Quantum Zeno effect

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The quantum Zeno effect is a quantum mechanical phenomenon first described by George Sudarshan and Baidyanaith Misra of the University of Texas in 1977. It describes the situation that 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.

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[edit] Definition

In general, the Zeno effect can be defined as class of phenomena when a transition is suppressed by some interaction which allows the interpretation of the final state in terms of "a transition has not yet occurred" or "a transition already occurred".

Although the definition above, appeared in Optical Review, was suggested for the interpretation of reflection of atoms by the "measuring" (absorbing) at the ridged mirror[1], 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 transition of a particle from one half-space to another (which could be used for atomic mirror in an atomic nanoscope[2]) , transition of a photon in waveguide from one mode to another, and it can be transition of an atom from one quantum state to another. It can be transition from the subspace without decoherent loss of a q-bit to a state with a q-bit lost in a quantum computer.[3] In this sense, for the q-bit correction, it is sufficient to watch, whether the decoherence already occurred or not yet. In principle, just frequent watching somebody walking on water could be sufficient to prevent the merging. All these can be considered as applications of the Zeno effect. However, for the actual walking on water, the frequency of measurements required is enormous, far away from human capacities. Therefore, practically, the concept of the Zeno effect is applied to atomic systems[4] (with distinguishable quantum states), rather than to macroscopic bodies.

[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 wavefunction 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. The probability that it will collapse back into the same state A is higher if the system has had less time to evolve away from it. In the limit as the time between measurements goes to zero, the probability of a collapse back to the original state A goes to one. Hence, the system doesn't evolve from A to B.

In reality, collapse of the wavefunction is not a discrete, instantaneous event. A measurement could be approximated by strongly coupling the quantum system to the noisy thermal environment for a brief period of time. The time it takes for the wavefunction 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, 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. One such experiment was performed in October 1989 by Wayne Itano, Dan Heinzen, John Bollinger and David Wineland at NIST (PDF). 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. Petrosky offers a refutation of this experiment in Physica A 170 (1991) 306-325.

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 overall.

[edit] See also

[edit] References

  1. ^ D.Kouznetsov, H.Oberst. Reflection of Waves from a Ridged Surface and the Zeno Effect. Optical Review, Vol. 12, No. 5 (2005) p. 363-366 URL: http://annex.jsap.or.jp/OSJ/opticalreview/TOC-Lists/vol12/12e0363tx.htm
  2. ^ D. Kouznetsov, H. Oberst, K. Shimizu, A. Neumann, Y. Kuznetsova, J.-F. Bisson, K. Ueda, S. R. J. Brueck. Ridged atomic mirrors and atomic nanoscope. J. Phys. B, v. 39 (2006) p. 1605-1623 URL: http://stacks.iop.org/0953-4075/39/1605
  3. ^ Quantum computer: URL: http://www.physorg.com/news11087.html
  4. ^ W.M.Itano, D.J.Heinsen, J.J.Bokkinger, D.J.Wineland. Quantum Zeno effect. PRA v.41, No.5, (1990), p.2396-2300 URL: http://www.boulder.nist.gov/timefreq/general/pdf/858.pdf
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