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Frontiers in Optics

Clock Synchronization using the Quantum Zeno Effect

S. U. Shringarpure, J. D. Franson

Published Jan 1, 2021• 0 citations
Publisher

Abstract

We investigate the use of the quantum Zeno effect to prevent the desynchronization of two-level atomic clocks by frequently measuring an observable of the combined state of the system.
DOI
10.1364/fio.2021.jth5a.21

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Prevention of a quantum system's time evolution by repetitive, frequent measurements of the system's state has been called the quantum Zeno effect (or paradox). Here we investigate theoretically and numerically the effect of repeated measurements on the quantum dynamics of multilevel systems that exhibit the quantum localization of classical chaos. The analysis is based on the wave function and Schr\"odinger equation, without introduction of the density matrix. We show how the quantum Zeno effect in simple few-level systems can be recovered and understood by formal modeling the effect of measurement on the dynamics by randomizing the phases of the measured states. This analysis is extended to investigate the dynamics of multilevel systems driven by an intense external force and affected by frequent measurements. We show that frequent measurements of such quantum systems results in delocalization of the quantum suppression of classical chaos. This result is the opposite of the quantum Zeno effect. The phenomenon of delocalization of the quantum suppression and restoration of quasi-classical time evolution of these systems, owing to repetitive frequent measurements, can therefore be called the quantum anti-Zeno effect. From this analysis we furthermore conclude that frequently or continuously observable quasiclassical systems evolve basically in a classical manner.
As we know,quantum Zeno effect may appear when frequent measurements are performed on an unstable quantum system.This effect is well popular in quantum information and quantum computation.However,most of the previous discussions on quantum Zeno effect were focused on two-level systems.In order to comprehend quantum Zeno effect and prevent the transition in different quantum systems better,we verified the existence of quantum Zeno effect in three-level systems.Furthermore,the existence of quantum Zeno effect in multilevel systems could also be fully verified similarly.
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.