In many applications of quantum optics, nonlinear physics, molecular chemistry and biophysics, one can encounter models in which the coupled quantum harmonic oscillator provides an explanation for many physical phenomena and effects. In general, these are harmonic oscillators coupled via coordinates and momenta, which can be represented as H^=∑i=12p^i22mi+miωi22xi2+H^int, where the interaction of two oscillators H^int=ik1x1p^2+ik2x2p^1+k3x1x2−k4p^1p^2. Despite the importance of this system, there is currently no general solution to the Schrödinger equation that takes into account arbitrary initial states of the oscillators. Here, this problem is solved in analytical form, and it is shown that the probability of finding the system in any states and quantum entanglement depends only on one coefficient R∈(0,1) for the initial factorizable Fock states of the oscillator and depends on two parameters R∈(0,1) and ϕ for arbitrary initial states. These two parameters R∈(0,1) and ϕ include the entire set of variables of the system under consideration.

Relatively recently, it became known that the interaction of photons with free electrons leads to quantum entanglement of photons. Such photons can be used in many applications of quantum technologies. Typically, to study quantum entanglement, photons are assumed to be monochromatic, although in reality they are not. This paper shows that if non-monochromatic photons are taken into account, their quantum entanglement, based on von Neumann entropy, can differ significantly from the case of monochromatic photons. It has been shown that the entanglement of non-monochromatic photons can be large and reach the maximum possible value. (c) 2024 Optica Publishing Group. All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.

X-ray crystallography is commonly used to determine crystal structures, whether continuous or ultrashort x rays are used. In this paper, it is shown that using only ultrashort pulses, it is possible to determine interplanar spacing in diamond layers, the distance between which can be only a few angstroms. The results obtained can be extended, with further development of the presented theory, to determine 3D objects in the crystal structure, the dimensions of which can be only a few angstroms.

Currently, the use of ultrashort pulses is one of the main methods for studying the structure and dynamics of ultrafast processes in atomic and molecular systems. In this paper, it is shown that ultrashort pulses can be used to determine the time dynamics of crystal plates with ultrahigh temporal and spatial resolution, the distance between which can be only a few angstroms. As an example, the dynamics of diamond layers with NV-centers is considered. The results obtained have prospects for developing the presented theory for more complex structural objects and dynamic processes in matter.

It is well known that the beam splitter is an integral part of many classical and quantum devices. The use of beam splitters in quantum technologies is currently particularly relevant. The emergence of new types of beam splitters provides new statistical characteristics of the separated photon beam and their control and new possibilities for use in various devices. This Letter presents a new, to the best of our knowledge, type of beam splitter based on free charged particles. This type of beam splitter has all the properties of a linear beam splitter with its reflection coefficient R, transmission coefficient T, and phase shift ϕ, which are presented in a simple analytical form. This type of beam splitter has interesting application prospects.

The X-ray diffraction analysis is one of the main methods to determine the structure of crystalline materials using both cw X rays and ultrashort pulses. Ultrashort pulses are usually utilized to observe dynamic processes in atomic and molecular systems. In this work, it has been shown that ultrashort pulses can have another important application in the determination of the interplanar distance between diamond layers with NV centers, which can be separated by only several angstroms. The obtained results can be extended to more complex structures and can be finally developed to a new three-dimensional tomography method with angstrom resolution.

The quantum harmonic oscillator is a model system that is actively used in many applications of quantum and nonlinear physics, molecular chemistry and biophysics. In this paper, a formula is obtained for the probability amplitude of the transition of a quantum harmonic oscillator from an oscillatory state with the number $\nu$ to a state with the number $\nu+n$ , which is affected by an external force depending on time using a method based on the Magnus and Baker-Campbell-Hausdorff decomposition. A formula is obtained for the special case of interaction of a quantum harmonic oscillator with an ultrashort pulse field. As an example, graphs of the probabilities of the oscillator transition from the first oscillatory state to the second and third, the average energy received and the rms fluctuation of the energy received for different values of the ratio of the carrier frequency of the pulse and the frequency of the oscillator are constructed. Conclusions are drawn about the correctness of using the concept of average energy in relation to this problem.

It is well known that the basis of diffraction analysis of matter is scattering, including the scattering of ultrashort laser pulses. In the theory of scattering of ultrashort pulses, the pulse duration parameter is usually not taken into account, which leads to some error. This error may be more significant than the considered effects in the scattering of the pulse on the studied structure. In this paper, it is shown that the pulse duration parameter should be taken into account when scattering X-ray pulses on oriented diamonds with NV centers. It is shown that the scattering spectra can be used to judge the orientation of NV centers in the diamond structure. The obtained results may be very different from the widely used theory of diffraction analysis, which confirms the necessity of taking into account the pulse duration parameter in the diagnosis of complex structures.

Currently, synthetic diamonds are finding new applications. Quantum devices can be created based on diamond plates with the desired concentration of defects in the structure of the crystal lattice. NV color centers can be used in quantum applications by irradiating plates with high-energy particles, followed by annealing at temperatures above 800°C to develop the spin-optical properties of the centers Diamond plates are subjected to electron irradiation and much less often to proton irradiation. As a result, synthetic diamond plates with NV centers ob-tained by proton irradiation are less studied, although proton irradiation makes it possible to obtain a layered structure of NV centers. In this work, single crystal diamond plates irradiated with protons were studied using polarization microscopy, IR spectroscopy and ODMR spectros-copy. It is shown that when creating NV centers, the distribution and concentration of C – defects in the sample, as well as mechanical stresses before and after irradiation (with subsequent an-nealing), can differ significantly from each other.

