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International Journal of Hybrid Information Technology

Some Common Aspects of Quantum and Classical Interferences

Youssef Khmou

Published Dec 31, 2017• 0 citations
Publisher

Abstract

In quantum information theory, the particles are characterized by wave behavior where they can be described by particle-wave duality, from this perspective, the waves phenomena were studied theoretically and experimentally for quantum particles such as diffraction and interferences.In the other hand, the classical electromagnetic and acoustics fields are described by wave forms where all wave phenomena are possible including diffraction, refraction and scattering.Focusing on interferences where the superposition principle is valid for both quantum and classical interferences, we present in this paper, some common properties between the quantum interferences and particular case of classical interferences.Based on far field and narrowband classical interferences, the interactions between elementary wave forms are treated using array signal processing, where angular interferometry of wave fields using closely sensors or antennas, permit to localize and estimate the characteristics of the far field sources.Based on the geometry of the displacement of the isotropic and identical antennas and the planar shape of the wave front passing near the array, we present some mathematical common concepts between quantum and classical interferences starting from wave propagation equation to the Von Neumann entropy, we present a detailed description of similarities between the two branches using some tools of operator theory.In the last part, we present a numerical simulation where we show that the introduction of the quantum entropy on classical system of antennas-sources permit to identify different phases of the system with respect to the signal to noise ratio.

