Incoherent and coherent pulses and multiphoton absorption probability

We deal with the models of a coherent pulse and of an incoherent one. The former pulse is described by using a polychromatic pure coherent state and the latter is obtained by an incoherent superposition of identical polychromatic elementary pulses shifted in time by a statistically distributed delay. For the incoherent pulse the ratio between its duration and its coherence time can assume any possible value. By using these pulse models the dependence ofs-photon absorption probability on the statistical properties of the incident pulsed light is investigated. It is found that, when the two pulses have the same spectral distribution and the same energy, the ratio between the probabilities fors-photon absorption induced by the incoherent pulse and that induced by the coherent pulse is given by\(s!\left[ {\frac{{I_{inc} }}{{I_{coh} }}} \right]^{s - 1} \), where Iinc and Icoh are the intensities of the incoherent pulse and of the coherent pulse, respectively, at the time in which the field interacts with the atomic system. This ratio shows that, when the two pulses have also the same duration and, therefore, the same intensity, the probability induced by the incoherent pulse is s! times higher than that induced by the coherent pulse. Explicit calculations on the multiphoton absorption probability are carried out for the pulses when their time shapes are Gaussian.