Dipole interaction of a multilevel system with a continuous-wave or Gaussian-pulsed laser

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Abstract
An algorithm [G. F. Thomas and W. J. Meath, J. Phys. B 16, 951 (1983)] for evaluating the evolution operator of a multilevel system dipole interacting with either a continuous-wave or Gaussian-pulsed source, based on its Riemann product integral representation in conjunction with Frazer’s method of mean coefficients, is appraised and extended. Our extension allows for the inclusion of spontaneous decay or a dissociation (or ionization) channel and useful relations are derived for the eigenvalues of the evolution operator for both the continuous wave and the Gaussian pulse. For the latter we now admit an arbitrary phase in the field and we derive a simple relation for cascading the state amplitudes of the system over the duration of an arbitrary number of identical phase-coherent pulses. As part of our appraisal, improvements in the implementation of the algorithm are provided. For a two-level system, the evolution operator is given as the chronologically ordered product of readily computed 2×2 matrices while for multilevel system it is conveniently evaluated using a resolvent method based on Leverrier’s algorithm for computing the Bateman matrices. The asymptotic behavior of the evolution operator and the fluence in the direction of propagation for both the continuous-wave and the Gaussian-pulsed sources are explored. Applications to model two-level systems illustrate the influence of the source’s phase and interaction duration on resonant and nonresonant transition probabilities, respectively. The saturation of a two-level system by a train of resonant phase-coherent Gaussian pulses is demonstrated.