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arXiv:2008.06336 · Indian Journal of Physics

Coherence and path indistinguishability for the interference of multiple single-mode fields

Rathindra Nath Das, Sobhan Kumar Sounda

Published Jun 30, 2022• 0 citations
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Abstract

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.

DOI
10.1007/s12648-022-02398-w

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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.
We derive the intensity and fringe visibility of an NNN-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>2N>2N>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.
We derive the intensity and fringe visibility of an NNN-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>2N>2N>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.
Over the past several decades, single photon-based path interference in double-slit experiment has been well demonstrated for the particle nature of photons satisfying complementarity theory, where the quantum mechanical interpretation of the single photon interference fringe is given by Born rule for complex amplitudes in measurements. Unlike most conventional methods using entangled photon pairs, here, a classical coherent light source is directly applied for the proof of the same self-interference phenomenon. Instead of double slits, we use a Mach-Zehnder interferometer as usual, where the resulting self-interference fringe of coherent single photons is exactly the same as that of the coherent photon ensemble of the laser, demonstrating that the classical coherence based on the wave nature is rooted in the single photon self-interference. This unexpected result seems to contradict our common understanding of decoherence phenomena caused by multi-wave interference among bandwidth distributed photons in coherence optics.