Abstract The main provisions of the construction of the single-particle wave function of a photon in the coordinate representation are expounded and its application to the description of single-photon interference phenomena is discussed. The connection between the concepts of electromagnetic field strengths used in quantum electrodynamics and the characteristics of wave packets in photon quantum mechanics is substantiated. For illustration, we consider the relationship between the structure of the photon wave function in coordinate representation and the polarization of photon in the formalism of quantum transition amplitudes. The meaning of the concept of linear polarization of a photon in the state of a wave packet is explained. The wave function is constructed in the coordinate representation of the state of two entangled photons at the exit from a nonlinear crystal by modeling the polarization vectors and Gaussian momentum distribution for each of the photons.
Abstract The main provisions of the construction of the single-particle wave function of a photon in the coordinate representation are expounded and its application to the description of single-photon interference phenomena is discussed. The connection between the concepts of electromagnetic field strengths used in quantum electrodynamics and the characteristics of wave packets in photon quantum mechanics is substantiated. For illustration, we consider the relationship between the structure of the photon wave function in coordinate representation and the polarization of photon in the formalism of quantum transition amplitudes. The meaning of the concept of linear polarization of a photon in the state of a wave packet is explained. The wave function is constructed in the coordinate representation of the state of two entangled photons at the exit from a nonlinear crystal by modeling the polarization vectors and Gaussian momentum distribution for each of the photons.
Abstract The general results of constructing and modeling the photon wave function in the coordinate representation in the framework of quantum mechanics are presented in order to explain single-photon interference phenomena, in particular Young’s experiment. The relevance of this function is emphasized in connection with modern single-photon and two-photon experiments. The necessity of replacing the explanation of obtaining coherent light sources using the concept of a train of supposedly real electromagnetic waves emitted by one atom, by the conditional emission by this atom of the photon wave function in the coordinate representation, which then experiences diffraction and interference, is substantiated. A single-photon wave function is simulated based on the consideration of the electric dipole radiation of an atom in classical electrodynamics, and a conclusion is drawn on the possibility to explain Young’s experiment. It is argued that although the photon wave function (as well as of particles having mass) is not a physical object, the application of this function significantly weakens the problem of wave-particle duality of light. It is assumed the “nature” of this function reflects the properties of a physical vacuum, but new experiments are required to clarify it.
Abstract The method developed in previous works for building the photon wave function in configuration representation is briefly described. The simulation of such function (wave packet) appropriate to femtosecond laser radiation, using the distribution of Gauss of photon momenta in the state of a single laser impulse is expounded. By other appropriate simulated wave function of photon the light interference in Young’s experiment is explained within the frame of quantum mechanics without the attraction of transition probability amplitudes used in approach of quantum electrodynamics. This allows us considering interference phenomena for photons and particles from the same basis of the quantum-mechanical principle of superposition employed to the wave function built in the configuration space. Using the building apparatus of photon quantum mechanics, the Malus law postulated in quantum theory is justified. The relevance of new experiments to study the interaction of quantum objects between themselves and the physical vacuum, which would reveal the origins of the mathematical description of quantum states using the wave function of these quantum objects, is substantiated. It is suggested that the ideas of constructing the wave function of a free photon in the coordinate representation can find relevance in the field of quantum cryptography.
In modern areas of photonics, the physical description of the interaction of photons with matter in the control, transmission and registration of single-photon and two-photon states implemented in practice is of great importance. An appropriate acceptable description may be faced with the need to take into account various kinds of interference effects associated with these states. Meanwhile, even the most “simple” case of single-photon interference in Young's experiment requires the use of a rather complex apparatus of quantum electrodynamics. This article explains one- and two-photon interference in Young's thought experiment based on the photon wave function (PWF) in coordinate representation. This explanation is illustrated by two examples of wavelengths: 10.6 μm and 1.5 cm. For both examples, two approaches to PWF modeling are used: “purely quantum-mechanical” and “quasi-classical”. In the first approach, a 6-component coordinate PWF is constructed using a spherically symmetric momentum distribution in a wave packet, followed by numerical and approximate analytical calculations. In the second approach, a one-component “quasi-classical” PWF is constructed, which corresponds to either electric dipole radiation or simulated spherically symmetric radiation. In all cases, the same pronounced interference pattern was obtained, which allows us to conclude that not only the quantum-mechanical coordinate PWF is able to explain the phenomena of one- and two-photon interference, but also a much simpler “quasi-classical” PWF. This conclusion sheds light on the theoretical interpretation of the measurement of the coordinate PWF in some recent experiments.
