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Revisiting Wave–Particle Duality: A Simulation of Single-Photon Interference in a Mach–Zehnder Interferometer

Iheka, Joy Ugochukwu

Published Nov 11, 2025• 0 citations
Publisher

Abstract

This project revisits wave-particle duality by simulating single-photon interference in a Mach–Zehnder interferometer using Python. Results from this research show that interference emerges not because photons are both waves and particles, but because their probability amplitudes add coherently in superposition, which simplifies the interpretation of complementarity and connects directly to modern applications of quantum photonics in communication and quantum information processing.

DOI
10.5281/zenodo.17579086

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This project revisits wave-particle duality by simulating single-photon interference in a Mach–Zehnder interferometer using Python. Results from this research show that interference emerges not because photons are both waves and particles, but because their probability amplitudes add coherently in superposition, which simplifies the interpretation of complementarity and connects directly to modern applications of quantum photonics in communication and quantum information processing.
Classical wisdom of wave–particle duality regulates that a quantum object shows either the particle or wave nature but never both. Consequently, it would be impossible to observe simultaneously the complete wave and particle nature of the quantum object. Mathematically the principle requests that the interference visibility V and which-path distinguishability D satisfy an orthodox limit of V 2 + D 2 ≤ 1 . The present work reports a new wave–particle duality test experiment using single photons in a modified Mach–Zehnder interferometer to demonstrate the possibility of breaking the limit. The key element of the interferometer is a weakly scattering total internal reflection prism surface, which exhibits a pronounced single-photon interference with a visibility of up to 0.97 and simultaneously provides a path distinguishability of 0.83. Apparently, the result of V 2 + D 2 ≈ 1.63 exceeds the orthodox limit set by the classical principle of wave–particle duality for single photons. We expect that more delicate experiments in the future should be able to demonstrate the ultimate limit of V 2 + D 2 ≈ 2 and shed new light on the foundations of contemporary quantum mechanics.
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.
The wave-particle duality of light plays a fundamental role in introductory courses on quantum mechanics. Traditionally the wave and particle aspects of light are demonstrated in separate experiments which makes it difficult for students to understand their complementary nature. We present an experiment using a single apparatus that demonstrates the wave aspect, the particle aspect, and most importantly, their coexistence. The apparatus is based on a Mach-Zehnder interferometer in which a light beam is attenuated so that at each instant there is only a single photon in the interferometer. In this way the observation of single photon interference becomes possible. By integrating the single photon events in a storage oscilloscope the evolution toward classical interference fringes can be shown in real time. A second strong laser beam, derived from the same pointer, but slightly displaced, traverses the interferometer at the same time, allowing the simultaneous demonstration of wave aspects. Special features of the setup are low cost, simplicity, didactical power and suitability for presentations in large lecture halls using both multimedia projections and audible signals.
This article explores the use of interferometry experiments, focusing on the Mach-Zehnder interferometer, as a didactic tool for teaching fundamental concepts of quantum physics, such as wave-particle duality, superposition, and interference. Using the interactive simulation “Interferometer experiments with photons, particles and waves” from the University of St Andrews, we demonstrate how different models – classical particles, electromagnetic waves, and single photons – can be applied to describe the observed phenomena, facilitating the understanding of the distinctions between the classical and quantum views of nature. The comparative analysis of the simulated experimental results serves as a basis for in-depth conceptual discussions in the classroom, making quantum physics more accessible and intuitive for high school and university students.
This thesis is a study about the insights and challenges provided by the concept of wave- particle duality for the understanding of physical entities. I specifically analyse the duality claim of photons and the related interference phenomena. To begin, I explore several notions of duality found in mathematics and various branches of science and present the similarities and differences amidst them. After this, with regard to wave-particle duality of radiation, I highlight the plurality associated with this concept based on a few important interpretations of duality. I then focus on the wave-particle duality claim about photons articulated in the context of two experiments: the anti-correlation experiment and photons’ behaviour in the Mach-Zehnder interferometer experiment. I argue that this claim can neither be substantiated through the complementarity principle nor by claiming that photons behave analogously to classical waves and particles. This detailed examination of the experiments brings to the forefront yet another confusion about photons that I subsequently evaluate. I discuss the controversy concerning the interpretation of the interference phenomenon of photons and identify the sources of this confusion. Through these arguments and conclusions drawn in this thesis, I demonstrate how philosophical analysis is crucial for the understanding of scientific entities.