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Annual Meeting Optical Society of America

Coherence between elastic and inelastic scattering of light from an atom

S. Bali, Frank A. Narducci

Published Jan 1, 1993• 0 citations
Publisher

Abstract

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.
DOI
10.1364/oam.1993.thl.6

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It has been predicted that when fluorescent photons emitted from an atom in the process of resonance fluorescence interfere with a portion of the coherent driving field, the visibility of the resulting interference exhibits nonclassical features and is zero at the moment when the atom is fully excited and when the fluorescent intensity is greatest.1 We show theoretically that a similar conclusion applies to interference between the fluorescent photons and the elastically scattered part of the driving field, which can be separated out with narrow band filters in practice. This involves the calculation of certain fourth order, three-time correlation functions that have not previously been studied. A possible application of the theory to an interference experiment will be discussed.
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.
The recent technical advances in the creation of rapidly rotating light polarizations are shown to provide new tools to explore elastic and inelastic scattering phenomena. In the case of inelastic scattering, the light fluoresced by atoms or molecules coherently excited by a rapidly rotating linear polarization is expected to exhibit new resonances. Such resonances, due to the transfer of coherence from light to atoms or molecules, are theoretically studied and experimentally observed. They provide simple methods to probe atomic internal constants, such as energy level life-times. The analogy between those resonances and the Hanle effect suggests new experiments in atomic physics. In the case of elastic scattering such as the one encountered during propagation through a dense turbid medium, the rotating linear polarization is shown to be an ideal tool to extract the ballistic photons from the large background of diffused light. This permits to image tiny objects embedded in a dense turbid medium, with an experimental resolution similar to the one obtained in usual homogeneous optical system.