Investigation of femtosecond optical delay and auto correlator in X-ray region

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We investigate X-ray auto correlator to determine the duration of femtosecond pulses from X-ray free-electron lasers. We successfully observe double core-hole creation in krypton and direct two-photon absorption in germanium, which are indispensable two-photon processes for the auto correlator. We estimate the pulse duration to be 2.5 fs by analyzing the X-ray fluorescence spectrum from the double core-hole state. We find a competition between K-shell two-photon absorption and L-shell one-photon absorption. We analyze the pulse-energy dependence of two-photon absorption including the competition effect. Finally, we successfully reproduce the observed pulse-energy dependence, and determine the cross section of two-photon absorption. The competition determines the highest intensity for the auto correlator with two-photon absorption.