in explored in Sec. \[sec:transient\], while in Sec. \[sec:exper\] a scheme for the experimental verification of the QPG operation is discussed in detail. Conclusions are given in Sec. \[sec:conclusion\].

Model {#sec:model}
=====

![(Color online) A schematic plot of the assumed single-photon pulse propagation through the gas cell of length $L$ and diameter $d$. The pulse length is assumed to coincide with the cell length $L$, and the pulse waist $w$ is assumed to be of order of cell diameter $d$.[]{data-label="fig:pulsescheme"}](pulse_scheme.eps)

In this Section, we present the model we have adopted for a full quantum description of the interaction of the two single-photon wave-packets with the atomic medium possessing the level structure outlined in Fig. \[fig:5levelscheme\]. To this end, we make the following two assumptions which, even though not simple to realize experimentally, are more technical than physical in nature:

1.  We assume perfect spatial mode matching between the input single-photon pulses entering the gas cell and the optical modes naturally excited by the driven atomic medium, and which are determined by the geometrical configuration of the gas cell and of the pump beams [@Duan02]. This allows us to describe the probe and trigger fields with the right polarization in terms 