Influence of the measurement on the decay law: the bang-bang case

TL;DR

This paper investigates how repeated pulsed measurements within a specific energy range influence the decay law of unstable quantum systems, demonstrating the occurrence of the Quantum Zeno Effect in this context.

Contribution

It extends the understanding of the Quantum Zeno Effect by analyzing its occurrence when measurements detect decay products only within a limited energy range.

Findings

Quantum Zeno Effect can occur with energy-restricted measurements

Repeated measurements influence the decay lifetime

Exponential decay law can be affected by measurement timing

Abstract

After reviewing the description of an unstable state in the framework of nonrelativistic Quantum Mechanics (QM) and relativistic Quantum Field Theory (QFT), we consider the effect of pulsed, ideal measurements repeated at equal time intervals on the lifetime of an unstable system. In particular, we investigate the case in which the `bare' survival probability is an exact exponential (a very good approximation in both QM and QFT), but the measurement apparatus can detect the decay products only in a certain energy range. We show that the Quantum Zeno Effect can occur in this framework as well.