The concepts of geometric phase and wave-particle duality are interlinked to several fundamental phenomena in quantum physics, but their mutual relationship still forms an uncharted open problem. Here we address this question by studying the geometric phase of a photon in double-slit interference. We especially discover a general complementarity relation for the photon that connects the geometric phase it exhibits in the observation plane and the which-path information it encases at the two slits. The relation can be seen as quantifying wave-particle duality of the photon via the geometric phase, thus corroborating a foundational link between two ubiquitous notions in quantum physics research.
The concepts of geometric phase and wave-particle duality are interlinked to several fundamental phenomena in quantum physics, but their mutual relationship still forms an uncharted open problem. Here we address this question by studying the geometric phase of a photon in double-slit interference. We especially discover a general complementarity relation for the photon that connects the geometric phase it exhibits in the observation plane and the which-path information it encases at the two slits. The relation can be seen as quantifying wave-particle duality of the photon via the geometric phase, thus corroborating a foundational link between two ubiquitous notions in quantum physics research.
A single photon exhibits wave-particle duality in the Young's double-slit interferometer. The duality characterized by an interference visibility and a which-path information has trade-off relation known as complementarity. These quantities are related to the first-order coherence, and the interference is based on the phase correlation between lights coming from two arms. However according to quantum optics theory, such a simple wave-particle picture is not enough to understand the nature because the theory showed an importance of higher-order coherence in the sense of both interference and statistical distribution of photons. Second-order intensity correlation is especially crucial to reveal distinctive quantum features of photons with no classical analogue. Here, in an intensity interferometric scenario as represented by the Hong-Ou-Mandel interferometer, we discuss a wave-particle duality of light based on a which-path information and a quantity characterizing a magnitude of the intensity interferometric effect. We show, for classical light, the two quantities obey the complementary principle similar to the case of the double-slit experiment, but do not for nonclassical light. The nonclassical light such as photons at two arms is allowed to show larger which-path information and intensity interference simultaneously beyond the complementary relation. Moreover, the violation reveals a new nonclassical nature of light although both of the above two quantities seem to be understandable classically, which is never found from a consideration of only one side of wave-particle duality.
A single photon exhibits wave-particle duality in the Young's double-slit interferometer. The duality character-ized by an interference visibilityVas the wave-like property and a which-path informationDas the particle-like property has tradeoff relationD2+V2≤1known as complementarity [1]–[3]. There are a lot of studies about the complementary nature of photons from various viewpoints such as delayed-choice experiments, theoretical works related to the uncertainty principle, and so on. More recently, studies have expanded the concept of the wave-particle duality to higher-order interferometric scenarios, in which the input light includes two or more pho-tons [4], [5]. Despite having a long history, all previous studies have been related to phase correlation of optical states, which reason would be why the main focus in the first place is the investigation of the mysterious quantum nature of a photon, including the superposition principle.
We report observations of Cross-Double-Slit Experiment and Which-Path-Cross-Double-Slit experiment. Cross-Double-Slit apparatus contains two double-slit, where first double-slit is perpendicular to second double-slit. The first double-slit and the second double-slit generate not only their own interference pattern perpendicular to each other, but also generate “Cross-interference-patterns”. When we do which-way experiment with one of two double-slit, say first double-slit, then its interference pattern disappeared, i.e., photons behave as particles; but the second double-slit’s interference pattern and the cross-interference-pattern still exist; which implies an significant phenomenon that in the same experiment, photons behave as both wave and particle, which is first time caught on film. Thus we suggest to re-study wave-particle duality, which is the basic mystery of quantum mechanics. We postulate that the particle nature of photons is intrinsic; while the wave-like of photons is manifest-behavior.
Abstract The double-slit experiment is a classic experiment that presents the clearest manifestation of wave-particle duality, one of the fundamental principles of quantum mechanics. The double-slit experiment still remains the phenomenon that demonstrates wave-particle duality at the most fundamental level. This phenomenon quantitatively and conceptually demonstrates that microscopic objects can behave like both waves and particles at the same time. This article provides an in-depth analysis of the physical nature of dualism, the mechanism of formation of the interference pattern, and the impact of the act of observation on the dynamics of quantum systems. The need for a new perspective on this topic is due to the fact that the current uncertainty in the interpretation of quantum reality has not yet been completely eliminated, and the boundaries between classical and quantum behavior in microscopic objects are still being explored. The results presented here restructure the deep mechanisms of the interference picture, more clearly frame the relationship between observation and wavefunction collapse, and provide a quantum. Since the article attempts to provide a complete answer to the mechanism of the formation of wave-particle duality, extensive space is given to sections such as historical development, theoretical models, modern research, etc. New approaches to this phenomenon have been developed using modern research and string theory. As a result, a new mathematical expression has been proposed that explains the reasons for the initial emergence of wave-particle duality, and is also important for string theory. The article explains the measurement problem with a more effective physical structure and ontological model.
We derive a generalized wave-particle duality relation for arbitrary multipath quantum interference phenomena. Beyond the conventional notion of the wave nature of a quantum system, i.e., the interference fringe visibility, we introduce a quantifier as the normalized quantum coherence, recently defined in the framework of quantum information theory. To witness the particle nature, we quantify the path distinguishability or the which-path information based on unambiguous quantum state discrimination. Then, the Bohr complementarity principle for multipath quantum interference can be stated as a duality relation between the quantum coherence and the path distinguishability. For two-path interference, the quantum coherence is identical to the interference fringe visibility, and the relation reduces to the well-known complementarity relation. The duality relation continues to hold in the case where mixedness is introduced due to possible decoherence effects.
We present a systematic framework to quantify the interplay between coherence and wave-particle duality in generic two-path interference systems. Our analysis reveals a closed-form duality ellipse (DE) equality, that rigorously unifies visibility (a traditional waveness measure) and predictability (a particleness measure) with degree of coherence, providing a complete mathematical embodiment of Bohr's complementarity principle. Extending this framework to quantum imaging with undetected photons (QIUP), where both path information and photon interference are inherently linked to spatial object reconstruction, we establish an imaging duality ellipse (IDE) that directly connects wave-particle duality to the object's transmittance profile. This relation enables object characterization through duality measurements alone and remains robust against experimental imperfections such as decoherence and misalignment. Our results advance the fundamental understanding of quantum duality while offering a practical toolkit for optimizing coherence-driven quantum technologies, from imaging to sensing.