Adiabatic excitation of multilevel systems

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Abstract
We derive and discuss the behavior of several multilevel models relevant to the problem of molecular multiphoton excitation under the action of a quasimonochromatic laser field, the amplitude of which rises slowly and falls rapidly on a certain internal time scale. Our method is suitable for the numerical solution of problems involving the adiabatic excitation of large multilevel systems. We find adiabatic inversion to be a general characteristic of the models considered. The fact that adiabatic inversion is accompanied by marked qualitative and quantitative changes in the expectation value of the dipole operator makes our results useful for understanding the propagation of laser pulses. An explicit expression that is especially convenient for numerical evaluation is presented for determining the limiting internal time scale, which is determined by the energy levels and transition moments of the system and the laser frequency. We illustrate the criterion for adiabatic inversion by applying it to a particular multilevel model. From a density-matrix treatment we conclude that collisional damping destroys the coherence required for adiabatic inversion. On the basis of our results we believe that the adiabatic approximation may be appropriate for some experiments of current interest.

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