Matrix elements of the dipole-dipole interaction between two two-level atoms distanced arbitrarily from each other

Abstract

Purpose. As a standard model for describing the processes of a resonant transmission of quantum information on arbitrary distances is the system of two identical two-level atoms, one of which is under radiation of the field of real photons. Such a system can serve as a basis for the construction of an element basis of quantum computers. The purpose of this paper is to study the different modes of dynamics of a system of two identical two-level atoms when they interacts with the field of real photons.Methods. In this paper, we propose a general approach to the description of the processes for the transfer of quantum information from one atom-qubit to another on the arbitrary interatomic distances, which includes two types of new physical effects: the attenuation of quantum states and the retardation of the dipole-dipole interaction. Results. The optical properties of a system of two identical two-level atoms in collective (symmetric $\Psi_s$ and antisymmetric $\Psi_a$) Bell states at arbitrary interatomic distances are investigated. The closed analytical expressions for the shifts and widths of the considered collective states are considered, taking into account the retarded dipole-dipole interaction of atoms. In calculation of the radial matrix elements of the dipole-dipole interaction, the wave functions of the model Fues potential are used. Conclusions. A detailed study of the mechanisms of resonant transmission of the excitation energy at arbitrary distances between the two-element atoms has an important practical significance for the physical realization of the logical operator CNOT.