Coherent X-ray-optical control of nuclear excitons.

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.

Time-Resolved sub-Ångström Metrology by Temporal Phase Interferometry near X-Ray Resonances of Nuclei.

We introduce an analytical phase-reconstruction principle that retrieves atomic scale motion via time-domain interferometry. The approach is based on a resonant interaction with high-frequency light and does not require temporal resolution on the time scale of the resonance period. It is thus applicable to hard x rays and γ rays for measurements of extremely small spatial displacements or relative-frequency changes. Here, it is applied to retrieve the temporal phase of a 14.4 keV emission line of an ^{57}Fe sample, which corresponds to a spatial translation of this sample. The small wavelength of this transition (λ=0.86 Å) allows for determining the motion of the emitter on sub-Ångström length and nanosecond timescales.

Compact hard x-ray split-delay system based on variable-gap channel-cut crystals.

We present the concept and a prototypical implementation of a compact x-ray split-delay system that is capable of performing continuous on-the-fly delay scans over a range of ∼10 ps with sub-100 nanoradian pointing stability. The system consists of four channel-cut silicon crystals, two of which have gradually varying gap sizes from intentional 5 deg asymmetric cuts. The delay adjustment is realized by linear motions of these two monolithic varying-gap channel cuts, where the x-ray beam experiences pairs of anti-parallel reflections, and thus becomes less sensitive in output beam pointing to motion imperfections of the translation stages. The beam splitting is accomplished by polished crystal edges. A high degree of mutual coherence between the two branches at the focus is observed by analyzing small-angle coherent x-ray scattering patterns. We envision a wide range of applications including single-shot x-ray pulse temporal diagnostics, studies of high-intensity x-ray-matter interactions, as well as measurement of dynamics in disordered material systems using split-pulse x-ray photon correlation spectroscopy.

Spectral Control of an X-Ray L-Edge Transition via a Thin-Film Cavity.

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.

Tunable Subluminal Propagation of Narrow-band X-Ray Pulses.

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. Subluminal light propagation is achieved by inducing a steep positive linear dispersion in the optical response of 57Fe 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.