Efficient Interaction of Heralded X-Ray Photons with a Beam Splitter.

We report the experimental demonstration of efficient interaction of multi-kilo-electron-volt heralded x-ray photons with a beam splitter. The measured heralded photon rate at the outputs of the beam splitter is about 0.01 counts/s which is comparable to the rate in the absence of the beam splitter. We use this beam splitter together with photon number and photon energy resolving detectors to show directly that when a single x-ray photon interacts with a beam splitter it can only be detected at either of the ports of the beam splitter but not at both simultaneously, leading to a strong anticorrelation between the detection events at the two output ports. Our experiment demonstrates the major advantage of x rays for quantum optics-the possibility to observe experimental results with high fidelity and with negligible background.

X-ray imaging of fast dynamics with single-pixel detector.

We demonstrate experimentally the ability to use a single-pixel detector for two-dimensional high-resolution x-ray imaging of fast dynamics. We image the rotation of a spinning chopper at 100 kHz and at spatial resolution of about 40 microns by using the computational ghost imaging approach. The technique we develop can be used for the imaging of fast dynamics of periodic and periodically stimulated effects with a large field of view and at low dose.

Observation of strong nonlinear interactions in parametric down-conversion of X-rays into ultraviolet radiation.

Nonlinear interactions between X-rays and long wavelength radiation can be used as a powerful atomic-scale probe for light-matter interactions and for properties of valence electrons. However, reported X-ray nonlinear effects were small and their observations required tremendous efforts. Here we report the observation of strong nonlinearities in parametric down-conversion (PDC) of X-rays to long wavelength radiation in gallium arsenide and lithium niobate crystals, with efficiencies about 4 orders of magnitude stronger than the efficiencies measured in any material studied before. Furthermore, we show that the efficiency in the ferroelectric phase of strontium barium niobite is two orders of magnitude stronger than in its paraelectric phase. This observation suggests that the lack of inversion symmetry is the origin for the strong observed nonlinearity. Additionally, we demonstrate the ability to use the effect for the investigation of the spectral response of non-centrosymmetric materials at wavelengths ranging from infrared to soft X-rays.

X-ray computational ghost imaging with single-pixel detector.

We demonstrate computational ghost imaging at X-ray wavelengths with only one single-pixel detector. We show that, by using a known designed mask as a diffuser that induces intensity fluctuations in the probe beam, it is possible to compute the propagation of the electromagnetic field in the absence of the investigated object. We correlate these calculations with the measured data when the object is present in order to reconstruct the images of 50 µm and 80 µm slits. Our results open the possibilities for X-ray high-resolution imaging with partially coherent X-ray sources and can lead to a powerful tool for X-ray three-dimensional imaging.

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.

X-ray ghost imaging with a laboratory source.

We describe an experiment demonstrating ghost imaging with an incoherent low brightness X-ray tube source. We reconstruct the images of 10 µm and 100 µm slits with very high contrast. Our results advance the possibilities that the high-resolution method of ghost diffraction will be utilized with tabletop X-ray sources.

Parametric Down-Conversion of X Rays into the Optical Regime.

We report the observation of parametrically down-converted x-ray signal photons at photon energies that correspond to idler photons at optical wavelengths. The count-rate dependence on the angles of the input beam and of the detector and on the slit sizes agrees with theory within the experimental uncertainties. The nonlinear susceptibility, which we calculated from the measured efficiencies, is comparable to the nonlinear susceptibility evaluated from the measurements of x-ray and optical wave mixing. The results of the present Letter advance the development of a spectroscopy method for probing valence-electron charges and the microscopic optical response of crystals with atomic-scale resolution.

Difference-frequency generation of optical radiation from two-color x-ray pulses.

We describe the process of difference-frequency generation of short optical pulses from two-color X-ray pulses. By assuming 10¹¹ photons per X-ray pulse, we predict that the optical count rate can exceed 107 photons per pulse. Similar to other effects involving nonlinear interactions of X-rays and optical radiation, the effect we describe can be used for microscopic studies of chemical bonds and as a probe for light-matter interactions on the atomic scale. Since the X-ray damage threshold is much higher than the optical damage threshold, the efficiency of difference-frequency generation from two X-ray pulses is expected to be orders of magnitude higher than the efficiency of effects such as sum/difference-frequency mixing between X-rays and optical intense short-pulse sources.

X-ray second harmonic generation.

We report clear experimental evidence for second harmonic generation at hard x-ray wavelengths. Using a 1.7 Å pumping beam generated by a free electron laser, we observe second harmonic generation in diamond. The generated second harmonic is of order 10 times the background radiation, scales quadratically with pump pulse energy, and is generated over a narrow phase-matching condition. Of importance for future experiments, our results indicate that it is possible to observe nonlinear x-ray processes in crystals at pump intensities exceeding 1016 W/cm2.

X-ray parametric down-conversion in the Langevin regime.

We experimentally and theoretically study the coincidence count rate for down-converted x-ray photons. Because of photoionization, parametric down-conversion at x-ray wavelengths generally involves loss and the theoretical description requires a Langevin approach. By working in a transmission geometry (Laue) rather than in the Bragg geometry of previous experiments, we obtain an improvement in the signal-to-noise ratio of 12.5, and find agreement between experiment and theory.

X-ray and optical wave mixing.

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.

Polarization entangled photons at x-ray energies.

We show that polarization entangled photons at x-ray energies can be generated via spontaneous parametric down-conversion. Each of the four Bell states can be generated by choosing the angle of incidence and polarization of the pumping beam.

An iterative approach to plan combination in radiotherapy.

Radiation therapy concerns the delivery of a proper dose of radiation to a tumor volume without causing irreparable damage to surrounding healthy tissue and critical organs. The problem of plan combination in radiation therapy treatment planning (RTTP) proposed, formulated and studied here, addresses a situation when for a specific clinical case, a set of several treatment plans is proposed, but each one of them violates the prescribed dose in at least one significant region of the volume that has to be treated. We represent treatment plans as vectors in the Euclidean space, and define their equivalence, acceptability and realizability. A simple linear algebraic model for combining them is then used in order to derive, from the given set of approximate plans, a combined treatment plan, which will be both acceptable, and technically realizable. In the event that such a combined plan dose not exist, the alternatives for relaxing the treatment requirements can be systematically considered.

Capacity limitations in human information processing.

The nature of processing demands during a letter-match task was investigated in an extension of the Posner and Boies (1971) paradigm. In Experiment I, a visual probe was employed in addition to an auditory probe in two different experimental conditions. The shape of the auditory probe reaction time (RT) function was similar to that found by Posner and Boies. However, in contrast to their findings, RT was greatly increased shortly after presentation of the first letter for the visual probe function. It was concluded that perceptual as well as postperceptual limitations on processing capacity exist. A second experiment provided further support for this hypothesis.