通过单光子波包的“巨克尔效应”产生大相移的不可能性
Impossibility of large phase shifts via the "giant Kerr effect" with single-photon wavepackets
摘要：
给出了两个单光子波包通过理想定域克尔介质相互作用系统的近似解析解，并进行了数值计算。结果表明，由于自发发射到最初未占用的时间模式，交叉相位调制的薛定谔图片是非常小的，只要光谱宽度的单光子脉冲是在介质的带宽。在这个极限下，所用的哈密顿量可以从电磁诱导透明条件下四能级原子的“巨克尔效应”导出;明确地示出了在该系统中的线性吸收随着脉冲的光谱宽度接近介质的透明带宽而增加，因此，只要吸收概率保持小，最大交叉相位调制被限制为基本上无用的值。这些结果与Shapiro及其同事基于因果关系和统一性的一般论点一致。
英文摘要：
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.
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