  An approximate analytical solution is presented, along with numerical
calculations, for a system of two single-photon wavepackets interacting via an
ideal, localized Kerr medium. It is shown that, because of spontaneous emission
into the initially unoccupied temporal modes, the cross-phase modulation in the
Schrodinger picture is very small as long as the spectral width of the
single-photon pulses is well within the medium's bandwidth. In this limit, the
Hamiltonian used can be derived from the "giant Kerr effect" for a four-level
atom, under conditions of electromagnetically-induced transparency; it is shown
explicitly that the linear absorption in this system increases as the pulse's
spectral width approaches the medium's transparency bandwidth, and hence, as
long as the absorption probability remains small, the maximum cross-phase
modulation is limited to essentially useless values. These results are in
agreement with the general, causality- and unitarity-based arguments of Shapiro
and co-workers.
