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Zusammenfassung Die resonante Anregung der⁴⁵Scandium‐Kernresonanz und die präzise Messung ihrer Energie eröffnen neue Möglichkeiten für Anwendungen in der Ultrapräzisions‐Röntgenspektroskopie bis hin zur Entwicklung einer Kernuhr. Damit kann zum Beispiel die Gravitationsrotverschiebung erstmals auf sehr kurzen Längenskalen überprüft werden. Darüber hinaus demonstriert dieses Experiment das große Potenzial von Self‐Seeding‐Röntgenlasern mit hoher Pulsrate als vielversprechende Plattform für die Spektroskopie von extrem schmalbandigen Kernresonanzen. Die nächsten Schritte in Richtung einer Kernuhr auf der Basis von⁴⁵Scandium erfordern eine weitere Erhöhung des spektralen Photonenflusses unter Verwendung verbesserter Röntgenlaserquellen bei 12,4 keV und die Entwicklung von Frequenzkämmen, die bis zu dieser Energie reichen. 

Abstract Resonant oscillators with stable frequencies and large quality factors help us to keep track of time with high precision. Examples range from quartz crystal oscillators in wristwatches to atomic oscillators in atomic clocks, which are, at present, our most precise time measurement devices¹. The search for more stable and convenient reference oscillators is continuing^2–6. Nuclear oscillators are better than atomic oscillators because of their naturally higher quality factors and higher resilience against external perturbations^7–9. One of the most promising cases is an ultra-narrow nuclear resonance transition in⁴⁵Sc between the ground state and the 12.4-keV isomeric state with a long lifetime of 0.47 s (ref. ¹⁰). The scientific potential of⁴⁵Sc was realized long ago, but applications require⁴⁵Sc resonant excitation, which in turn requires accelerator-driven, high-brightness X-ray sources¹¹that have become available only recently. Here we report on resonant X-ray excitation of the⁴⁵Sc isomeric state by irradiation of Sc-metal foil with 12.4-keV photon pulses from a state-of-the-art X-ray free-electron laser and subsequent detection of nuclear decay products. Simultaneously, the transition energy was determined as$${\mathrm{12,389.59}}_{+0.12\left({\rm{syst}}\right)}^{\pm 0.15\left({\rm{stat}}\right)}\,{\rm{eV}}$$ ${\mathrm{12,389.59}}_{+0.12\left(\mathrm{syst}\right)}^{\pm 0.15\left(\mathrm{stat}\right)}\mathrm{eV}$with an uncertainty that is two orders of magnitude smaller than the previously known values. These advancements enable the application of this isomer in extreme metrology, nuclear clock technology, ultra-high-precision spectroscopy and similar applications. 

Abstract Amplification of attosecond pulses produced via high harmonic generation is a formidable problem since none of the amplifiers can support the corresponding PHz bandwidth. Producing the well defined polarization state common for a set of harmonics required for formation of the circularly/elliptically polarized attosecond pulses (which are on demand for dynamical imaging and coherent control of the spin flip processes) is another big challenge. In this work we show how both problems can be tackled simultaneously on the basis of the same platform, namely, the plasma-based X-ray amplifier whose resonant transition frequency is modulated by an infrared field. 

Synopsis We suggest a technique to amplify a train of attosecond pulses, produced via high-harmonic generation of an infrared laser field, in active medium of a plasma-based X-ray laser driven by a replica of the same IR field as used to produce high harmonics forming a train of attosecond pulses. 

Abstract The induced transparency of opaque medium for resonant electromagnetic radiation is a powerful tool for manipulating the field-matter interaction. Various techniques to make different physical systems transparent for radiation from microwaves to x-rays were implemented. Most of them are based on the modification of the quantum-optical properties of the medium under the action of an external coherent electromagnetic field. Recently, an observation of acoustically induced transparency (AIT) of the⁵⁷Fe absorber for resonant 14.4-keV photons from the radioactive⁵⁷Co source was reported. About 150-fold suppression of the resonant absorption of photons due to collective acoustic oscillations of the nuclei was demonstrated. In this paper, we extend the AIT phenomenon to a novel phase-locked regime, when the transmitted photons are synchronized with the absorber vibration. We show that the advantages of synchrotron Mössbauer sources such as the deterministic periodic emission of radiation and controlled spectral-temporal characteristics of the emitted photons along with high-intensity photon flux in a tightly focused beam, make it possible to efficiently implement this regime, paving the way for the development of the acoustically controlled interface between hard x-ray photons and nuclear ensembles. 

Synopsis We suggest a technique to generate a train of attosecond pulses in “water window” range by hydrogen-like C⁵⁺plasma-based X-ray laser with two sequentical active plasma channels irradiated by two different optical laser fields with orthogonal polarizations. We show also the possibility to transform the radiation of a plasma-based X-ray laser dressed by an optical laser field into a train of attosecond pulses in a resonant absorber irradiated by the different optical field. 

Abstract We study the process of propagation of high harmonics of optical radiation in an active medium of a plasma-based X-ray laser, simultaneously irradiated by an intense optical field of fundamental frequency. It is shown that for moderate plasma dispersion of the active medium at the frequency of the modulating optical field, the energy and relative amplitudes of the harmonics at the output of the medium are determined by their phases at the entrance to the medium, as well as by the time-delay of the harmonics with respect to the modulating field. These dependences are due to interference of high-order harmonics with a set of multi-frequency fields generated by each of the harmonics in the process of coherent scattering in a modulated active medium. The possibilities of using these effects to increase the efficiency of harmonic amplification, to control the harmonic spectrum, and determine the relative phases at the entrance to the medium are discussed on the example of the active medium of hydrogen-like Li²⁺ions (with a 13.5 nm wavelength of an inverted transition). 

Optical quantum memories are key elements in modern quantum technologies to reliably store and retrieve quantum information. At present, they are conceptually limited to the optical wavelength regime. Recent advancements in x-ray quantum optics render an extension of optical quantum memory protocols to ultrashort wavelengths possible, thereby establishing quantum photonics at x-ray energies. Here, we introduce an x-ray quantum memory protocol that utilizes mechanically driven nuclear resonant⁵⁷Fe absorbers to form a comb structure in the nuclear absorption spectrum by using the Doppler effect. This room-temperature nuclear frequency comb enables us to control the waveform of x-ray photon wave packets to a high level of accuracy and fidelity using solely mechanical motions. This tunable, robust, and highly flexible system offers a versatile platform for a compact solid-state quantum memory at room temperature for hard x-rays.