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Optics Letters

Coherence and indistinguishability

L. Mandeļ

Published Dec 1, 1991• 237 citations
Publisher

Abstract

It has long been known that the interference produced by two light beams is related both to their mutual coherence and also to the intrinsic indistinguishability of the photon paths. With the help of a decomposition of the density operator it is shown that the degree of indistinguishability equals the degree of coherence. This provides the fundamental link between the wave and the particle descriptions.

DOI
10.1364/ol.16.001882

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It has long been known that the interference produced by two light beams is related both to their mutual coherence and also to the intrinsic indistinguishability of the photon paths. With the help of a decomposition of the density operator it is shown that the degree of indistinguishability equals the degree of coherence. This provides the fundamental link between the wave and the particle descriptions.
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.
It is well known that in classical optics, the visibility of interference, in a two-beam light interference, is related to the optical coherence of the two beams. A wave-particle duality relation can be derived using this mutual coherence. The issue of wave-particle duality in classical optics is analyzed here, in the more general context of multipath interference. New definitions of interference visibility and path distinguishability have been introduced, which lead to a duality relation for multipath interference. The visibility is shown to be related to a new multipoint optical coherence function.
The wave-particle duality of a photon is the bedrock of quantum optics, where both natures are mutually exclusive. Contrary to the conventional understanding of quantum features such as photon bunching on a beam splitter and Bell inequality violation based on the particle nature of photons, a new interpretation is presented for the fundamental understanding of the same quantum features using the wave nature of photons. For this, phase quantization of an optical system interacting with photons is investigated and applied it to a particular quantum phenomenon to fully understand the fundamental concept of indistinguishability between two photons in the quantum feature. This talk opens the door to randomness-based quantum determinacy.
The wave-particle duality that manifests in the Young's double-slit interferometry satisfying the well known Englert-Greenberger-Yasin inequality has recently been shown to obey a universal triality relation involving coherence, predictability and rather surprisingly entanglement. In the present work, we explicitly demonstrate the persistence of the triality relation in the quantum induced coherence interferometer and the classical configuration recovers the well known duality inequality. Furthermore, we explore the origin of coherence and entanglement, in the induced coherence interferometer, and means to control them. We show that path indistinguishability (or intrinsic indistinguishability of the sources) in our setup plays a complementary role in influencing both interference and entanglement. We bring out manifestly the nature of coherence in both classical and quantum versions of induced coherence interferometers.
Interference of light fields, first postulated by Young, is one of the fundamental pillars of physics. Dirac extended this observation to the quantum world by stating that each photon interferes only with itself. A precondition for interference to occur is that no welcher-weg information labels the paths the photon takes; otherwise, the interference vanishes. This remains true, even if two-photon interference is considered, e.g., in the Hong-Ou-Mandel-experiment. Here, the two photons interfere only if they are indistinguishable, e.g., in frequency, momentum, polarization, and time. Less known is the fact that two-photon interference and photon indistinguishability also determine the photon statistics in the overlapping light fields of two independent sources. As a consequence, measuring the photon statistics in the far field of two independent sources reveals the degree of indistinguishability of the emitted photons. In this Letter, we prove this statement in theory using a quantum mechanical treatment. We also demonstrate the outcome experimentally with a simple setup consisting of two statistically independent thermal light sources with adjustable polarizations. We find that the photon statistics vary indeed as a function of the polarization settings, the latter determining the degree of welcher-weg information of the photons emanating from the two sources.