  Being able to reliably transfer the quantum state from one system to another
is crucial to developing quantum networks. A standard way to accomplish this
transfer of information is by making use of an intermediate information carrier
(e.g., a photon) that is emitted by the first system and absorbed by the
second. For such a scenario one can develop an effective description by
eliminating the intermediate degrees of freedom, which yields an effective
direct coupling between the two systems. If, however, the spectral properties
of the two systems are different, the photon's time-frequency shape needs to be
appropriately modified before it reaches the second system. We study here the
effective description that results when we thus manipulate the intermediate
photon. We examine a unitary transformation, $U$, that time reverses, frequency
translates, and stretches the photon wave packet. We find that the concomitant
modifications to the effective description can best be understood in terms of a
change to the state's time argument, $\rho(t) = \rho_1(\tilde{t}) \otimes
\rho_2(t)$, where $\tilde{t}$ is a fictitious time for the first system that is
stretched and runs backward. We apply this theory to three-level
$\Lambda$-systems inside optical cavities, and we numerically illustrate how
performing the unitary transformation $U$ results in improved quantum state
transfer.
