Wave-Particle Duality in N-Path Interference

Abstract

Bohr's principle of complementarity, in the context of a two-slit interference experiment, is understood as the quantitative measures of wave and particle natures following a duality relation ${\mathcal{D}}^2+{\mathcal{V}}^2\le 1$. Here $\mathcal{D}$ is a measure of distinguishability of the two paths, and $\mathcal{V}$ is the visibility of interference. It is shown that such a relation can be formulated for $N-$slit or $N-$path interference too, with the proviso that the wave nature is characterized by a measure of {\em coherence} ($\mathcal{C}$). This new relation, ${\mathcal{D}}^2+{\mathcal{C}}^2\le 1$ is shown to be tight, and reduces to the known duality relation for the case $N=2$. A recently introduced similar relation (Bagan et al., 2016) is shown to be inadequate for the purpose.

5 pages, 2 figures, revised version, accepted in Annals of Physics

References in corpus (3)

• Equivalence of wave-particle duality to entropic uncertainty
• Entropic framework for wave-particle duality in multipath interferometers
• Measuring Quantum Coherence in Multi-Slit Interference

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