Evidence for Collective Nonlinear Interactions in X Ray into Ultraviolet Parametric Down-Conversion

We present the observation of peculiar nonmonotonic photon energy dependencies of the count rates and of the rocking curves of parametric down-conversion of x rays into ultraviolet far from any atomic resonances. The observations cannot be explained by models that consider only atomic or bond charge responses and suggest that collective phenomena contribute to the effect. We propose an interpretation that includes nonlinear interactions with plasmons, which can explain the existence of peaks in this energy range. Our Letter implies that nonlinear interactions between x rays and either ultraviolet or visible radiation can be utilized as a powerful atomic-scale probe for collective effects in solids.

Figure 1

Calculated nonlinear current density including the interactions with bulk plasmons in diamond. The arrows indicate the spectral regions where we observe the peaks in the experiment.

Figure 2

(a) Phase-matching scheme where the indices $p$, $s$, and $i$ stand for pump, signal, and idler, respectively. The dashed line indicates the Bragg diffraction direction. (b) Experimental setup. The synchrotron radiation (SR) illuminates a diamond crystal, which is tuned to an angle satisfying the phase-matching conditions. The PDC signal is collected by a spherically bent analyzer crystal, which images the beam at the selected energy onto a two-dimensional detector.

Figure 3

Rocking curves of the PDC signal for corresponding idler photon energies at 25, 28, 30, and 32 eV. The dashed lines are guides for the eye. (Inset) Comparison between the measured centers of the PDC rocking curves and offset from Brag predicted by the simulations. See discussion in the text.

Figure 4

Experimental results showing the spectral dependencies on the idler photon energy of (a) the efficiency of the PDC and (b) the peak position of the signal beam. (a) The arrows point to photon energies at which the theory that includes the interaction with plasmons predicts peaks. (Inset) Simulation of the PDC process and the arrows point at energies that correspond to the position of the measured spectral peaks. (b) (inset) The rocking curves of the PDC at the photon energies near the sharp change in the peak position as a function of the idler photon energy.