Current Physics - Online First

In the rapidly developing areas of photonics associated with quantum teleportation of photons, quantum cryptography, and quantum computing, ideas are becoming increasingly relevant about the certain localized states of single or several entangled photons moving in space and time. As is known, in quantum mechanics, localized states of particles can only be described using wave functions in coordinate representation – the corresponding wave packets.

To explain Young's one- and two-photon experiments using coordinate 6-component quantum mechanical and 1-component quasi-classical photon wave functions.

The article outlines the method developed in authors' previous work in constructing the 6-component coordinate wave function of free photons in the form of the wave packet (an integral over the entire momentum space and sum over two possible values +1 and -1 of the helicity). The basis functions are the circularly polarized monochromatic waves, corresponding to certain values of the momentum, helicity, and photon energy operators and forming a complete orthonormal set of generalized eigenfunctions of these operators. This photon wave function (PWF) is normalized to the unit probability of finding the photon anywhere in space. Both the basis functions and the coordinate PWF satisfy a Schrödinger-type equation derived from the Maxwell-Lorentz equations written in quantum mechanical form first introduced by Majorana. Then the results of modeling and consideration of the space-time evolution of the wave packet with Gaussian momentum distribution corresponding to the directed photon emission for 80 fs are briefly presented. Further, in view of the possibility of constructing the coordinate PWF, the basic formula for the wave-particle duality of photons and particles is formulated. It is emphasized that the photon is fundamentally different from “ordinary” particles, since, according to the authors, the photon is the result of the propagation of a certain complex spin wave in a physical vacuum, the details of which can only be considered simultaneously with the study of the structure of the physical vacuum at Planckian distances.

Young's one- and two-photon experiments are explained using various options for modeling 6-component coordinate PWFs, including approximate functions corresponding to spherically symmetric and electric dipole photon radiation.

This explanation is illustrated using specific examples of radiation and, at the same time, is compared with numerical simulations for spherically symmetric radiation and the use of 1-component quasi-classical PWFs.

Circular Rydberg States (CRS) were studied theoretically and experimentally in numerous works. In particular, in the previous paper by one of us, there were derived analytical expressions for the energy of classical CRS in collinear electric (F) and magnetic (B) fields of arbitrary strengths imposed on a hydrogenic system (atom or ion). For the magnetic field B of any strength, the author of that study gave formulas for the dependency of the classical ionization threshold Fc(B) and the energy at this threshold Ec(B). He also analyzed the stability of the motion by going beyond the CRS. In addition, for two important particular cases previously studied in the literature – classical CRS in a magnetic field only and classical CRS in an electric field only – some new results were also presented in that paper, especially concerning the Stark effect.

In the present paper, we study analytically axially-symmetric CRS of a heliumic system (He atom or He-like ion) subjected to an electric or magnetic field of arbitrary strength.

In this investigation, analytical techniques were applied.

We showed that in the case of the Stark effect, the difference in the unperturbed structure of the heliumic systems (compared to hydrogenic systems), i.e., the non-negligible size, causes the decrease of the classical ionization threshold, as well as increases the energy and the orbit radius of the outer electron at the ionization threshold. Also, the allowance for the non-negligible size of the internal subsystem increases the maximum possible absolute value of the induced electric dipole moment. In the case of the Zeeman effect, we demonstrated that the non-negligible size of the inner system increases the energy and the orbit radius of the outer electron.

The allowance for the non-negligible size of the internal subsystem can strongly affect the properties of the axially symmetric circular states. We believe that our results are of fundamental importance.