The description of photon-matter interaction upon control, transmission, and detection of single-photon, two-photon, and multiphoton states, including the entangled ones, will play an ever-increasing role in many areas of photonics. An appropriate description requires taking into consideration various types of interference effects associated with these states. However, the relatively complex apparatus of second quantization of the electromagnetic field is used even in the simplest single-photon experiments equivalent to the Young’s one, e.g., the experiments with the Mach–Zehnder interferometer. In the present work, the Young’s single-photon mental experiment is explained using the coordinate photon wave function (PWF). The explanation is illustrated by specific examples of the single-photon states at certain wavelengths and different duration of radiation within the framework of two approaches: the quantum mechanical and the “quasi-classical.” In the first approach, a 6-component coordinate PWF is constructed based on the spherically symmetric momentum distribution in a wave packet, followed by approximate analytical calculations. In the second approach, a one-component quasi-classical PWF corresponding to the electric-dipole radiation is constructed. The same pronounced interference pattern was obtained in both cases, which makes is possible to draw the conclusion that the coordinate PWF allows explaining the one- and two-photon interference phenomena. This conclusion sheds the light on theoretical interpretation of the measurement of the coordinate PWF carried out in some of the recent experiments.
The formation of an obvious interference pattern in the distribution of the probability of the simultaneous hit of two alone photons radiated synchronously from two independent single-photon sources, playing the slits role of Young's experiment first screen, at different points of the second screen, is demonstrated by modeling the photon coordinate wave function. This function is single-photon wave packet built within the framework of the developed quantum mechanics of the photon in previous authors works, which expresses a superposition of six-component “plane waves with circular polarization” - the eigenfunctions of the operators of photon momentum, of its energy and helicity. The results received make it eventual to justify the description of one-and two-photon interference in framework of “primary” quantization of the electromagnetic field, without resorting to the probability amplitudes of quantum field theory, which, in turn, makes it possible to develop a metaphysical interpretation of experiments with single photons, such as quantum computing, quantum teleportation, quantum cryptography. It seems that this interpretation can serve as an impetus for the development of new practical devices and the setting up of new experiments to reveal the physical nature of quantum interactions through the exchange of photons and, in particular, the physical essence displayed by the idea of quantum object wave function.
The main principles of photon quantum mechanics describing its one-particle states with the help of the wave function in coordinate representations are given.This wave function (packet) is the superposition of the basic bivectors that are generalized eigenfunctions of energy, momentum, and helicity operators.The quantum-mechanical approach is offered for an explanation of the interference Young's experiment.This explanation is especially important for new interpretation of the non-laser method of obtaining the interference by the amplitude division, as in this case it is traditionally assumed that the radiation of one light train of a single atom interferes with itself.In our explanation, not both "halves" of some real train ("scrap") of the electromagnetic wave interfere with each other, but the both terms of the photon's wave function do this.Nevertheless, the wave function is not directly measured by experience, and therefore it does not exist as a physical object.The attraction of the wave function to the explanation of single-photon interference obtained "by the division of the wave front" is obviously also necessary.Therefore, the situation for the photons emitted by individual atoms (and also, obviously, by laser), is absolutely similar to the situation with the particles having mass, whose distribution in space is described by wave function in coordinate representation.It is pointed out that in fact the photon is not some "formed" quantum particle, but it is a quasi-particle arising when a certain spin wave propagates in a physical vacuum at Planck distances.