DOI
10.14257/ijhit.2017.10.12.02

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In quantum information theory, the particles are characterized by wave behavior where they can be described by particle-wave duality, from this perspective, the waves phenomena were studied theoretically and experimentally for quantum particles such as diffraction and interferences.In the other hand, the classical electromagnetic and acoustics fields are described by wave forms where all wave phenomena are possible including diffraction, refraction and scattering.Focusing on interferences where the superposition principle is valid for both quantum and classical interferences, we present in this paper, some common properties between the quantum interferences and particular case of classical interferences.Based on far field and narrowband classical interferences, the interactions between elementary wave forms are treated using array signal processing, where angular interferometry of wave fields using closely sensors or antennas, permit to localize and estimate the characteristics of the far field sources.Based on the geometry of the displacement of the isotropic and identical antennas and the planar shape of the wave front passing near the array, we present some mathematical common concepts between quantum and classical interferences starting from wave propagation equation to the Von Neumann entropy, we present a detailed description of similarities between the two branches using some tools of operator theory.In the last part, we present a numerical simulation where we show that the introduction of the quantum entropy on classical system of antennas-sources permit to identify different phases of the system with respect to the signal to noise ratio.
Abstract In the explanations of the double slit experiment it is usually assumed that the superposition of the diffracted waves by two separate slits (one open and another closed) is the same as superimposing the diffracted waves when both slits are open at the same time. This naïve use of the superposition principle is generally not valid in either classical electromagnetism or quantum mechanics. As we will see, the diffraction diagram of one of the slits is altered when the other is open and when the slits are closer, the interaction between them is greater. In this work we will analyse the interaction between different types of sources (antennas, loudspeakers and, of course, slits) and we will show how this interaction explains the apparent anomalies in energy conservation and also the recent results of Young’s interference that show that the total diffracted intensity is reduced or increased depending on the distance between the slits. We also make a brief comment on the contributions of our work to the supposed looped trajectories of energy in interference phenomena.
Phase lies at the heart of quantum physics and quantum information theory. A quantum bit is qualitatively different from a classical bit as it allows for the coherent superposition of possibilities, which demonstrate different behaviours depending on the phase between them. These behaviours constitute as interference phenomena, and lie behind the existence of algorithms in quantum computing which are arguably faster than the best classical alternatives. The concept of phase is deeply steeped in the structure of Hilbert spaces: the mathematical framework that underlies quantum theory. What if quantum theory did not hold in all scenarios, or was only a limiting case of some broader theory? In this case, would we still be able to meaningfully talk about phase and interference? In this thesis, we will adopt an operational generalisation of quantum theory known as the framework of generalised probabilistic theories. We will provide a reasonable definition of phase in this framework. Using this, we shall explore single-particle interferometry set-ups (particularly Mach-Zehnder interferometers): experiments whose output is highly dependent on the phase between the spatially disjoint branches through which a particle might be traversing. By applying physically-motivated locality considerations, we identify the crucial role that the uncertainty principle and its generalisations play in quantum theory as an enabler of non-trivial interference. By taking into account relativity of simultaneity, we will also provide a physical motivation for why standard quantum theory provides the best description of the location of a particle traversing such a system. Finally, we apply our generalised definition of phase in the related context of particle exchange behaviour, and identify a method for classifying post-quantum particles. All of this will demonstrate that phase between possibilities and its consequences are not uniquely quantum phenomena. Much of the behaviour we might ascribe to phase in quantum theory in fact holds generally true for phase in probabilistic theories.
Optical interference is regarded as a classical phenomenon and is usually completely described in classical terms, in which optical fields are represented by classical waves. Does it mean that optical interference, which is fundamentally ascribable to the phenomenon of a superposition of wave amplitudes, cannot be applied to test quantum phenomena? The superposition principle is at the heart of quantum physics and one could expect that it should distinguish the quantum nature of light from thewave nature. Our experience based on extensive theoretical analysis and experimental observations shows that classical and quantum theories of optical interference readily explain the presence of an interference pattern resulting from the first-order coherence. However, there are interference effects involving the higher order (second-order) coherence that distinguish the quantum (photon) nature of light from the wave nature. Quantum interference has recently returned to prominence because of its utility in manipulating spontaneous emission and other radiative properties of atomic systems. In this chapter, we present elementary concepts and definitions of both the classical and quantum theory of optical interference and discuss similarities and differences between these two approaches [80].
Abstract Quantum interference plays a central role in the realm of quantum particles, revealing their wave‐like nature and probabilistic behavior. It relies on the concept of superposition, where the probability amplitudes of different processes that contribute to the given phenomenon interfere with each other. When combined, their phases can interfere either constructively or destructively. Quantum interference manifests in three distinct forms: optical interference, arising from the interaction of light waves and forming the basis for technologies such as lasers and optical filters; interference via atoms, which involves manipulating atomic states to control light–matter interactions and enables techniques like Stimulated Raman Adiabatic Passage and Electromagnetically Induced Transparency in quantum information processing; and interference of atoms with themselves, in which the matter waves of single atoms interfere with each other, as employed in precision measurements such as atom interferometry–a crucial tool for applications in quantum mechanics and precision navigation. These diverse forms of quantum interference have profound implications for numerous scientific disciplines, demonstrating that interference can involve particles beyond just photons.
Diffraction and interference of matter waves are key phenomena in quantum mechanics. Here we present some results on particle diffraction in a wide variety of situations, ranging from simple slit experiments to more complicated cases such as atom scattering by corrugated metal surfaces and metal surfaces with simple and isolated adsorbates. The principal novelty of our study is the use of the so-called Bohmian formalism of quantum trajectories. These trajectories are able to satisfactorily reproduce the main features of the experimental results and, more importantly, they provide a causal intuitive interpretation of the underlying dynamics. In particular, we will focus our attention on: (a) a revision of the concepts of near and far field in undulatory optics; (b) the transition to the classical limit, where it is found that although the quantum and classical diffraction patterns tend to be quite similar, some quantum features are maintained even when the quantum potential goes to zero; and (c) a qualitative description of the scattering of atoms by metal surfaces in the presence of a single adsorbate.
One of the earliest and most important tenets of quantum mechanics is the wave-particle duality: light behaves sometimes like a wave and at other times as particle and similarly an electron can also behave both like a particle and as a wave. When the formal laws of quantum mechanics are formulated, the central quantity that describes the particles is the wave function. This points to the need for a good understanding of the properties of the waves. This chapter introduces the concepts and most essential applications that are required to follow the discussion of quantum mechanical laws and systems. The basic characteristics of the waves, such as the superposition principle are presented, and the interference and the diffraction phenomena are discussed. The Young’s double slit experiment in analysed and the formation of interference pattern is explicitly shown. The Rayleigh criterion for the microscopic resolution is also derived.