Abstract
The motion of a two-level atom in a standing-wave laser fieldis studied using an approximation to the resolvent operator inthe form of a truncated eigenfunction expansion, with the fieldtreated in the occupation-number representation. The formalismprovides expressions for the time-dependent S-matrix fortransitions into both ground and excited atomic states. Theeffective Hamiltonian for purely elastic scattering is constructed, allowing for the direct study of scattering in theBragg regime. Contact with standard treatments of Braggscattering in terms of Mathieu functions is obtained byimposition of additional approximations. Comparison ofnumerical results obtained with and without imposition of theseapproximations provides an indication of their range ofvalidity. The dependence of excitation probabilities on fieldstrength and detuning is studied. These numerical illustrationsprovide evidence that in cases of physical interest excitationprobabilities can be significant and can be reliably estimatedfor a broad range of field parameters using the present formalism.
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