Quantum Zeno effect

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The quantum Zeno effect is a quantum mechanical phenomenon first predicted by soviet physicist Leonid Khalfin in 1958.^[1] Later it was described by George Sudarshan and Baidyanaith Misra of the University of Texas in 1977.^[2] It describes the situation in which an unstable particle, if observed continuously, will never decay. This occurs because every 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, with no observer in any conventional sense.

The quantum Zeno effect takes its name from Zeno's arrow paradox, which is the argument that since an arrow in flight does not move during any single instant it couldn't possibly be moving at all.

Contents 1 Definition 2 Periodic measurement of a quantum system 3 Experiments and discussion 4 Significance to Cognitive Science 5 See also 6 External links 7 References

[edit] Definition

In general, the Zeno effect can be defined as a class of phenomena wherein transition is suppressed by an interaction that produces a state that can be interpreted as indicating either "a transition has not yet occurred" or "a transition already occurred".

Although the definition above, which appeared in Optical Review, was suggested for the interpretation of reflection of atoms by "measurement" (absorption) at a ridged mirror,^[3] it covers various versions of the 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,^[4]) 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.^[5] 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.^[6] By its nature, the effect appears only in systems with distinguishable quantum states, and hence is inapplicable to classical phenomena and macroscopic bodies.

It has to be remarked that, contrary to what was stated at the beginning, the Zeno's paradox in quantum mechanics was not discovered by Sudarshan Chiu and Misra. To be precise it was already known for many years; just to give an example, W. Yourgrau, on pg 191 of his "Problems in the Philosophy of Science" (Amsterdam, 1968) mentions it clearly and appropriately refers to it as "the Turing Paradox." Quantum mechanically its first rigorous derivation appears in a paper by A. Degasperis, L. Fonda and G.C. Ghirardi on Il Nuovo Cimento A, vol 21,471 published in 1974.

[edit] 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.

[edit] 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 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.

In 1989, David Wineland and his group at NIST (PDF) 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 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. The transition of an atom from one half-space to another, suppressed by the "measurement"^[3] (decoherence at the interaction with ridges) at the ridged mirror also should be considered as experimental evidence of the Zeno effect.

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 Schroedinger equation of the quantum system. Even more, the detailed description of experiments with the "Zeno effect", and especially at the limit of high frequency of measurements (high efficiency of suppression of transition, or high reflectivity of a ridged mirror) usually cannot be performed with just speculation based on the idealized measurement,^[4] and require analysis of the mechanism of the interaction.

[edit] Significance to Cognitive Science

The quantum Zeno effect is becoming a central concept in the exploration of controversial and as-yet 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.

[edit] See also

• Interference
• Zeno's paradoxes

[edit] External links

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

[edit] References