The validity of an experiment testing the influence of acceleration on time dilation using a rotating Mössbauer absorber and a Synchrotron Mössbauer Source.

Three experiments are reviewed, performed (in 2014-2016) at ID18 of ESRF to measure the influence of acceleration on time dilation by measuring the relative shift between the absorption lines of two states of the same rotating absorber with accelerations anti-parallel and parallel to the incident beam. Statistically significant data for rotation frequencies up to 510 Hz in both directions of rotation were collected. For each run with high rotation, a stable statistically significant `vibration-free' relative shift between the absorption lines of the two states was measured. This may indicate the influence of acceleration on time dilation. However, the measured relative shift was also affected by the use of a slit necessary to focus the beam to the axis of rotation to a focal spot of sub-micrometre size. The introduction of the slit broke the symmetry in the absorption lines due to the nuclear lighthouse effect and affected the measured relative shift, preventing to claim conclusively the influence of acceleration on time dilation. Assuming that this loss of symmetry is of first order, the zero value of the relative shift, corrected for this loss, falls always within the experimental error limits, as predicted by Einstein's clock hypothesis. The requirements and an indispensable plan for a conclusive experiment, once the improved technology becomes available, is presented. This will be useful to future experimentalists wishing to pursue this experiment or a related rotor experiment involving a Mössbauer absorber and a synchrotron Mössbauer source.

Spin waves and spin-state transitions in a ruthenate high-temperature antiferromagnet.

Ruthenium compounds serve as a platform for fundamental concepts such as spin-triplet superconductivity1, Kitaev spin liquids2-5 and solid-state analogues of the Higgs mode in particle physics6,7. However, basic questions about the electronic structure of ruthenates remain unanswered, because several key parameters (including Hund's coupling, spin-orbit coupling and exchange interactions) are comparable in magnitude and their interplay is poorly understood, partly due to difficulties in synthesizing large single crystals for spectroscopic experiments. Here we introduce a resonant inelastic X-ray scattering (RIXS)8,9 technique capable of probing collective modes in microcrystals of 4d electron materials. We observe spin waves and spin-state transitions in the honeycomb antiferromagnet SrRu2O6 (ref. 10) and use the extracted exchange interactions and measured magnon gap to explain its high Néel temperature11-16. We expect that the RIXS method presented here will enable momentum-resolved spectroscopy of a large class of 4d transition-metal compounds.

Spectral narrowing of x-ray pulses for precision spectroscopy with nuclear resonances.

Spectroscopy of nuclear resonances offers a wide range of applications due to the remarkable energy resolution afforded by their narrow linewidths. However, progress toward higher resolution is inhibited at modern x-ray sources because they deliver only a tiny fraction of the photons on resonance, with the remainder contributing to an off-resonant background. We devised an experimental setup that uses the fast mechanical motion of a resonant target to manipulate the spectrum of a given x-ray pulse and to redistribute off-resonant spectral intensity onto the resonance. As a consequence, the resonant pulse brilliance is increased while the off-resonant background is reduced. Because our method is compatible with existing and upcoming pulsed x-ray sources, we anticipate that this approach will find applications that require ultranarrow x-ray resonances.

Advances in testing the effect of acceleration on time dilation using a synchrotron Mössbauer source.

New results, additional techniques and know-how acquired, developed and employed in a recent HC-1898 experiment at the Nuclear Resonance Beamline ID18 of ESRF are presented, in the quest to explore the acceleration effect on time dilation. Using the specially modified Synchrotron Mössbauer Source and KB-optics together with a rotating single-line semicircular Mössbauer absorber on the rim of a specially designed rotating disk, the aim was to measure the relative spectral shift between the spectra of two states when the acceleration of the absorber is anti-parallel and parallel to the source. A control system was used for the first time and a method to quantify the effects of non-random vibrations on the spectral shift was developed. For several runs where the effect of these vibrations was negligible, a stable statistically significant non-zero relative shift was observed. This suggests the influence of acceleration on time.

Interferometric phase detection at x-ray energies via Fano resonance control.

Modern x-ray light sources promise access to structure and dynamics of matter in largely unexplored spectral regions. However, the desired information is encoded in the light intensity and phase, whereas detectors register only the intensity. This phase problem is ubiquitous in crystallography and imaging and impedes the exploration of quantum effects at x-ray energies. Here, we demonstrate phase-sensitive measurements characterizing the quantum state of a nuclear two-level system at hard x-ray energies. The nuclei are initially prepared in a superposition state. Subsequently, the relative phase of this superposition is interferometrically reconstructed from the emitted x rays. Our results form a first step towards x-ray quantum state tomography and provide new avenues for structure determination and precision metrology via x-ray Fano interference.

Synchrotron radiation Mössbauer spectra of a rotating absorber with implications for testing velocity and acceleration time dilation.

