We report a systematic investigation of cross-phase modulation using techniques of light storage (LS) and stationary light pulse (SLP) based on the effect of electromagnetically induced transparency. Two light fields are stopped in the medium to prolong the interaction time, which enhances the efficiency of optical nonlinearity. We numerically study the properties of the signal SLP field such as lifetime, light pulse storage efficiency, and stored peak intensity as functions of optical density (OD) and coupling field intensity. The strong nonlinearity between LS and SLP photons leads to a phase shift of up to $\pi$ at the single-photon level. Meanwhile, both the LS and SLP photons maintain energy transmission higher than 20%, as the OD of the SLP subsystem is larger than 700. The energy transmission and phase shift can be further improved by increasing the OD of the medium. The performance of the quantum phase gate between two single photons is expected by applying such strong photon interaction.

中文翻译：

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静止光脉冲大交叉相位调制的数值研究

我们报告了基于电磁感应透明效应的使用光存储 (LS) 和固定光脉冲 (SLP) 技术的交叉相位调制的系统研究。两个光场在介质中停止以延长相互作用时间，从而提高光学非线性效率。我们数值研究了信号 SLP 场的特性，例如寿命、光脉冲存储效率和存储的峰值强度作为光密度 (OD) 和耦合场强度的函数。LS 和 SLP 光子之间的强非线性导致相移高达$\pi$在单光子水平。同时，由于SLP子系统的OD大于700，LS和SLP光子的能量传输都保持在20%以上。通过增加介质的OD可以进一步改善能量传输和相移。通过应用如此强的光子相互作用，预计两个单光子之间的量子相位门的性能。