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Using the Kohn-Sham density functional theory, we numerically study the four-wave mixing response of a carbon atom model system exposed to a train of femtosecond two color ω-3ω random phase coherent X-ray pulses near the K-edge. The phase-sensitivity cancellation of the 5ω anti-Stokes component previously described in two- and three-level systems in the infrared and optical regions is extended into the X-ray. Resonances with the absorption lines in the XANES and EXAFS regions produce 5ω peak intensities that increase near the phase-sensitivity cancellation frequencies. Based on this effect, we predict that highly selective intense X-ray 5ω photon energies can be achieved in real systems. The high localization of the ω-3ω four-wave mixing nonlinear technique that we address entails a new valuable tool in X-ray spectroscopies of chemical species as it can readily be extended to different photon energies in other atomic absorption edges, with broad applications.

Localized Core Four-Wave Mixing Buildup in the X-ray Spectrum of Chemical Species