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An approximate analytical solution is presented, along with numericalcalculations, for a system of two single-photon wavepackets interacting via anideal, localized Kerr medium. It is shown that, because of spontaneous emissioninto the initially unoccupied temporal modes, the cross-phase modulation in theSchrodinger picture is very small as long as the spectral width of thesingle-photon pulses is well within the medium's bandwidth. In this limit, theHamiltonian used can be derived from the "giant Kerr effect" for a four-levelatom, under conditions of electromagnetically-induced transparency; it is shownexplicitly that the linear absorption in this system increases as the pulse'sspectral width approaches the medium's transparency bandwidth, and hence, aslong as the absorption probability remains small, the maximum cross-phasemodulation is limited to essentially useless values. These results are inagreement with the general, causality- and unitarity-based arguments of Shapiroand co-workers.

Impossibility of large phase shifts via the "giant Kerr effect" with single-photon wavepackets