Group velocity control is demonstrated for x-ray photons of 14.4 keV energy via a direct measurement of the temporal delay imposed on spectrally narrow x-ray pulses. Sub-luminal light propagation is achieved by inducing a steep positive linear dispersion in the optical response of 57 Fe Mössbauer nuclei embedded in a thin film planar x-ray cavity. The direct detection of the temporal pulse delay is enabled by generating frequency-tunable spectrally narrow x-ray pulses from broadband pulsed synchrotron radiation. Our theoretical model is in good agreement with the experimental data.Strong nonlinear interaction of light with matter is a key requirement for fundamental and applied quantum optical technologies alike. Since conventional materials typically exhibit weak nonlinearities, the ultimate quest for strong nonlinear interactions of individual quanta has led to the development of a number of methods to significantly enhance nonlinear light-matter interactions. Among the most prominent ones are coherently prepared media based on electromagnetically induced transparency, sub-luminal light and related effects [1,2], as well as cavity-enhanced light matter interactions [3].Recently, nuclear quantum optics featuring the interaction of x-ray light with Mössbauer nuclei in the few keV transition energy range has gained considerable momentum, both theoretically [4-9] and experimentally [10][11][12][13][14][15][16][17][18][19]. Interestingly, these experiments operate with less than one resonant x-ray photon per pulse on average due to restrictions in the available x-ray light sources. This raises the question, whether coherent or cavity-based enhancement techniques could be utilized to realize nonlinear light-matter interactions in nuclear quantum optics despite the low number of resonant photons.Here, we report a first step towards this goal, and demonstrate group velocity control of spectrally narrow x-ray pulses (SNXP). Sub-luminal light propagation is achieved by inducing a steep positive linear material dispersion, and verified by direct measurements of the temporal delay imposed on the SNXP. For this, we suitably manipulate the optical response of the ω 0 = 14.4 keV Mössbauer resonance (single nucleus linewidth γ = 4.7 neV) of a large ensemble of 57 Fe nuclei embedded in a thin film planar x-ray cavity. Our approach thereby combines coherent control, as well as cooperative and cavity enhancements of light-matter interaction in a single setup. To enable the direct detection of the temporal pulse delay, we further propose and implement a flexible scheme to generate frequency-tunable SNXP from broadband synchrotron radiation for applications in xray quantum optics. Our theoretical model is in good agreement with the experimental data.Sub-luminal light was first demonstrated in the visible frequency range [20][21][22], and by now has been implemented in a number of platforms [2], particularly also in cavity settings [23,24]. Manipulation of light propagation has also been reported in the x-ray regime. In Ref.[12], a...

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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.

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By embedding a thin layer of tantalum in an x-ray cavity, we observe a change in the spectral characteristics of an inner-shell transition of the metal. The interaction between the cavity mode vacuum and the L III-edge transition is enhanced, permitting the observation of the collective Lamb shift, superradiance, and a Fano-like cavity-resonance interference effect. This experiment demonstrates the feasibility of cavity quantum electrodynamics with electronic resonances in the x-ray range with applications to manipulating and probing the electronic structure of condensed matter with high-resolution x-ray spectroscopy in an x-ray cavity setting.

Coherent control of quantum dynamics is key to a multitude of fundamental studies and applications1. In the visible or longer-wavelength domains, near-resonant light fields have become the primary tool with which to control electron dynamics2. Recently, coherent control in the extreme-ultraviolet range was demonstrated3, with a few-attosecond temporal resolution of the phase control. At hard-X-ray energies (above 5–10 kiloelectronvolts), Mössbauer nuclei feature narrow nuclear resonances due to their recoilless absorption and emission of light, and spectroscopy of these resonances is widely used to study the magnetic, structural and dynamical properties of matter4,5. It has been shown that the power and scope of Mössbauer spectroscopy can be greatly improved using various control techniques6–16. However, coherent control of atomic nuclei using suitably shaped near-resonant X-ray fields remains an open challenge. Here we demonstrate such control, and use the tunable phase between two X-ray pulses to switch the nuclear exciton dynamics between coherent enhanced excitation and coherent enhanced emission. We present a method of shaping single pulses delivered by state-of-the-art X-ray facilities into tunable double pulses, and demonstrate a temporal stability of the phase control on the few-zeptosecond timescale. Our results unlock coherent optical control for nuclei, and pave the way for nuclear Ramsey spectroscopy17 and spin-echo-like techniques, which should not only advance nuclear quantum optics18, but also help to realize X-ray clocks and frequency standards19. In the long term, we envision time-resolved studies of nuclear out-of-equilibrium dynamics, which is a long-standing challenge in Mössbauer science20.

We report on the use of synthetic single-crystal diamonds for high purity x-ray polarimetry to improve the polarization purity of present-day x-ray polarimeters. The polarimeter setup consists of a polarizer and an analyzer, each based on two parallel diamond crystals used at a Bragg angle close to 45 •. The experiment was performed using one (400) Bragg reflection on each diamond crystal and synchrotron undulator radiation at an x-ray energy of 9838.75 eV. A polarization purity of 8.9×10 −10 was measured at the European Synchrotron Radiation Facility (ESRF), which is the best value reported for two-reflection polarizer/analyzer setups. This result is encouraging and a first step to improve the resolution of x-ray polarimeters further by using diamond crystal polarizers and analyzers with four or six consecutive reflections.

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