Waveparticle duality in multipath interferometers: General concepts and threepath interferometers
Abstract
For twopath interferometers, the whichpath predictability $\mathcal{P}$ and the fringe visibility $\mathcal{V}$ are familiar quantities that are much used to talk about waveparticle duality in a quantitative way. We discuss several candidates that suggest themselves as generalizations $P$ of $ mathcal{P}$ for multipath interferometers, and treat the case of three paths in considerable detail. To each choice for the \emph{path knowledge} $P$, the \emph{interference strength} $V$  the corresponding generalization of $\mathcal{V}$  is found by a natural, operational procedure. In experimental terms it amounts to finding those equalweight superpositions of the path amplitudes which maximize $P$ for the emerging intensities. Mathematically speaking, one needs to identify a certain optimal one among the Fourier transforms of the state of the interfering quantum object. Waveparticle duality is manifest, inasmuch as P=1 implies V=0 and V=1 implies P=0, whatever definition is chosen. The possible values of the pair $(P,V)$ are restricted to an area with corners at $(P,V)=(0,0)$, $(P,V)=(1,0)$, and $(P,V)=(0,1)$, with the shape of the border line from $(1,0)$ to $(0,1)$ depending on the particular choice for $P$ and the induced definition of $V$.
 Publication:

arXiv eprints
 Pub Date:
 September 2007
 arXiv:
 arXiv:0710.0179
 Bibcode:
 2007arXiv0710.0179E
 Keywords:

 Quantum Physics
 EPrint:
 28 pages, 6 figures