Mining companies play an important role in the country's economy. Mine dump trucks provide technological processes in the open method of mining, being the main source of emissions of harmful substances, including the black carbon, which has an extremely negative impact on human health and the environment. The most effective way to solve this problem is to use the replacement of diesel fuel with a more environmentally friendly one. The article presents possible options for such a replacement.

The quantum entanglement of photons is one of the interesting and important manifestations of the quantum world, which is already being used in quantum technologies. The study of new methods of quantum entanglement of photons is one of the promising areas of quantum optics. In this work, it is shown that photons, in a two-mode electromagnetic field, can be quantum entangled when they interact with free electrons. It is shown that the quantum entanglement of such photons can be very large and such photons can be a good source of high quantum entanglement. In addition, it is shown that free electrons can be a beam splitter for a two-mode electromagnetic field.

At present, there is no non-perturbative theory of scattering of nonclassical electromagnetic waves by free electrons that describes the scattering process completely with the help of quantum physics. In this paper, such a theory is presented, which takes into account the statistics and the number of scattered photons. This theory is completely analytical for an arbitrary number of electrons in the system and, in a particular case, is equivalent to the previous theory of scattering as the number of incident photons tends to infinity. It is shown that this theory can differ greatly from the previously known theory of Thomson scattering in the non-perturbative case and at relatively small numbers of incident photons. In addition, this theory is applicable to the scattering of ultrashort pulses by free electrons.

It is well known that the scattering matrix plays an important role in quantum optics. This matrix converts the incoming characteristics of scattered radiation into output characteristics. Currently, only special cases of such a scattering matrix are known, which are determined by a specific problem. In this work, a general form of the scattering matrix is obtained, which can be applied to a wide range of problems. It is shown that previously well-known and widely used scattering matrices can be obtained from the resulting scattering matrix. The results obtained can be used to describe new quantum states, the scattering matrices of which have not yet been studied.

It is well known that the interaction of radiation with matter can be described using classical or quantum physics in relation to three systems: incoming radiation, matter, and scattered radiation. Currently, there is no general non-perturbative theory of electromagnetic wave scattering by free electrons, which describes the scattering process using quantum physics. In this paper, such a non-relativistic theory is presented, where statistics and the number of incoming photons is taken into account, and in scattering, statistics with the number of scattered photons is obtained. This theory is completely analytical, considering an arbitrary number of electrons in the system and, in a particular case, goes over into the previously known theory of scattering as the number of incident photons tends to infinity. It is shown that this theory can differ greatly from the previously known theory of Thomson scattering in the non-perturbative case and at relatively small numbers of incident photons. In addition, this theory is applicable to the scattering of ultrashort pulses by free electrons. This theory has good prospects for application in quantum optics, since it fully takes into account the quantum nature of the incident and scattered radiation when interacting with an arbitrary number of free electrons, including in the non-perturbative case.

It is well known that X-ray crystallography is based on X-ray diffraction (XRD) for atoms and molecules. The diffraction pattern arises as a result of scattering of incident radiation, which makes it possible to determine the structure of the scattering substance. With the advent of ultrashort radiation sources, the theory and interpretation of X-ray diffraction analysis have remained the same. This work shows that when an attosecond laser pulse is scattered on a DNA molecule, including during its nicking and bending, the pulse duration is an important characteristic of the scattering. In this case, the diffraction pattern changes significantly compared to the previously known scattering theory. The results obtained must be used in XRD theory to study DNA structures, their mutations and damage, since the previously known theory can produce large errors and, therefore, the DNA structure can be “decoding” incorrectly.

The theory of the beam splitter (BS) in quantum optics is well developed and based on fairly simple mathematical and physical foundations. This theory has been developed for any type of BS and is based on the constancy of the reflection coefficients R (or the transmission coefficient T, where R+T=1) and the phase shift ϕ. It has recently been shown that the constancy of these coefficients cannot always be satisfied for a waveguide BS, where R and ϕ depend in a special way on photon frequencies. Based on this, this review systematizes the concept of BS in quantum optics into “Conventional” and frequency-dependent BS, and also presents the theory of such BS. It is shown that the quantum entanglement, photon statistics at the output ports, and the Hong–Ou–Mandel (HOM) effect for such BS can be very different. Taking into account the fact that the waveguide BS is currently acquiring an important role in quantum technologies due to the possibility of its miniaturization, this review will be useful not only for theoreticians, but also for experimenters.

The theory of scattering of ultrashort laser pulses (USP) is the basis of diffraction analysis of matter using modern USP sources. At present, the peculiarities of interaction of USP with complex structures are not well developed. In general, the research focuses on the features of the interaction of USP with simple systems, these are atoms and simple molecules. Here we present a theory of scattering of ultrashort laser pulses on molecules with a multi-atomic structure, taking into account the specifics of the interaction of USP with such a substance. The simplicity of the obtained expressions allows them to be used in diffraction analysis. As an example, the scattering spectra of deoxyribonucleic acid (DNA) and ribonucleic acid (RNA) are presented. It is shown that the theory developed here is more general in the scattering theory and passes into the previously known one if we consider the duration of the USP to be sufficiently long.

The scattering of X-ray ultrashort pulses (USPs) is an important aspect of the diffraction analysis of matter using modern USP sources. The theoretical basis, which considers the specifics of the interaction of ultrashort pulses with complex polyatomic structures, is currently not well developed. In general, research is focused on the specifics of the interaction of ultrashort pulses with simple systems—these are atoms and simple molecules. In this work, a theory of scattering of X-ray ultrashort pulses by complex polyatomic structures is developed, considering the specifics of the interaction of ultrashort pulses with such a substance. The obtained expressions have a rather simple analytical form, which allows them to be used in diffraction analysis. As an example, it is shown that the obtained expressions can be used to study the structures of deoxyribonucleic (DNA) and ribonucleic (RNA) acids.