A study on the shape of two-photon wavefunctions after the nonlinear interaction with a one-dimensional atom

We study the interaction of Gaussian one- and two-photon pulses with a single two-level atom based on a one-dimensional model of pulse propagation to and from the atom. The characteristic time scale of the atomic response is the dipole relaxation time 1/Gamma. We therefore compare the effect of the non-linear two-photon interaction for a long pulse length of 10/Gamma with a short pulse of $1/\Gamma$. Our results indicate that the effect of the non-linear interaction is particularly strong for the short pulse length of 1/Gamma.