Density Matrix Equations and Diagrams for High Resolution Non-Linear Laser Spectroscopy: Application to Ramsey Fringes in the Optical Domain

  • Christian J. Bordé


We present a semiclassical approach to the line shape problem in high resolution laser spectroscopy which includes,in a unified density matrix formalism, the influences of the beam geometry, of the molecular recoil and of the second-order Doppler effect. A fully covariant second-quantized extension of the formalism is outlined. We give also a general derivation of intensities for all non-linear processes using Racah algebra in Liouville space. We describe diagrammatic representations of the perturbative solutions of the equations suitable for all laser spectroscopy techniques. Simple topological rules characterize Doppler-free processes. The diagrams and their associated diagrammatic rules are illustrated by their applications to the computation of Ramsey fringes in the case of single photon, Doppler-free two-photon and saturation spectroscopies. Finally we show how light-shifts can be calculated by this method and find, as expected, that the shifts for Ramsey fringes are reduced by the ratio of the laser beam radius to the zone separation when compared to the shifts for the single zone signal.


Density Matrix Line Shape Matrix Equation Density Operator Laser Spectroscopy 
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Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • Christian J. Bordé
    • 1
  1. 1.Laboratoire de Physique des Lasers, Associé au CNRS n°282Université Paris-NordVilletaneuseFrance

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