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Physical Review A

Zeno and anti-Zeno effects in multimode parametric down-conversion

Alfredo Luis

Published Jul 2, 2002• 9 citations
Publisher

Abstract

We present a simple multimode analysis of the Zeno and anti-Zeno effects in spontaneous parametric down-conversion. In this process the input vacuum is an unstable state decaying into a reservoir of down-converted modes by emitting a pair of photons. We show that the Zeno and the anti-Zeno effects are two particular examples of quantum propagation depending on the effective spectrum of down-converted modes. We show that this evolution can be easily tailored on demand and that these quantum phenomena admit a very simple explanation in terms of standard interference concepts.

DOI
10.1103/physreva.66.012101

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QUANTUM HAMLET EFFECT- A NEW EXAMPLE

Simply speaking quantum Zeno effect for an unstable quantum system represents total decay probability decrease by frequent decay detections.Analogously simply speaking quantum anti-Zeno effect for an unstable quantum system represents total no-decay probability decrease by frequent decay detections.Also, some authors considered optical, i.e. polarization detection analogy of quantum Zeno and anti-Zeno effects.In this work we consider basic standard quantum mechanical concepts in quantum Zeno and anti-Zeno effect.We use simplest (Malus law) form of mentioned ideas on the photon polarization detection analogy of quantum Zeno and anti-Zeno effects and we suggest some new situations (non-equivalent time durations of the quantum dynamical evolutions between different frequent detections).Correspondingly we define new quantum effects, quantum Hamlet effect (when, by frequent detections, final total polarization angle and state converge but total probability for appearance of this state diverges) and quantum anti-Hamlet effect (when, by frequent detections, final total polarization angle and state diverge but total probability for appearance of this state converges).Also, we consider a rough classical mechanical analogy of Zeno effect.Finally we consider frequent interference of single photon at beam splitters and obtain for different values of reflection and transmission coefficients analogies of quantum Zeno and anti-Zeno effect as well as analogy of usual exponentially decreasing decay law.

•Aug 16, 2016•0 citations

Multimode theory for the Zeno effect in parametric down-conversion

Solange Bessa Cavalcanti, Geraldo A. Barbosa, Jandir M. Hickmann

We propose a multi-mode theory to demonstrate the Zeno effect--inhibition of transitions via frequent measurements- -in the context of parametric down-conversion.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jul 19, 1999•2 citations
We present a simple multimode analysis of the Zeno and anti-Zeno effects in spontaneous parametric down-conversion. In this process the input vacuum is an unstable state decaying into a reservoir of down-converted modes by emitting a pair of photons. We show that the Zeno and the anti-Zeno effects are two particular examples of quantum propagation depending on the effective spectrum of down-converted modes. We show that this evolution can be easily tailored on demand and that these quantum phenomena admit a very simple explanation in terms of standard interference concepts.
The distortion of a spontaneous down-conversion process caused by an auxiliary mode coupled to the idler wave is analyzed. In general, a strong coupling with the auxiliary mode tends to hinder the down-conversion in a nonlinear medium. On the other hand, provided that the evolution is disturbed by the presence of a phase mismatch, the coupling may increase the speed of down-conversion. These effects are interpreted as being manifestations of quantum Zeno and anti-Zeno effects, respectively, and they are understood by using the dressed mode picture of the device. The possibility of using the coupling as a nontrivial phase-matching technique is pointed out.
A simple model of indirect pre-measurements on an unstable quantum state is presented in this paper. The model is completely solvable and the solutions are used to compare the time evolution of the unstable state with and without the influence of the pre-measurement. We find that by choosing the details of the process of pre-measurement appropriately, it is possible to observe both suppression and enhancement of the rate of decay of the unstable state. When the pre-measurements are assumed to lead on to actual measurements, we see that the quantum Zeno effect, and in some instances the 'anti-Zeno' effect, can be produced by repeating the measurement many times in succession. The Zeno effect can appear in our model either as a real consequence of repeated measurements or sometimes merely as an artefact of the manner in which the observations on the system are performed. The anti-Zeno effect appears almost exclusively as an artefact of the details of the measurement. Numerical investigations are included to delineate the regimes in which the quantum Zeno effect and possibly the anti-Zeno effect can occur.
Simply speaking quantum Zeno effect for an unstable quantum system represents total decay probability decrease by frequent decay detections.Analogously simply speaking quantum anti-Zeno effect for an unstable quantum system represents total no-decay probability decrease by frequent decay detections.Also, some authors considered optical, i.e. polarization detection analogy of quantum Zeno and anti-Zeno effects.In this work we consider basic standard quantum mechanical concepts in quantum Zeno and anti-Zeno effect.We use simplest (Malus law) form of mentioned ideas on the photon polarization detection analogy of quantum Zeno and anti-Zeno effects and we suggest some new situations (non-equivalent time durations of the quantum dynamical evolutions between different frequent detections).Correspondingly we define new quantum effects, quantum Hamlet effect (when, by frequent detections, final total polarization angle and state converge but total probability for appearance of this state diverges) and quantum anti-Hamlet effect (when, by frequent detections, final total polarization angle and state diverge but total probability for appearance of this state converges).Also, we consider a rough classical mechanical analogy of Zeno effect.Finally we consider frequent interference of single photon at beam splitters and obtain for different values of reflection and transmission coefficients analogies of quantum Zeno and anti-Zeno effect as well as analogy of usual exponentially decreasing decay law.