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Chinese Journal of Physics

Effect of Dipole-dipole Interaction on the Radiation of Two Excited Atoms

Kung-Chen Liu

Published Oct 1, 1975• 4 citations
OpenAlex

Abstract

The extended Weisskopf-Wigner method developed by Ernst and Stehle is used to investigate the radiation of two initially excited atoms with dipole-dipole interaction. It is found that the lifetime for the system is the same as that without dipole-dipole interaction but the energy shift is just the dipole-dipole interaction.

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An explicit calculation of conservation of probability and energy in a two-atom system is presented. One of the atoms is excited initially and undergoes spontaneous emission. The field radiated by this atom can be scattered by the second atom. It is seen that the Weisskopf-Wigner approximation must be applied using a specific prescription to guarantee conservation of probability and energy. Moreover, for consistency, it is necessary to take into account the rescattering by the source atom of radiation scattered by the second atom.
Summary form only given. Though the resonant dipole-dipole interaction (RDDI) has been suggested for realization of entangling dynamics several years ago, it was only recently that several authors have investigated this interaction in more detail as a method for entangling neutral atoms in optical traps. Unfortunately, the considered entangled states of two-level atoms have very short lifetimes due to radiative decay. This is explained by the fact that radiative decay and RDDI have the same physical nature, and we cannot avoid the former while making use of the later. In the work we solve this conceptual problem by presenting new methods for creation of radiatively stable entanglement in a system of two dipole-interacting three-level atoms.
The Weisskopf-Wigner theory of the natural linewidth of a single isolated atom is extended to a system of $N(\ensuremath{\gg}1)$ identical nonoverlapping atoms which are all in the same excited state at time t=0t=0t=0. The positions ${\mathrm{X}}_{1}\ensuremath{\cdots}{\mathrm{X}}_{N}$ of the atoms are assumed to fill a volume U\mathcal{U}U of given shape and size with macroscopically constant density. Emission of radiation from this system takes place only in the form of one narrow, but nonzero-width, bundle of nearly equal photons, which contains all the emitted radiation. If the density of atoms within U\mathcal{U}U exceeds a certain threshold, the rate of emission of photons has the form of a typical spike. All effects depend sensitively on the shape and size of U\mathcal{U}U and on the density of atoms within U\mathcal{U}U, and cannot be explained in conventional terms of spontaneous or stimulated emission of radiation.
Lux aeterna luceat eis. Let there be light. Take the rest of the week off. Atomic energy levels deduced from optical spectra comprise one of the most precisely known sets of physical measurements that exist. However, the precision of the determinations of the relative oscillator strengths of these spectral lines from the relative intensities of spectral lines is much less precise. Fortunately, time-dependent methods for the study of the dynamics of the emission process exist (and are being developed) that permit the transition probability rates, oscillator strengths, and reaction rates to be determined with ever-increasing precision. In most elementary quantum mechanics textbooks, the section on the emission of radiation is the least satisfactory section of the book. Whereas the development of relationships among various spatial overlap integrals between state vectors for various operators (such as the electrostatic dipole moment) can be formulated in a very elegant ab initio manner, the connection of these matrix elements to the time dependence of the system often seems driven by a posteriori assumptions that are extended beyond their justifiable range of applicability. As Fermi observed in stating his Golden Rule , “the transition probability and energy perturbation can be calculated with the help of perturbation theory ( i.e. , there is no better way known).” The Weisskopf–Wigner approximation offers a scheme for making precise calculations, but does not provide the rigor that has characterized so many other areas of quantum mechanics.
Abstract Radiation damping of three atoms in a radiation field is studied for both a linear and closed‐chain configuration. One atom of the system is initially excited. Use is made of the Heitler‐Ma perturbation procedure up to second order. The discussion is developed in terms of the symmetry of the interactions within the system. The interactions arising from dipole transitions perpendicular to the plane of the closed chain are shown to be similar to the interactions in a two‐atom system, and the results are extended to cover larger rings.
The interaction energy between two atoms, one of which is excited, is investigated. The form of the interaction depends on the relation between the distance R separating the atoms and the wavelength k1—1 of the transition from the ground state to the excited state. If k1R<1 the photon may be trapped between the two atoms leading to the well-known dipole—dipole interaction. If k1R>1 the interaction is small, the state of the interacting atoms is not a stationary state and the photon is emitted after a time determined by the spontaneous emission probability.