Wave-particle duality in multi-path interferometers: General concepts and three-path interferometers

Abstract

For two-path interferometers, the which-path predictability P and the fringe visibility ν are familiar quantities that are much used to talk about wave-particle duality in a quantitative way. We discuss several candidates that suggest themselves as generalizations P of P for multi-path interferometers, and treat the case of three paths in considerable detail. To each choice for the path knowledge P , the interference strength V - the corresponding generalization of ν - is found by a natural, operational procedure. In experimental terms, it amounts to finding those equal-weight superpositions of the path amplitudes which maximize P for the emerging intensities. Mathematically speaking, one needs to identify a certain optimum one among the Fourier transforms of the state of the interfering quantum object. Wave-particle 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. © 2008 World Scientific Publishing Company.