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Optics Letters

Experimental display of the extended polarization coherence theorem

P. Sánchez, J. Gonzales, V. Avalos, Fabio J. Auccapuclla, E. Suarez, F. De Zela

Published Feb 13, 2019• 6 citations
Publisher

Abstract

We report experimental results that show the interplay between visibility, distinguishability, and the degree of polarization, as ruled by a recent extension of the polarization coherence theorem (PCT). Theorems of this kind address duality in both quantum and classical scenarios. We particularly focus on the inherent vector nature of the polarization degree of freedom and display various effects that lie beyond the scope of the original PCT. Our results exhibit features that can be shared by quantum and classical phenomena, whenever these phenomena reflect some hidden or exposed coherence.

DOI
10.1364/ol.44.001052

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We report experimental results that show the interplay between visibility, distinguishability, and the degree of polarization, as ruled by a recent extension of the polarization coherence theorem (PCT). Theorems of this kind address duality in both quantum and classical scenarios. We particularly focus on the inherent vector nature of the polarization degree of freedom and display various effects that lie beyond the scope of the original PCT. Our results exhibit features that can be shared by quantum and classical phenomena, whenever these phenomena reflect some hidden or exposed coherence.
Light is neither wave nor particle, but both, according to Bohr’s complementarity principle, which was first devised to qualitatively characterize quantum phenomena. Later, quantification was achieved through inequalities such as V2+D2≤1, which engage visibility V and distinguishability D. Recently, equality V2+D2=P2—the polarization coherence theorem (PCT)—was established, incorporating polarization P and addressing both quantum and classical coherences. This shows that Bohr’s complementarity is not restricted to quantum phenomena. We derive an extension of the PCT that also applies to quantum and classical light fields carrying intertwined, dichotomic observables, such as polarization and two-path alternative. We discuss how constraints critically depend on the chosen measurement strategy. This may prompt various experiments to exhibit complementary features that possibly lurk behind hidden coherences.
For light fields, the manifestation of correlations between fluctuating electric field components at different space–time points is referred to as coherence, whereas these correlations appearing between orthogonal electric field components at a single space–time point are referred to as polarization. In this context, a natural question is as follows: how are coherence and polarization interconnected? Very recently, a tight equality P2=V2+D2, namely, the “polarization coherence theorem” (PCT) connecting polarization P with interference visibility V (measure of coherence) and distinguishability D (measure of which-path information) has been proposed [Optica4, 1113 (2017)OPTIC82334-253610.1364/OPTICA.4.001113]. We here report a direct observation of the PCT for classical light fields using a Mach–Zehnder interferometer along with a synthesized source producing a complete gamut of degrees of polarizations. Our experimental demonstration could motivate ongoing experimental efforts toward probing the hidden coherences and complementarity features.
We present an extension of the polarization coherence theorem (PCT) for the case in which two qubits play similarly important roles. The standard version of the PCT: V2+D2=P2, involves three measures, visibility V, distinguishability D, and the degree of polarization P, all of which refer to a single qubit, regardless of its physical realization. This is also the case with the inequality that is implied by the PCT: V2+D2≤1, which was originally derived in an attempt to quantify Bohr’s complementarity principle. We show that all of these constraints hold true, no matter how the involved qubits are physically realized, either as quantum or else as classical objects.
The dual wave–particle nature of light and the degree of polarization are fundamental concepts in quantum physics and optical science, but their exact relation has not been explored within a full vector-light quantum framework that accounts for interferometric polarization modulation. Here, we consider vector-light quantum complementarity in double-pinhole photon interference and derive a general link between the degree of polarization and wave–particle duality of light. The relation leads to an interpretation for the degree of polarization as a measure describing the complementarity strength between photon path predictability and so-called Stokes visibility, the latter taking into account both intensity and polarization variations in the observation plane. It also unifies results advanced in classical studies by showing that the degree of polarization can be viewed as the ability of a light beam to exhibit intensity and polarization-state fringes. The framework we establish thus provides novel aspects and deeper insights into the role of the degree of polarization in quantum-light complementarity and photon interference.
Visibility VVV and distinguishability DDD quantify wave-ray duality: V2+D2≤1V^2 + D^2 \le 1V2+D2≤1. We join them to polarization PPP via the Polarization Coherence Theorem, a tight equality: P2=V2+D2P^2 = V^2 + D^2P2=V2+D2.
Recent times have seen a spurt of research activity focused on "completing" certain wave-particle duality relations using entanglement or polarization. These studies use a duality relation involving path-predictability, and not path-distinguishability. Quantum origins of these results are explored here, in the more general framework of multipath quantum interference. Multipath interference with a path-detector is theoretically analyzed to find the connection between predictability and distinguishability. It is shown that entanglement is what quantitatively connects distinguishability with predictability. Thus, a duality relation between distinguishability and coherence can also be viewed as a triality between predictability, entanglement, and coherence. There exist two different kinds of duality relations in the literature, which pertain to two different kinds of interference experiments, with or without a path-detector. Results of this study show that the two duality relations are quantitatively connected via entanglement. The roots of the new, to the best of our knowledge, results in the classical optical domain, including the polarization coherence theorem, can be understood in the light of this work.