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Fringe Visibility from Feynman Path Integrals: Normalization and Photon Distinguishability

Travis Taylor

Published Jun 11, 2026• 0 citations
Publisher

Abstract

We derive the intensity and fringe visibility of an \(N\)-slit quantum interference system directly from the Feynman path integral by partitioning the amplitude into slit-conditioned path classes and incorporating internal quantum states to account for distinguishability. Applying Born's rule and tracing over unobserved degrees of freedom yields the standard coherence-theoretic intensity expression, establishing an explicit equivalence between the path-integral and Dirac formulations of multi-slit interference. We show that a naive uniform-coherence model leads to unphysical visibility values for \(N>2\), motivating a normalization-consistent decomposition into indistinguishable and distinguishable photon populations. The resulting visibility relation depends explicitly on the relative populations of coherent and incoherent photons and reproduces the standard two-slit limit while exhibiting the correct fully coherent and fully distinguishable limits. These results connect path-integral interference directly to experimentally measurable coherence properties and provide a normalization-consistent description of multi-slit visibility.

DOI
10.1364/opticaopen.32592276

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Abstract A well-known result for the interference of two single-mode fields is that the degree of coherence and the degree of indistinguishability are the same when we consider the detection of a single photon. In this article, we present the relation between the degree of coherence, path indistinguishability and the fringe visibility considering interference of multiple numbers of single-mode fields while being interested in the detection of a single photon only. We will also mention how Born’s rule of interference for multiple sources is reflected in these results.
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