Theory of pump-probe spectroscopy using an amplitude approach

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 origin of the dispersion-like structure can be traced to interference terms in the absorption spectrum or to a radiative shift. The probe gain which occurs without level inversion cannot be viewed as a parametric process, in its normal sense.