Light-matter interactions are ubiquitous, and underpin a wide range of basic research fields and applied technologies. Although optical interactions have been intensively studied, their microscopic details are often poorly understood and have so far not been directly measurable. X-ray and optical wave mixing was proposed nearly half a century ago as an atomic-scale probe of optical interactions but has not yet been observed owing to a lack of sufficiently intense X-ray sources. Here we use an X-ray laser to demonstrate X-ray and optical sum-frequency generation. The underlying nonlinearity is a reciprocal-space probe of the optically induced charges and associated microscopic fields that arise in an illuminated material. To within the experimental errors, the measured efficiency is consistent with first-principles calculations of microscopic optical polarization in diamond. The ability to probe optical interactions on the atomic scale offers new opportunities in both basic and applied areas of science.Light-matter interactions have advanced our understanding of atoms, molecules and materials, and are also central to a number of areas of applied science. Although optical interactions have received a great deal of study, the microscopic details of how light manipulates matter are poorly understood in many circumstances. A material's optical response is complex, being determined by coupled many-body interactions that vary on the scale of atoms rather than on the scale of a long-wavelength applied field. Data are needed to combat this complexity, and so far it has not been possible to probe the microscopic details of light-matter interactions. X-ray and optical wave mixing, specifically sum-frequency generation (SFG), was proposed nearly half a century ago as an atomic-scale probe of light-matter interactions 1,2 . The process is, in essence, optically modulated X-ray diffraction: X-rays inelastically scatter from optically induced charge oscillations and probe optically polarized charge in direct analogy to how standard X-ray diffraction probes ground-state charge. Furthermore, the optically induced microscopic field is determined because it is closely related to the induced charge [3][4][5][6] . So far it has not been possible to measure these two quantities directly. X-ray and optical wave mixing has frequently been discussed 1,2,4,[7][8][9][10][11][12] , but it has not yet been demonstrated owing to a lack of sufficiently intense X-ray sources. More generally, although there have been theoretical studies of nonlinear X-ray scattering [13][14][15][16][17][18] , experimental observations have largely been confined to the spontaneous processes of X-ray parametric down-conversion [19][20][21][22][23] and resonant inelastic X-ray scattering 24,25 . X-ray free-electron lasers offer unprecedented brightness and new scientific opportunities 26 . Here we use an X-ray laser to demonstrate X-ray/optical SFG through the nonlinear interaction of the two fields in single-crystal diamond. Optically modulated X-ray diffract...

X-ray scattering is typically used as a weak linear atomic-scale probe of matter. At high intensities, such as produced at free-electron lasers, nonlinearities can become important, and the probe may no longer be considered weak. Here we report the observation of one of the most fundamental nonlinear X-ray-matter interactions: the concerted nonlinear Compton scattering of two identical hard X-ray photons producing a single higher-energy photon. The X-ray intensity reached 4 × 10 20 W cm −2 , corresponding to an electric field well above the atomic unit of strength and within almost four orders of magnitude of the quantum-electrodynamic critical field. We measure a signal from solid beryllium that scales quadratically in intensity, consistent with simultaneous non-resonant two-photon scattering from nearly-free electrons. The high-energy photons show an anomalously large redshift that is incompatible with a free-electron approximation for the ground-state electron distribution, suggesting an enhanced nonlinearity for scattering at large momentum transfer.

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Conventional spectroscopy uses classical light to detect matter properties through the variation of its response with frequencies or time delays. Quantum light opens up new avenues for spectroscopy by utilizing parameters of the quantum state of light as novel control knobs and through the variation of photon statistics by coupling to matter. This Roadmap article focuses on using quantum light as a powerful sensing and spectroscopic tool to reveal novel information about complex molecules that is not accessible by classical light. It aims at bridging the quantum optics and spectroscopy communities which normally have opposite goals: manipulating complex light states with simple matter e.g. qubits vs. studying complex molecules with simple classical light, respectively. Articles cover advances in the generation and manipulation of state-of-the-art quantum light sources along with applications to sensing, spectroscopy, imaging and interferometry.