In this work, we study the influence of Doppler broadening on cross-Kerr nonlinearity in a four-level inverted-Y atomic system under electromagnetically induced transparency (EIT) condition. The first- and third-susceptibilities in the presence of Doppler effect are derived as a function of probe, signal and coupling beams and temperature of medium. Under EIT condition, cross-Kerr nonlinearity is enhanced several orders of magnitude compared to that without EIT. The Doppler effect leads to a reduction in the transparent efficiency and thus reduces the amplitude of cross-Kerr nonlinear coefficient. For hot atomic gaseous medium, such consideration of the Doppler effect may be useful for experimental observations and apply to photonic devices operating at different temperature conditions.

中文翻译：

---

多普勒展宽对四级倒 Y 系统中交叉克尔非线性的影响：一种分析方法

在这项工作中，我们研究了多普勒展宽对电磁感应透明 (EIT) 条件下四能级倒 Y 原子系统中交叉克尔非线性的影响。存在多普勒效应时的第一和第三磁化率是作为探头、信号和耦合光束以及介质温度的函数而得出的。在EIT条件下，与没有EIT的情况相比，交叉克尔非线性增强了几个数量级。多普勒效应导致透明效率降低，从而降低了交叉克尔非线性系数的幅度。对于热原子气态介质，多普勒效应的这种考虑可能对实验观察有用，并适用于在不同温度条件下工作的光子器件。