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arXiv:cond-mat/0504673

The independent scattering approximation in the saturated regime

Tom Savels, Allard P. Mosk, Ad Lagendijk

Published Apr 26, 2005• 0 citations
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Abstract

We show that a saturable single-frequency elastic T-matrix approach to scattering of light by atoms agrees remarkably well with a master equation description in the regime of unsaturated atoms, or for large separation between the atoms. If the atoms are in each other's near-field and the saturation of the atoms is high enough, the two approaches yield different results.

DOI
10.48550/arxiv.cond-mat/0504673

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We show that a saturable single-frequency elastic T-matrix approach to scattering of light by atoms agrees remarkably well with a master equation description in the regime of unsaturated atoms, or for large separation between the atoms. If the atoms are in each other's near-field and the saturation of the atoms is high enough, the two approaches yield different results.
We measure the resonant forward scattering of light by a highly saturated atomic medium through the flashes emitted immediately after an abrupt extinction of the probe beam. The experiment is done in a dilute regime where the phenomena are well captured using the independent scattering approximation. Comparing our measurements to a model based on Maxwell-Bloch equations, our experimental results are consistent with contributions from only the elastic component, whereas the attenuation of the coherent transmission power is linked to the elastic and inelastic scatterings. In the large saturation regime and at the vicinity of the atomic resonance, we derive an asymptotic expression relating the elastic scattering power to the forward-scattered power.
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In the field of atom optics, the basis of many experiments is a two-level atom coupled to a light field. The evolution of this system is governed by a master equation. The irreversible components of this master equation describe the spontaneous emission of photons from the atom. For many applications, it is necessary to minimize the effect of this irreversible evolution. This can be achieved by having a far detuned light field. The drawback of this regime is that making the detuning very large makes the time step required to solve the master equation very small, much smaller than the time scale of any significant evolution. This makes the problem very numerically intensive. For this reason, approximations are used to simulate the master equation, which are more numerically tractable to solve. This paper analyzes four approximations: The standard adiabatic approximation, a more sophisticated adiabatic approximation (not used before), a secular approximation, and a fully quantum dressed-state approximation. The advantages and disadvantages of each are investigated with respect to accuracy, complexity, and the resources required to simulate. In a parameter regime of particular experimental interest, only the sophisticated adiabatic and dressed-state approximations agree well with the exact evolution.
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.
A fully quantum-mechanical treatment of resonant light scattering is presented. The incident field is assumed to be described by a coherent state, and is allowed to be intense enough to cause saturation. Complete solutions are obtained for the correlated atom-field pure state vector, including multiphoton contributions of arbitrary order. The frequency spectrum of the scattered field is evaluated and is found to agree exactly with the result previously obtained by means of the quantum fluctuation-regression theorem. A derivation of the fluctuation-regression theorem and of the optical Bloch equations is given which is fully quantum mechanical and which relies upon no assumption of statistical factorization of atom and field states. The accuracy of the result found for the scattered - field spectrum is thus shown to be limited only by the assumption of the smallness of the saturated linewidth compared to the (optical) atomic resonance frequency. The one-photon approximation is analyzed in some detail. The method of adding an imaginary term to the upper-atomic-state energy is clarified, and it is shown how the vacuum and one-photon amplitudes thereby obtained may be used, within a simple and plausible iteration scheme, to construct the complete multiphoton spectrum. A variety of commonly used injection schemes and methods of representing atomic relaxation are discussed, and comparisons are made with results found by other authors. The entire analysis is performed with the aid of a canonical transformation which replaces the applied field by a ccc number. It is thus proved quite rigorously and generally that the use of a ccc-number applied field is a fully quantum-mechanical procedure, provided only that radiation-reaction terms are retained.