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arXiv:quant-ph/0201020 · Physica A Statistical Mechanics and its Applications

Adiabatic approximation in the density matrix approach: non-degenerate systems

A.C. Aguiar Pinto, K.M. Fonseca Romero, M. T. Thomaz

Published Aug 1, 2002• 8 citations
arXivHTMLPDF
DOI
10.1016/s0378-4371(02)00829-4

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An adiabatic approximation for the Liouville density-matrix equation which includes decay terms is developed. The adiabatic approximation employs the eigenvectors of the non-normal Liouville operator. The approximation is valid when there exists a complete set of eigenvectors of the non-normal Liouville operator (i.e., the eigenvectors span the density-matrix space), the time rate of change of the Liouville operator is small, and an auxiliary matrix is nonsingular. Numerical examples are presented involving efficient population transfer in a molecule by stimulated Raman scattering, with the intermediate level of the molecule decaying on a time scale that is fast compared with the pulse durations of the pump and Stokes fields. The adiabatic density-matrix approximation can be simply used to determine the density matrix for atomic or molecular systems interacting with cw electromagnetic fields when spontaneous emission or other decay mechanisms prevail.