Quantum Zeno Effect

The quantum Zeno effect is an effect from quantum mechanics , in which the transition of a quantum mechanical system from one state to another, e.g. B. by emitting light from an excited atom , can be stopped by repeated measurements . The effect is reminiscent of the arrow paradox of the Greek philosopher Zenon von Elea . The term comes from George Sudarshan and B. Misra.

Pictorial reasoning

If an atom spontaneously decays, according to the laws of quantum mechanics, this does not happen at a predetermined point in time, but randomly, i.e. H. according to purely statistical principles. This event can most easily be understood as a superposition (superposition) of the states A (not disintegrated) and B (disintegrated). From this superposition there is then a certain probability with which the decay will occur. In a spontaneously disintegrating system, this probability increases with the passage of time. If at a certain point in time it is checked whether the atom has already decayed or not, one finds either state A (atom not decayed) or B (atom disintegrated). This corresponds to a quantum mechanical measurement with the basic property that only eigenstates of the measurement operator (i.e. A or B) and no superimposed states can be detected. The probability of finding condition A or B is given by the weight portion of the respective measured condition in the overlay, which shifts more and more from A to B over time. The measurement process itself reduces the wave function to state A or B, which is then referred to as a collapse of the wave function .

If the individual atom is in state A (not disintegrated) at the beginning, then the proportion of state B (disintegrated) is extremely small after a short time. In the event of a measurement, there is a very high probability that it will not have decayed. In this case, through the observation, it goes back to the eigenstate A (100% not decayed), and the decay process begins again.

Overall, when observed frequently, one gets a decay rate that is significantly below the unobserved rate of decay. If the intervals between the observations are allowed to approach zero, which is equivalent to permanent observation, the decay probability also approaches zero, i.e. H. the constantly observed atom should no longer decay because of this observation.

The quantum Zeno effect has been experimentally confirmed by several groups around the world using methods of laser technology and atomic physics.

A German-language popular scientific review appeared in 1994 after measurements at the Ludwig Maximilians University in Munich: the movement of a quantum system was demonstrably brought to a standstill by a series of dense measurements alone, which underpins the theoretical modeling of the quantum Zeno effect.

General requirement

Preconditions from quantum theory for the occurrence of the effect:

1. The measurement operator and the time evolution operator do not interchange with one another.
2. The system develops coherently (undisturbed) between the measurements.

Analogy: A reverse Zeno effect in optics

Optical Zeno effect

An experiment that can also be described in the context of classical physics and that serves to get closer to an understanding of the Zeno effect consists of a polarized light source and several polarizers , as shown in the adjacent figure.

Initially (Fig. (0)) the light from the light source is polarized purely vertically. This orientation does not change with free propagation, so it will never be horizontally polarized. A horizontal polarizer therefore always leads to extinction.

If one adds a polarizer that is rotated against the direction of polarization of the light , the intensity decreases proportionally for the observer , since only the projection of the plane of vibration onto the polarizer axis is allowed to pass. What is particularly interesting is that this polarizer is a quantum mechanical measurement . According to this, the polarization plane is parallel to the polarizer axis (Fig (1)), which corresponds to a quantum mechanical state preparation. ${\displaystyle \alpha }$ ${\displaystyle \cos ^{2}\alpha }$

If you now add polarizers one behind the other, in the limit case: which are each rotated by only an infinitesimal angle to one another , the loss per polarizer is minimal and in the limit case approaches zero. It is thus possible to rotate the polarization direction purely through loss-free measurements carried out one after the other. H. change the expected magnitude of the observable. This scenario roughly corresponds to the continuous measurement described above. ${\displaystyle n}$ ${\displaystyle n\rightarrow \infty }$ ${\displaystyle \mathrm {d} \alpha }$

Criticism and other aspects

So far, no stopping of radioactive decay has been confirmed by experimental measurements of an ensemble of radioactive atoms or even a single radioactive atom, as the theory of the quantum Zeno effect would require. Above all, the opposite, the inversion of the Zeno effect, is not an analogy, but only a contrary or polar contrast. The experiments by Itano and co-workers relate to stable isotopes of ⁹ Be in mixtures with ²⁶ Mg , with transitions in the UV- Area stimulated and observed. Since the quantum mechanical system in this case was defined a priori by the observer or was disturbed, the observation of an indeterminate system cannot be assumed, which calls into question the experimental approach. In fact, it is more likely that the corresponding quantum mechanical process, in particular radioactive decay, will even be accelerated if it is examined with a high observation frequency.

Literature and web links

• Christian Speicher: "Deceptive movement in the quantum world. A modern version of Zeno's paradox. Measurement as an intervention with far-reaching consequences." - Nature and Science (supplement to the Frankfurter Allgemeine Zeitung ), April 6, 1994, N1 f.
• PDF, Quantum Mechanical Paradoxes (1.01 MB)
• NZZ research and technology, popular science. Article about the QM Zeno effect ( Memento from May 27, 2008 in the Internet Archive )
• http://www.spektrum.de/magazin/zeno-und-der-quanten-schnellkochtopf/828346

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1. ^ B. Misra and ECG Sudarshan: The Zeno's paradox in quantum theory. J. Math. Phys. 18, 756-763 (1977)
2. ↑ ^{a b} W. M. Itano, DJ Heinzen, JJ Bollinger, DJ Wineland : Quantum Zeno effect. Phys. Rev. A 41, 2295-2300 (1990)
3. ↑ MC Fischer, B. Gutiérrez-Medina MG Raizen: Observation of the Quantum Zeno and Anti-Zeno effects in an Unstable System. Physical Review Letters 87, 040402 (2001)
4. ↑ Chr. Wunderlich, Chr. Balzer, and PE Toschek: Evolution of an Atom Impeded by Measurement: The Quantum Zeno Effect. In: Journal of Nature Research A . 56, 2001, pp. 160-164 ( PDF , free full text).
5. ^ Chr. Balzer, R. Huesmann, W. Neuhauser, PE Toschek, The Quantum Zeno Effect - Evolution of an Atom Impeded by Measurement. Opt. Comm. 180 (2000) 115-120, quant-ph / 0105004
6. ↑ Chr. Balzer, Th. Hannemann, D. Reiss, Chr. Wunderlich, W. Neuhauser, PEToschek: A relaxationless demonstration of the Quantum Zeno Paradox on an individual atom. Optics Communications Vol. 211, 235-241 (2002), quant-ph / 0406027
7. ↑ Christian Speicher: "Deceptive movement in the quantum world. A modern version of Zeno's paradox. Measurement as an intervention with far-reaching consequences." - Nature and Science (supplement to the Frankfurter Allgemeine Zeitung ), April 6, 1994, N1 f.
8. ↑ Zeno's Quantum Paradox Reversed: Watching A Flying Arrow Increase Its Speed