Optical Kerr nonlinearity is important for various applications in both classical and quantum regimes. It has been shown that Kerr nonlinearity can be considerably enhanced based on electromagnetically induced transparency in cold atoms. However, in a hot atomic ensemble the Kerr nonlinearity is usually weakened by the Doppler effect. Here we show that the Kerr nonlinearity can be enhanced by tuning the wave-number mismatch between the probe and control fields in hot atoms. When the wave number of the control field, denoted by $k_c$, is larger than that of the probe field, denoted by $k_p$, the transition strength for the probe field from the ground to two dressed states created by the control field becomes stronger, leading to an increased nonlinear dispersion and absorption. Upon increasing the ratio $k_c/k_p$ further, the effective number of atoms contributing to the interaction decreases such that the nonlinear dispersion and absorption are eventually reduced. Nevertheless, the peak nonlinear dispersion and absorption are enhanced by factors of up to 3 and 2, respectively, for $k_c/k_p>1$ in comparison to the case of $k_c/k_p=1$. Our results may be beneficial for a variety of applications where the Kerr nonlinearity is crucial.

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• Electromagnetically induced transparency
• Nonlinear optics
• Photorefractive & Kerr effects