Resonant enhancement of high-order optical nonlinearities based on atomic coherence

We show that the effect of coherent population trapping may result in resonant enhancement of ${\chi }^{\mathrm{}\left(5\right)\mathrm{}}$ or higher-order nonlinearities. The enhancement is accompanied by suppression of the other linear and nonlinear susceptibility terms. This effect has promise for a realistic scheme of photon phase gates necessary for practical implementation of quantum processing protocols.