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

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 $\mathcal{V}$. 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 $\mathcal{P}$ which depends on the particle's decay rate $\hat{I}“$. We further demonstrate that in a matter-wave Mach-Zehnder interferometer using an excited atom with an appropriately tuned cavity, $\mathcal{P}$ is related to $\mathcal{V}$ through the duality relation ${\mathcal{P}}^2+{\mathcal{V}}^2=1$.

7 pages, 1 figure