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


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 Ψs and antisymmetric Ψa) 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

Keywords: quantum computer, dipole-dipole interaction, effects of retardation, Fues potential