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arXiv:cond-mat/0410640 · Physical Review A

Light scattering from three-level systems: The T matrix of a point dipole with gain

Tom Savels, Allard P. Mosk, Ad Lagendijk

Published Apr 18, 2005• 21 citations
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Abstract

We present an extension of the $T$-matrix approach to scattering of light by a three-level system, using a description based on a Master equation. More particularly, we apply our formalism to calculate the $T$ matrix of a pumped three-level atom, providing an exact and analytical expression describing the influence of a pump on the light-scattering properties of an atomic three-level system.

DOI
10.1103/physreva.71.043814

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We present an extension of the TTT-matrix approach to scattering of light by a three-level system, using a description based on a Master equation. More particularly, we apply our formalism to calculate the TTT matrix of a pumped three-level atom, providing an exact and analytical expression describing the influence of a pump on the light-scattering properties of an atomic three-level system.
We have solved a master equation to obtain the diagonal elements of the density matrix for laser light. The master equation represents a generalization of a master equation derived earlier for a single radiation mode interacting with NNN stationary two-level atoms. The generalization takes into account the pumping scheme which characterizes a three-level laser. For positive temperatures and a lossless cavity, the equilibrium solution of the master equation gives the correct statistical-mechanical description of the atoms and radiation. For negative temperatures, the distribution function for the number of photons in the mode is either exponential or peaked, depending on whether the laser is operating below or above threshold. The calculated intensity fluctuations are in good agreement with semiclassical results for lasers operating slightly above threshold.
We have solved a master equation to obtain the diagonal elements of the density matrix for laser light. The master equation represents a generalization of a master equation derived earlier for a single radiation mode interacting with NNN stationary two-level atoms. The generalization takes into account the pumping scheme which characterizes a three-level laser. For positive temperatures and a lossless cavity, the equilibrium solution of the master equation gives the correct statistical-mechanical description of the atoms and radiation. For negative temperatures, the distribution function for the number of photons in the mode is either exponential or peaked, depending on whether the laser is operating below or above threshold. The calculated intensity fluctuations are in good agreement with semiclassical results for lasers operating slightly above threshold.
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.