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arXiv:1204.1512 · Journal of Physics B Atomic Molecular and Optical Physics

Diagrammatic approach to coherent backscattering of laser light by cold atoms: double scattering revisited

V Shatokhin, Thomas Wellens, Andreas Buchleitner

Published Oct 1, 2012• 3 citations
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Abstract

We present a diagrammatic derivation of the coherent backscattering spectrum from two two-level atoms using the pump-probe approach, wherein the multiple scattering signal is deduced from single-atom responses, and provide a physical interpretation of the single-atom building blocks.
DOI
10.1088/0953-4075/45/21/215501

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We study coherent backscattering of intense laser light from three immobile two-level atoms using the master equation approach. The master equation is solved analytically, and the triple scattering spectrum is expressed in quadratures. We show that this solution can be obtained via a self-consistent combination of single-atom spectral responses, and is equivalent to the solution following from the diagrammatic pump-probe approach. We deduce the general expressions for single-atom building blocks which can be used in simulations of multiple inelastic scattering of laser light in the bulk atomic medium.
We study coherent backscattering of intense laser light from three immobile two-level atoms using the master-equation approach. The master equation is solved analytically, and the triple scattering spectrum is expressed in quadratures. We show that this solution can be obtained via a self-consistent combination of single-atom spectral responses, and is equivalent to the solution following from the diagrammatic pump-probe approach. We deduce the general expressions for single-atom building blocks which can be used in simulations of multiple inelastic scattering of laser light in the bulk atomic medium.
We present a generalization of the diagrammatic pump-probe approach to coherent backscattering (CBS) of intense laser light for atoms with degenerate energy levels. We employ this approach for a characterization of the double-scattering signal from optically pumped atoms with the transition ${J}_{g}\ensuremath{\rightarrow}{J}_{e}={J}_{g}+1$ in the helicity-preserving polarization channel. We show that, in the saturation regime, the internal degeneracy becomes manifest for atoms with ${J}_{g}\ensuremath{\ge}1$, leading to a faster decrease of the CBS enhancement factor with increasing saturation parameter than in the nondegenerate case.
This thesis presents the author's work on multiple scattering of intense laser light by cold atoms in chapter 2 and nonlinear coherent backscattering in chapter 3. The basic concepts and most important results should be understandable from reading these chapters on their own, whereas we refer to the subsequent collection of articles (P1-P11) for more detailed treatments. In chapter 2.1, we review scattering of light by a single two-level atom, with special emphasis on the fact that the atoms are nonlinear and inelastic scatterers, which will be relevant for multiple scattering. In chapter 2.2, we treat double scattering by two distant atoms, before we generalize this technique to a dilute disordered sample of many atoms in chapter 2.3. Both 2.2 and 2.3 apply in the perturbative regime of low laser intensity, where, by analyzing scattering of two photons, we clarify the different roles of nonlinearity and inelasticity concerning the coherent backscattering interference. Chapter 2.4 discusses the master equation as a complementary approach, applicable at arbitrarily high laser intensity, but only for a small number of atoms. In addition, we present an equivalent new approach, which explicitly takes advantage of the large distance between the atoms, and thereby combines the advantages of the master equation and the scattering approach. As discussed in chapter 2.5, this new approach opens the way to a non-perturbative theory for multiple scattering of intense laser light by dilute atomic clouds. Chapter 3 presents our diagrammatic theory for nonlinear coherent backscattering of classical (or single-particle quantum) waves. In chapter 3.1, we explain the most important assumptions of the theory: weak disorder and small nonlinearity, in particular existence of a stable, stationary solution of the nonlinear wave equation. In chapter 3.2, we explain why - contrary to seemingly convincing intuitive reasoning - the nonlinearity indeed changes the height of the coherent backscattering interference peak. In order to describe this effect quantitatively, a diagrammatic theory is sketched in chapters 3.3 and 3.4, where the nonlinear Born series and the nonlinear ladder and crossed diagrams are introduced. Chapter 3.5 presents the transport equations which result from the complete summation of ladder and crossed diagrams - non-perturbatively in the strength of the nonlinearity. We discuss the conditions under which the nonlinearity reduces or enhances the coherent backscattering interference, as compared to the linear case. In order to confirm the validity of the diagrammatic analysis, we compare these results with numerical simulations in chapter 3.6. We conclude with a short account of our work on speckle instabilities for nonlinear point scatterers in chapter 3.7. Finally, chapter 4 describes some future perspectives of our work, in particular the application of the diagrammatic theory to describe the impact of nonlinearity on weak localization and Anderson localization, and possible extensions to the quantum many-particle regime.
We give a detailed derivation of the master-equation description of the coherent backscattering of laser light by cold atoms. In particular, our formalism accounts for the nonperturbative nonlinear response of the atoms when the injected intensity saturates the atomic transition. Explicit expressions are given for total and elastic backscattering intensities in the different polarization channels, for the simplest nontrivial multiple-scattering scenario of intense laser light multiply scattering from two randomly placed atoms.