stored in a cylindrical Penning 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 of ultraviolet 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.

In 2001, Mark G. Raizen and his group at the University of Texas at Austin, observed the quantum Zeno and anti-Zeno effects for an unstable quantum system, 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.

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 a ridged mirror) usually do not behave as expected for an idealized measurement, and require analysis of the mechanism of the interaction.

Significance 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 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. With becoming humility, Stapp and co-workers do not claim finality of their theory, but only:

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. A summary of the situation is provided by Davies:

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.

See also

External links

  • Zeno.qcl A computer program written in QCL which demonstrates the Quantum Zeno effect

References

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  2. 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)
  3. P. Facchi, D. A. Lidar, & S. Pascazio Unification of dynamical decoupling and the quantum Zeno effect Physical Review A 69, 032314 (2004)
  4. 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?
  5. A. Degasperis, L. Fonda & G.C. Ghirardi (1974), "Does the lifetime of an unstable system depend on the measuring apparatus?", Il Nuovo Cimento A, 21 (3): pp. 471-484 {{citation}}: |pages= has extra text (help)
  6. Christof Teuscher & Douglas Hofstadter (2004). Alan Turing: Life and Legacy of a Great Thinker. Springer. p. p. 54. ISBN 3540200207. {{cite book}}: |page= has extra text (help); line feed character in |author= at position 18 (help)
  7. John von Neumann (1932). Mathematische Grundlagen der Quantenmechanik. Springer. p. Chapter V.2. ISBN 3540592075. (See also: J. von Neumann (1955). Mathematical Foundations of Quantum Mechanics. Princeton: Princeton University Press. p. p. 366. ISBN 0691028931. {{cite book}}: |page= has extra text (help)); Michael B. Mensky (2000). Quantum Measurements and Decoherence. Springer. p. §4.1.1, pp. 315 ff. ISBN 0792362276.; Ch. Wunderlich & Ch. Balzer (Benjamin Bederson & H Walther, editors) (2003). Advances in Atomic, Molecular, and Optical Physics: Vol. 49. Academic Press. ISBN 0120038498. {{cite book}}: |author= has generic name (help)
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  14. This definition is a paraphrase of the introductory remarks in Raizen et al. 's paper cited later in this article.
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