Collision-Induced Coherence in Four Wave Light Mixing

  • N. Bloembergen
  • A. R. Bogdan
  • M. W. Downer
Part of the Springer Series in Optical Sciences book series (SSOS, volume 30)


The evolution of the density matrix of a material system under the influence of one or more traveling electromagnetic waves is central in determining the linear and nonlinear optical response. The role of spontaneous emission and collisional processes may, under certain conditions which apply to a rather large variety of experimental situations, be represented by phenomenological damping terms in the equations of motion for the diagonal and off-diagonal elements of the density matrix [1]. General expressions for the third order nonlinear susceptibility have been given by many authors [2–4]. The bookkeeping of the many terms occurring in third order perturbation theory may be systematized by the use df double-sided Feynman type diagrams [5,6,7]. It is important to consider explicitly the evolution of both bra vectors <ψ| and ket vectors |ψ> in the presence of damping. Authors who use only one sided diagrams irretrievably lose some terms which have physical significance. One must not calculate the evolution in the absence of damping, and then formally add the damping by considering some frequencies as complex quantities. In the latter case one always ends up with resonant denominators which contain only separations ωgn from the initially occupied state, ρ gg (o) =1, to states |n>. The correct expression also contains denominators with frequency separations ωnn, between two initially unoccupied excited states.


Spontaneous Emission Helium Pressure Order Perturbation Theory Nonlinear Optical Response Satellite Resonance 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • N. Bloembergen
    • 1
  • A. R. Bogdan
    • 1
  • M. W. Downer
    • 1
  1. 1.Division of Applied SciencesmHarvard UniversityCambridgeUSA

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