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Experimental Evidence of TEF Manipulation

Sebastian Virtosu

Published Dec 19, 2025• 0 citations
Publisher

Abstract

In the canonical Einstein photon-path experiment (and its modern realizations using single-photon interferometry or weak measurement), researchers sought to observe the dual nature of light by controlling the degree of \emph{path distinguishability} ($D$) and \emph{interference visibility} ($V$). The standard quantum mechanical complementarity relation reads: \begin{equation} D^2 + V^2 \le 1, \label{eq:SM_complementarity} \end{equation} where $D$ quantifies how well one can know which path the photon took, and $V$ measures the visibility of the interference fringes. In the Standard Model (SM) framework, the experiment is interpreted as a probabilistic trade-off between the wave and particle aspects of the photon, regulated by the act of measurement. Observation---or potential observability---is taken as the mechanism collapsing a superposed state into a definite outcome.

DOI
10.5281/zenodo.17983489

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In the canonical Einstein photon-path experiment (and its modern realizations using single-photon interferometry or weak measurement), researchers sought to observe the dual nature of light by controlling the degree of \emph{path distinguishability} (DDD) and \emph{interference visibility} (VVV). The standard quantum mechanical complementarity relation reads: \begin{equation} D^2 + V^2 \le 1, \label{eq:SM_complementarity} \end{equation} where DDD quantifies how well one can know which path the photon took, and VVV measures the visibility of the interference fringes. In the Standard Model (SM) framework, the experiment is interpreted as a probabilistic trade-off between the wave and particle aspects of the photon, regulated by the act of measurement. Observation---or potential observability---is taken as the mechanism collapsing a superposed state into a definite outcome.
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.
One of the most puzzling consequences of interpreting quantum mechanics in terms of concepts borrowed from classical physics, is the so-called wave-particle duality. Usually, wave-particle duality is illustrated in terms of complementarity between path distinguishability and fringe visibility in interference experiments. In this work, we instead propose a new type of complementarity, that between the continuous nature of waves and the discrete character of particles. Using the probabilistic methods of quantum field theory, we show that the simultaneous measurement of the wave amplitude and the number of photons in the same beam of light is, under certain circumstances, prohibited by the laws of quantum mechanics. Our results suggest that the concept of “interferometric duality'' could be eventually replaced by the more general one of “continuous-discrete duality''.
The mathematics of quantum theory is based on operators rather than numbers. In optics this simple fact allows statistical quantities, such as the fluctuations in the electric field of a light beam, to be smaller than is allowed by classical physics. Experiments that measure these quantities can generally be divided into two types, depending on whether they measure the wave or the particle properties of light. This is in line with the "complementarity principle" of quantum mechanics, which states that the wave and particle aspects of a system cannot be observed at the same time.
Updating the wave-particle duality Maria C. Bosca e-mail: bosca@ugr.es Departamento de Fisica Atomica, Molecular y Nuclear Universidad de Granada E-18071. Granada Spain The wave-particle-duality, the fundamental component of the new quantum formalism in Bohr’s opinion, must be reformulated by incorporating the results of some experiments accomplished in the last decades of twentieth century. The Bohr´s complementarity principle stated the mutual exclusiveness and joint full completeness of the two (classical) descriptions of quantum systems; after Einstein-Podolsky-Rosen’paper, the wave-particle duality, or wave-particle complementarity, could be expressed by stating that it is impossible to build up an experimental arrangement in which we observe at the same time both corpuscular and wave aspects. In a two-slit experiment, they would correspond, respectively, to the which-way knowledge and the observation of interference pattern. Bohr showed this mutual exclusivity in numerous examples , and linked it to the unavoidable disturbance inherent in any measurement event. In quantum mechanical formalism, the complementarity principle has a clear mathematical expression: two observables are complementary if precise knowledge of one of them implies that all possible outcomes of the other are equally probable; their extension to classical concepts (as wave and particle) is not concerned. In 1991 Scully et al published a variant of the two-slit experiment that incorporates two micromasers cavities and a laser beam to provide which-path information without net momentum transferred during the interaction ; the impossibility of know which slit an atom went through and still observe the interference fringes is preserved by the establishing of quantum correlations between the measuring apparatus and the system being observed. They claimed that complementarity, of which wave-particle duality would be to them a manifestation, is more fundamental than the uncertainty principle . In 1996 B-G. Englert, following an approach originally due to Wooters and Zurek , derived , without making use of Heisenberg’s uncertainty relation, an inequality that quantifies the mutual compatibility relation between fringe visibility and which-way information. The inequality, that they denominated as “interferometric duality”, has the expression D^2 + V^2 ≤ 1, where D stands for the distinguishability of the ways and V for the fringe visibility; both of them are mathematical expressions that can be measured to check experimentally the inequality . Today, it is clear that intermediate particle-wave behaviours exist and, in addition to that, there are single experiments in which both classical wave-like and particle-like behaviours are showed total and simultaneously on an individual system. For instance, in the Bose’s double-prism experiment , tunnelling and perfect anticoincidence were observed in single photon states. Consequently, the meaning of the wave-particle duality must incorporate the simultaneous use of the two classical descriptions in the interpretation of experiments, loosing their original mutual exclusivity , which is incorporated as an extreme case in the new interferometric duality, a continuous quantum concept . The wave-particle duality, therefore, must be formulated as an interpretative addition to quantum mechanics, to which is possible to renounce if any pretension of visualize quantum phenomena in terms of classical concepts and intuitions is abandoned.