TWO-PHOTON INTERFERENCE FROM TWO INDEPENDENT SOURCES IN THE SCHEME OF YOUNG’S EXPERIMENT IN THE FRAMEWORK OF MODELING THE COORDINATE WAVE FUNCTION OF THE PHOTON
С помощью моделирования волновой функции фотона в координатном представлении демонстрируется возникновение отчетливой интерференции в вероятности попадания двух одиночных фотонов в разные точки второго экрана в схеме опыта Юнга, если эти фотоны одновременно испускаются независимыми источниками. By modeling the photon wave function in the coordinate representation, the emergence of distinct interference in the probability density of hitting of the two single photons into different points of the second screen in scheme of Young’s experiment is demonstrated, if these photons were simultaneously emitted by independent sources.
С помощью моделирования волновой функции фотона в координатном представлении демонстрируется возникновение отчетливой интерференции в вероятности попадания двух одиночных фотонов в разные точки второго экрана в схеме опыта Юнга, если эти фотоны одновременно испускаются независимыми источниками. By modeling the photon wave function in the coordinate representation, the emergence of distinct interference in the probability density of hitting of the two single photons into different points of the second screen in scheme of Young’s experiment is demonstrated, if these photons were simultaneously emitted by independent sources.
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.
Объясняется одно- и двухфотонный опыт Юнга с помощью 6-компонентной квантовой и 1-компонентной «квазиклассической» волновых функций фотона в координатном представлении, которые моделируются различными механизмами дифракции фотона на отверстиях или одновременного излучения двух фотонов (двумя) независимыми источниками. Это объяснение сопоставляется с хорошо известным вариантом объяснения интерференции частицы «сама с собой» при ее прохождении «сразу через оба отверстия» в опыте Юнга с помощью постулированных амплитуд Фейнмана. Утверждается, что эти амплитуды не могут быть волновыми функциями, в прямом смысле, описывающими некоторые состояния квантовых частиц. Во всех случаях, в предположении линейной поляризации фотонов, получена схожая ярко выраженная интерференционная картина, позволяющая сделать вывод, что координатная волновая функция фотона способна объяснить явления одно- и двухфотонной интерференции. В свою очередь, этот вывод дает возможность ассоциировать измеряемую координатную волновую функцию фотона (и двух фотонов в запутанном состоянии), в некоторых недавних экспериментах, с «квазиклассической» волновой функцией фотона (и двух фотонов), хотя она и не учитывает его (их) поляризационных свойств. Young's single- and two-photon experiments are explained using 6-component quantum and 1-component "quasi-classical" photon wave functions in coordinate representation, which are modeled by various mechanisms ofphoton diffraction on holes or types of simultaneous emission of two photons by (two) independent sources. This explanation is compared with the well-known version of the explanation of the interference of a particle "with itself when it passes "through both holes at once" in Young's experiment using Feynman's postulated amplitudes. It is argued that these amplitudes cannot be wave functions, in the literal sense, describing some states of quantum particles. In all cases, under the assumption of linear polarization of photons, a pronounced interference pattern was obtained, allowing us to conclude that the coordinate wave function of the photon is capable of explaining the phenomena of single- and two-photon interference. In turn, this conclusion makes it possible to associate the coordinate wave function of the photon (and two photons in an entangled state), measured in some recent experiments, with the "quasi-classical" wave function of the photon (and two photons), although it does not take into account its (their) polarization properties.
Конструируется волновая функция в координатном представлении двух запутанных фотонов в состоянии на выходе из нелинейного кристалла путем моделирования векторов поляризации и применения гауссовского импульсного распределения для каждого из фотонов. The wave function is constructed in the coordinate representation of two entangled photons in a state at the exit from a nonlinear crystal by modeling the polarization vectors and applying a Gaussian momentum distribution for each of the photons.
The time evolution of the interference pattern obtained from numerical simulation of directed radiation to a given point on the screen is demonstrated. This pattern arises from three identical single-photon sources simultaneously emitting photons in a thought experiment of the Young's experiment type. The simulation uses a 6-component coordinate wave function of a photon – a wave packet as a superposition (integral) of generalized eigenfunctions of the photon's energy, momentum, and helicity operators. This wave function is determined by only two free parameters: the wavelength and the emission time of each photon, understood as the average time interval during which a photon can be emitted by a single-photon source. Calculations were performed for a wavelength of 0.05 cm, emission time of 4 ps, distance between radiation sources of 0.25 cm, and distance from sources to the screen of 0.905 cm. As a result, the interference pattern is established for six consecutive time moments from 29.2 to 34.2 ps, covering the most interesting region of its dynamics. A comparison is made between the interference pattern and similar results previously obtained by numerical simulation of two-photon interference under the same radiation parameters and Young's experiment geometry. It is emphasized that the performed simulation of three-photon interference can find application for the theoretical description of possible interference processes accompanying the implementation of quantum computations based on qutrits as basic elements of quantum computers.
The two-photon interference appearing in a mental experiment similar to the Young’s experiment as a result of simultaneious emission of two photons by (two) independent point sources under the assumption that their radiation is described in the electric-dipole approximation in the classical electrodynamics is simulated within the framework of the photon quantum mechanics by using a six-component photon wave function in the coordinate representation and, for comparison, in the proposed “quasi-classical” approach by using the one-component photon wave function. The relevance of introduction of the photon wave function is emphasized in comparison to the concept of the photon being a “train” of real electromagnetic waves. The task of setting up new experiments that could initiate the analysis of the physical nature of quantum phenomena that occur in the physical vacuum and are formally described by the wave function in the quantum mechanics or by transition amplitudes in the quantum electrodynamics is proposed.
The Young’s single- and double-slit experiments are explained using six-component quantum and one-component quasi-classical photon wave functions in the coordinate representation, which are modeled by different mechanisms of photon diffraction on slits or simultaneous emission of two photons by (two) independent sources. This explanation is compared with the well-known statement about the interference of a particle with itself when passing through both slits simultaneously in the Young’s experiment on the basis of the postulated Feynman amplitudes. It is argued that these amplitudes cannot be wave functions, in the literal sense, describing some states of quantum particles. In all cases, under the assumption of the linear polarization of photons, a pronounced interference pattern has been obtained, which suggests that the coordinate wave function of a photon can explain the phenomena of the one- and two-photon interference. This conclusion, in turn, makes it possible to associate the coordinate wave function of a photon (two photons, in the entangled state) measured in some recent experiments with the quasi-classical wave function of a photon (two photons), although it does not take into account its (their) polarization properties.