Quantum Zeno effect for a free-moving particle

Abstract

Although the quantum Zeno effect takes its name from Zeno's arrow paradox, the effect of frequently observing the position of a freely moving particle on its motion has not been analyzed in detail in the frame of standard quantum mechanics. We study the evolution of a moving free particle while monitoring whether it lingers in a given region of space, and explain the dependence of the lingering probability on the frequency of the measurements and the initial momentum of the particle. Stopping the particle entails the emergence of Schrödinger cat states during the observed evolution, closely connected to the high-order diffraction modes in Fabry-Pérot optical resonators.