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Quantum Zeno effect

From Academic Kids

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

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.

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 Itano, Heinzen, Bollinger and Wineland at NIST (PDF (http://www.boulder.nist.gov/timefreq/general/pdf/858.pdf)). Approximately 5000 9Be+ ions were stored in a cylindrical Penning trap and laser cooled to below 250mK. 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 reason we can't use the Zeno effect as a science-fiction-like stasis field to freeze large objects is because there is no way to couple them so strongly to the environment. Ordinary molecular forces are clearly insufficient. A much easier way to freeze a large object would be to cool it down to near absolute zero. At absolute zero the system is in its ground state and there is no macroscopic evolution. This is known as the third law of thermodynamics. Note that the Zeno effect allows a system to be frozen into an excited state, not just the ground state, so in some sense it is more versatile.

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.

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