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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.

 

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.

 

Abstract Recently, an observation of acoustically induced transparency (AIT) of a stainless-steel foil for resonant 14.4-keV photons from a radioactive 57 Co Mössbauer source due to collective uniform oscillations of atomic nuclei was reported [Phys Rev Lett 124,163602, 2020]. In this paper, we propose to use the steep resonant dispersion of the absorber within the AIT spectral window to dramatically reduce a propagation velocity of γ-ray and x-ray photons. In particular, we show that a significant fraction (more than 40%) of a 97-ns γ-ray single-photon wave packet from a 57 Co radioactive source can be slowed down up to 3 m/s and delayed by 144 ns in a 57 Fe-enriched stainless-steel foil at room temperature. We also show that a similarly significant slowing down up to 24 m/s and a delay by 42 ns can be achieved for more than 70% of the 100-ns 14.4-keV x-ray single-photon pulse from a synchrotron Mössbauer source available at European Synchrotron Radiation Facility (ESRF) and Spring-8 facility. The propagation velocity can be widely controlled by changing the absorber vibration frequency. Achieving the propagation velocity on the order of 1–50 m/s would set a record in the hard x-ray range, comparable to what was obtained in the optical range. 

A technique to transform the waveform of a 14.4 keV photon (time dependence of the photon detection probability or, equivalently, the intensity of the single-photon wave packet) into a regular sequence of short, nearly bandwidth-limited pulses with a controlled number of pulses is proposed. It is based on coherent forward scattering of single X-ray photons from a synchrotron Mössbauer source (SMS) in an optically thick, vibrating, recoilless 57Fe resonant absorber. The possibility of compressing the waveform of an SMS photon into a single short bell-shaped pulse is predicted. The experiment is proposed for compressing a 100 ns duration 14.4 keV single-photon wave packet produced by SMS at the European Synchrotron Radiation Facility (ESRF) into a single bell-shaped pulse of less than 20 ns duration and more than twice the peak intensity. Such single-photon coherent pulses are promising for applications in the fast-developing field of X-ray quantum optics, including possible implementation of quantum memory. 

In a recent work (Antonov et al., Physical Review Letters 123, 243903 (2019)), it was shown that it is possible to amplify a train of attosecond pulses, which are produced from the radiation of high harmonics of the infrared field of the fundamental frequency, in the active medium of a plasma-based X-ray laser modulated by a replica of the infrared field of the same frequency. In this paper, we show that much higher amplification can be achieved using the second harmonic of the fundamental frequency for modulating of a hydrogen-like active medium. The physical reason for such enhanced amplification is the possibility to use all (even and odd) sidebands induced in the gain spectrum in the case of the modulating field of the doubled fundamental frequency, while only one set of sidebands (either even or odd) could participate in amplification in the case of the modulating field of the fundamental frequency due to the fact that the spectral components of the high-harmonic field are separated by twice the fundamental frequency. Using the plasma of hydrogen-like C5+ ions with an inverted transition wavelength of 3.38 nm in the water window as an example, it is shown that the use of a modulating field at a doubled fundamental frequency makes it possible to increase the intensity of amplified attosecond pulses by an order of magnitude in comparison with the previously studied case of a fundamental frequency modulating field. 

Attosecond pulses formed by high order harmonics (HHs) of an infrared (IR) laser field is a powerful tool for studying and controlling ultrafast dynamics of electrons in atoms, molecules and solids at its intrinsic time-scale. However, in the X-ray range the energy of attosecond pulses is rather limited. Their amplification is an important but very challenging problem since none of the existing amplifiers can support the corresponding PHz bandwidth. In our previous work [1] we proposed a method for the attosecond pulse amplification in hydrogen-like active medium of a recombination plasma-based X-ray laser dressed by a replica of the fundamental frequency IR field used for the HH generation. Due to the IRfield-induced sub-laser-cycle Stark shift and splitting of the lasing energy levels the gain of the active medium is redistributed over the combination frequencies, separated from the resonance by even multiples of the frequency of the IR field. If the incident HHs forming an attosecond pulse train are tuned in resonance with the induced gain lines and the active plasma medium is strongly dispersive for the modulating IR field, then during the amplification the relative phases of harmonics and (under the optimal choice of the IR field strength) the shape of the amplified pulses will be preserved. In the present work we show the possibility of boosting the efficiency of HH amplification by modulating the active medium of an X-ray laser with the second harmonic of the fundamental frequency IR field. We show that under the action of a laser field (with arbitrary frequency) the gain redistribution occurs not only over the even combination frequencies discussed in [1], but also over the odd frequencies separated from the resonance by odd multiples of the laser frequency. Besides, nearly half of the medium gain is contained in the even induced gain lines, and nearly half in the odd. If the modulating field is the second harmonic of the IR field, used for the generation the HHs and attosecond pulses, then the seeding HHs can be tuned in resonance with both even and odd gain lines simultaneously, which will make the overall gain much higher as compared to the previously considered case of the fundamental frequency modulating field (when only the even gain lines play the role). By the example of the C5+ X-ray laser with 3.38 nm wavelength of the inverted transition we show the possibility of increasing the efficiency of 430 as pulse amplification by 8.5 times when the active medium is modulated with the second harmonic of the fundamental frequency IR field with wavelength 2.1 µm.