A theory of pump probe spectroscopy is carried out using an amplitude approach in a bare state basis. The interplay between absorption and emission is clearly defined in this approach. Both closed and open systems are considered. The theory is applied to a calculation of the dispersion-like structure that appears when the probe frequency is nearly equal to the pump frequency, in the limit of large pump field detuning. The theory is extended to include a class of problems in which the recoil atoms undergo on the absorption or emission of radiation leads to resonance structures. The relationshp of these recoil-induced resonances to the collective atomic recoil laser is discussed. The probe gainwhich occurs without level inversion in these systems cannot be viewed as a parametric process, in its normal sense.
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