Many Mössbauer spectroscopy (MS) experiments have used a rotating absorber in order to measure the second-order transverse Doppler (TD) shift, and to test the validity of the Einstein time dilation theory. From these experiments, one may also test the clock hypothesis (CH) and the time dilation caused by acceleration. In such experiments the absorption curves must be obtained, since it cannot be assumed that there is no broadening of the curve during the rotation. For technical reasons, it is very complicated to keep the balance of a fast rotating disk if there are moving parts on it. Thus, the Mössbauer source on a transducer should be outside the disk. Friedman and Nowik have already predicted that the X-ray beam finite size dramatically affects the MS absorption line and causes its broadening. We provide here explicit formulas to evaluate this broadening for a synchrotron Mössbauer source (SMS) beam. The broadening is linearly proportional to the rotation frequency and to the SMS beam width at the rotation axis. In addition, it is shown that the TD shift and the MS line broadening are affected by an additional factor assigned as the alignment shift which is proportional to the frequency of rotation and to the distance between the X-ray beam center and the rotation axis. This new shift helps to align the disk's axis of rotation to the X-ray beam's center. To minimize the broadening, one must focus the X-ray on the axis of the rotating disk and/or to add a slit positioned at the center, to block the rays distant from the rotation axis of the disk. Our experiment, using the (57)Fe SMS, currently available at the Nuclear Resonance beamline (ID18) at the ESRF, with a rotating stainless steel foil, confirmed our predictions. With a slit installed at the rotation axis (reducing the effective beam width from 15.6 µm to 5.4 µm), one can measure a statistically meaningful absorption spectrum up to 300 Hz, while, without a slit, such spectra could be obtained up to 100 Hz only. Thus, both the broadening and the alignment shift are very significant and must be taken into consideration in any rotating absorber experiment. Here a method is offered to measure accurately the TD shift and to test the CH.

Intensity interferometry of single x-ray pulses from a synchrotron storage ring.

We report on measurements of second-order intensity correlations at the high-brilliance storage ring PETRA III using a prototype of the newly developed adaptive gain integrating pixel detector. The detector records individual synchrotron radiation pulses with an x-ray photon energy of 14.4 keV and repetition rate of about 5 MHz. The second-order intensity correlation function is measured simultaneously at different spatial separations, which allows us to determine the transverse coherence length at these x-ray energies. The measured values are in a good agreement with theoretical simulations based on the Gaussian Schell model.

X-ray resonant photoexcitation: linewidths and energies of Kα transitions in highly charged Fe ions.

Photoabsorption by and fluorescence of the Kα transitions in highly charged iron ions are essential mechanisms for x-ray radiation transfer in astrophysical environments. We study photoabsorption due to the main Kα transitions in highly charged iron ions from heliumlike to fluorinelike (Fe24+ to Fe17+) using monochromatic x rays around 6.6 keV at the PETRA III synchrotron photon source. Natural linewidths were determined with hitherto unattained accuracy. The observed transitions are of particular interest for the understanding of photoexcited plasmas found in x-ray binary stars and active galactic nuclei.

Milli-electronvolt monochromatization of hard X-rays with a sapphire backscattering monochromator.

A sapphire backscattering monochromator with 1.1 (1) meV bandwidth for hard X-rays (20-40 keV) is reported. The optical quality of several sapphire crystals has been studied and the best crystal was chosen to work as the monochromator. The small energy bandwidth has been obtained by decreasing the crystal volume impinged upon by the beam and by choosing the crystal part with the best quality. The monochromator was tested at the energies of the nuclear resonances of (121)Sb at 37.13 keV, (125)Te at 35.49 keV, (119)Sn at 23.88 keV, (149)Sm at 22.50 keV and (151)Eu at 21.54 keV. For each energy, specific reflections with sapphire temperatures in the 150-300 K region were chosen. Applications to nuclear inelastic scattering with these isotopes are demonstrated.

X-ray interferometry with microelectronvolt resolution.

We demonstrate an interferometer for hard x rays with two back-reflecting sapphire crystal mirrors--a prototype x-ray Fabry-Pérot interferometer. A finesse of 15 and 0.76 mu eV broad Fabry-Pérot transmission resonances are measured by the time response of the interferometer. Interference patterns are observed directly in spectral dependences of reflectivity.

Anomalous isotopic effect on the lattice parameter of silicon.

The difference Delta(a)=a(30)-a(28) of the lattice parameter of 30Si and 28Si crystals is measured over a temperature range from 4.7 to 700 K. In disagreement with existing knowledge, the strongest isotopic effect is not detected at the lowest achieved temperature T=4.7 K. An anomalous behavior is observed: The relative difference |Delta(a)/a| attains its maximum value of 56.8(5) ppm at T=75(10) K. The anomalous behavior is attributed to the influence of phonon modes with negative Grüneisen parameters. At T=700 K the effect still amounts to 30% of the maximal value. The experimental data are consistent with an approach based on the density-functional perturbation theory.

gamma-Ray wavelength standard for atomic scales.

The wavelength of the 57Fe Mössbauer radiation is measured with a relative uncertainty of 0.19 ppm by using almost exact Bragg backscattering from a reference silicon crystal. Its value is determined as lambda(M) = 0.860 254 74(16)x10(-10) m. The corresponding Mössbauer photon energy is E(M) = 14 412.497(3) eV. The wavelength of the 57Fe Mössbauer radiation is easily reproducible with an accuracy of at least 10(-11)lambda(M) and could be used as a length standard of atomic dimensions.