accurate but difficult control of the atomic densities. A different way of achieving group velocity matching, but which is still asymmetric for probe and trigger has been proposed in Ref. [@Ottaviani03], which employs a five-level *M* scheme similar to the one discussed here, but with a different atomic population distribution. In that case, the two group velocities can be tuned and made equal simply by tuning the frequencies and intensities of the two classical pump fields. Instead, Ref. [@Petrosyan02] considered a six level scheme in which probe and trigger are affected by EIT and XPM in a symmetric fashion, so that the corresponding group velocities are equal by construction. The present proposal achieves group velocity matching just in the same way (see also Refs. [@tripod], where a four-level tripod system, symmetric between probe and trigger, has been proposed for XPM).

The paper is organized as follows. In Sec. \[sec:model\] we describe the model used in the remainder of the paper. Sec. \[sec:perturbative\] shows the results of a perturbative calculation for the CPS. These are used as a motivation to pass to a density matrix based calculations in Sec. \[sec:SSOperation\], describing a QPG operation in a steady-state. Then, the transient regime 