Investigations of Single-Atom Interference Effects Through Elastic Scattering

S. Bali, Frank A. Narducci

We are in the process of investigating non-classical effects in the interference between fluorescence from a single atom and a coherent, classical reference beam, when the elastic portion of the fluorescence is used as the classical reference.

Evgeniĭ E. Nikitin, M. Ya. Ovchinnikova

Christoph Ira Westbrook

F. L. Arnot

Abstract The interference of electrons is now a well established fact. It has been shown that when a homogeneous beam of electrons falls upon a regular arrangement of scattering centres, such as a crystal, a ruled grating, or a complex gaseous molecule, the angular distribution of the scattered electrons shows interference maxima and minima. The analagous, though distinct, phenomonon of the diffraction of electrons has, however, only recently been demonstrated. Evidence of the diffraction of electrons was first obtained about two years ago by Bullard and Massey, and the author. While investigating the angular distribution of elastically scattered electrons in mercury vapour I found well-marked maxima and minima. In this case the scattering was produced, not by an ordered arrangement of scattering centres, but by a random distribution of atoms. It has been shown theoretically that the results obtained can be satisfactorily explained on the assumption of scattering by a single centre, and consequently they represent a true diffraction effect.

J. R. Ott

This thesis concerns the theoretical investigation of interference phenomena related to elastic and inelastic scattering of quantized light. The presented work is naturally divided into two parts, the first is concerning elastic scattering while the second explores inelastic scattering. In the first part we use a scattering-matrix formalism combined with results from random-matrix theory to investigate the interference of quantum optical states on a multiple scattering medium. We investigate a single realization of a scattering medium thereby showing that it is possible to create entangled states by interference of squeezed beams. Mixing photon states on the single realization also shows that quantum interference naturally arises by interfering quantum states. We further investigate the ensemble averaged transmission properties of the quantized light and see that the induced quantum interference survives even after disorder averaging. The quantum interference manifests itself through increased photon correlations. Furthermore, the theoretical description of a measurement procedure is presented. In this work we relate the noise power spectrum of the total transmitted or reflected light to the photon correlations after ensemble averaging. This analysis enables us to describe an experimental observation of the quantum nature of light that survives the averaging over disorder. In the second part we investigate inelastic scattering. This we do by first treating the scattering of light on dipoles embedded in an arbitrary dielectric environment. By considering the two different models for dipole interaction known as the minimal-coupling and electric-dipole interaction Hamiltonians, we find exact relations between the electric field and the dipole operators in the Heisenberg picture, while keeping the model of the dipoles arbitrary. Due to the exact treatment of the electric-field operators, we obtain kernels known from classical scattering theory to describe the propagation of the field from the dipoles. Using the found electric field operators we derive the Heisenberg equations of motion for the dipoles while treating them as quantum two-level systems and using the Born–Markov and rotating-wave approximations. Postponing the rotating-wave approximation to the very end of the formal calculations allows us to identify the different physical parameters of the dipole evolution in terms of physical quantities known from optics. Finally, we use our Heisenberg picture formalism to treat a dilute cloud of two-level atoms, by simplifying the equations of motion using a single-scattering approximation for the interaction between the atoms. This enables us to derive expressions for the steady-state population and fluorescence spectrum, where we find cooperative effects in both the elastic and the inelastic spectra.