Abstract
The use of the matrix density formalism, and of a multiscale expansion, allows the derivation of a macroscopic nonlinear evolution equation for a short light pulse (a nonlinear Schroedinger (NLS) equation), directly from the microscopic equations of the quantum mechanics. We consider the simple case of a monochromatic plane wave, interacting with independent two-level atoms, to show that such a computation is possible. For their linear part, the results agree with that of the linear dispersion theory, but the obtained nonlinear coefficient appreciably differs from that derived from the computation of the so-called nonlinear susceptibilities, except in one simple particular situation.
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