A Priori Which-Way Information in Quantum Interference with Unstable Particles

TL;DR

This paper explores how the inherent decay properties of unstable particles influence quantum interference, demonstrating a fundamental relation between path predictability and fringe visibility in interferometry.

Contribution

It introduces the concept of a priori which-way information based on decay rates, linking it to interference visibility through a duality relation in quantum interferometry.

Findings

Path predictability depends on decay rate even without decay occurring.

A duality relation ${ m P}^2 + { m V}^2 = 1$ is established for unstable particles.

Interference visibility is reduced by a priori which-way information.

Abstract

If an unstable particle used in a two-path interference experiment decays before reaching a detector, which-way information becomes available which reduces the detected interference fringe visibility ${\cal V}$. Here we argue that even when an unstable particle does {\em not} decay while in the interferometer, {\em a priori} which-way information is still available in the form of path predictability ${\cal P}$ which depends on the particle's decay rate $\Gamma$. We further demonstrate that in a matter-wave Mach-Zehnder interferometer using an excited atom with an appropriately tuned cavity, ${\cal P}$ is related to ${\cal V}$ through the duality relation ${\cal P}^{2} + {\cal V}^{2} = 1$.