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Journal of Physics Condensed Matter

Zeno effect on the Debye–Waller factor

A.C. Levi

Published Jul 13, 2010• 0 citations
Publisher

Abstract

The Debye-Waller factor may be close to one, hence ineffective for decoherence, if it is caused by high-frequency vibrations. This appears as a manifestation of the Zeno effect, where the quantum properties of a system do not deteriorate (or do so very slowly) if the system is subjected to frequently repeated interactions. In the case of atom-surface scattering, the decoherence time is shown to be long for high frequencies, such that the oscillation period is short in comparison to the duration of a collision. For a periodic perturbation the restoration of coherence, in the case where many oscillation periods take place during a prescribed time, is shown.

DOI
10.1088/0953-8984/22/30/304003

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The Debye-Waller factor may be close to one, hence ineffective for decoherence, if it is caused by high-frequency vibrations. This appears as a manifestation of the Zeno effect, where the quantum properties of a system do not deteriorate (or do so very slowly) if the system is subjected to frequently repeated interactions. In the case of atom-surface scattering, the decoherence time is shown to be long for high frequencies, such that the oscillation period is short in comparison to the duration of a collision. For a periodic perturbation the restoration of coherence, in the case where many oscillation periods take place during a prescribed time, is shown.
A number of scattering situations can naively be expected to show essentially classical features, because of a (generalized) Debye-Waller factor causing decoherence and destroying interference and diffraction phenomena. It is shown, however, that such decoherence may be quenched in several ways: A-the momentum transfer to a large system may be separated into subtransfers to individual atoms, each subtransfer being too small to cause a strong Debye-Waller effect; B-(more significantly) the high-frequency vibrations may be ineffective in causing strong decoherence, because the corresponding correlation functions remain non-vanishing for too short a time. When this Debye-Waller factor quenching takes place, coherence is restored and typical quantum wave-like phenomena reappear.
We show that Born-Oppenheimer surfaces can intrinsically decohere, implying loss of coherence among constituent electronic basis states. We consider the example of interatomic forces due to resonant dipole-dipole interactions within a dimer of highly excited Rydberg atoms, embedded in an ultracold gas. These forces rely on a coherent superposition of two-atom electronic states, which is destroyed by continuous monitoring of the dimer state through a detection scheme utilizing the background gas atoms. We show that this intrinsic decoherence of the molecular energy surface can gradually deteriorate a repulsive dimer state, causing a mixing of attractive and repulsive character. For sufficiently strong decoherence, a Zeno-like effect causes a complete cessation of interatomic forces. We finally show how short decohering pulses can controllably redistribute population between the different molecular energy surfaces.
It is accepted that among the ways through which a quantum phenomenon decoheres and becomes a classical one is what is termed in the literature the Zeno effect. This effect, named after the ancient Greek philosopher Zeno of Elea (born about 485 B.C), were used in 1977 to analytically predict that an initial quantum state may be preserved in time by merely repeating a large number of times, in a finite total time, the experiment of checking its state. Since then this effect has been experimentally validated and has become an established physical fact. It has been argued by Simonius that the Zeno effect must be related not only to quantum phenomena but also to many macroscopic and classical effects. Thus, since it operates in both quantum and classical regimes it must cause to a more generalized kind of decoherence than the restricted one that ``classicalizes'' a quantum phenomenon. We show that this generalized decoherence, {\it obtained as a result of dense measurement}, not only gives rise to new phenomena that are demonstrated through new responses of the densely interacted-upon system but also may physically {\it establish} them. For that matter we have found and established the analogous {\it space Zeno effect} which leads to the necessity of an ensemble of related observers (systems) for the remarked physical validation of new phenomena. As will be shown in Chapters 3-5 of this work the new phenomena (new responses of the system) that result from the space Zeno effect may be of an unexpected nature. We use quantum field theory in addition to the more conventional methods of analysis and also corroborate our analytical findings by numerical simulations.
The quantum Zeno effect arises due to frequent observations. That implies the existence of some experimenter and its interaction with the system. In this contribution, we examine what happens for a closed system if one considers a quantum Zeno type of question, namely what is the probability of a system, remaining always in a particular subspace. This has implications to the arrival time problem that is also discussed. We employ the decoherent histories approach to quantum theory, as this is the better developed formulation of closed system quantum mechanics, in particular, dealing with questions that involve time in a non-trivial way. We get a very restrictive decoherence condition, that implies that even if we do introduce an environment, there will be very few cases that we can assign probabilities to these histories, but in those cases the quantum Zeno effect is still present.
The evolution of a quantum system undergoing very frequent measurements takes place in a subspace of the total Hilbert space (quantum Zeno effect). The dynamical properties A quantum system, prepared in a state that does not belong to an eigenvalue of its total Hamiltonian, starts to evolve quadratically in time [1, 2]. This behavior leads to the so-called quantum Zeno phenomenon: by performing frequent measurements on the system, in order to check whether it is still in its initial state, one can “slow
Quantum Zeno effect can be applied to quantum information processing，and can reveal the nature of quantum measurement. In addition, it has also many potential applications. This suggests that studying the quantum Zeno effect has great theoretical and experimental significance. In this work, the system of a two-level atom interacting with a single mode field is considered and the dynamics of the system subjected to successive projection measurements is studied, and the quantum Zeno effect is presented. Moreover, the influence of the quantum Zeno effect on atomic population inversion is discussed. Based on Schrödinger equation, the survival probability of the initial state of the two-level atom subjected to frequently repeated measurements can be obtained. The survival probability depends on the time interval between measurements. It is seen that the exponential decay of the system under slowly frequent measurements is presented instead of the naturally oscillatory process. For slowly repeated measurements the atomic population inversion and the survival probability of initial state decline rapidly at the early time and then both of them become unchanged. As the time intervals of the measurements are sufficiently short, the quantum Zeno effect occurs. These results have also shown how the measurement can inhibit the atomic population inversion.