# Approaching the Attosecond Frontier of Dynamics in Matter with the Concept of X-ray Chronoscopy
## 4 Summary  
Herein, an innovative methodology, called X-ray chronoscopy, was proposed to access the attosecond frontier using the current XFEL pulses. The method is based on measuring the change of an X-ray pulse temporal profile induced by interaction with a medium. The concept of X-ray chronoscopy uses non-invasive terahertz streaking methodology to characterize the X-ray pulse time distribution with sub-femtosecond resolution [17; 18]. The proposed approach requires two terahertz streaking camera setups arranged in the camera-sample-camera sequence to measure time distribution of the X-ray pulses incident on and transmitted through the sample. Through the analysis of the pulse temporal profiles measured before and after the sample, one can determine the evolution of the atomic-state populations and shell occupancies over the course of the pulse penetration through the medium. Note that many recent studies on nonlinear interactions report on the complexity of the measured data [27; 33; 51]. The reason is that often the nonlinear signal overlaps with the one resulting from linear X-ray-matter interaction, which in many cases, makes data analysis and interpretation unattainable. The proposed X-ray chronoscopy method, in its principle of operation, will not have this limitation. Any linear interaction of X-rays with matter will only be reflected as a constant component (i.e., absorption coefficient at a given energy) in the ratio of temporal X-ray beam profiles measured before and after the sample. The concept of time-dependent measurements was investigated with a simple two-level model of saturable absorption in an elemental iron target for a series of intensities and the excited state lifetimes. The analysis showed that the saturable absorption leads to an increased transparency of the medium over the course of pulse propagation through  
Figure 4: The influence of saturable absorption on linear attenuation coefficient (**a**) and transmission (**b**). (**b**) contains additional data taken from Ref. [38] measured and calculated for incidence X-ray pulse length of 7 fs as well as another dataset obtained with the XATOM code [50]. the target, and the saturation intensity depends on the material characteristics, such as the excited state lifetime, which agrees with the previously published data [38]. Finally, the saturable absorption leads to deformation of the X-ray pulse time distribution. The relative uncertainty, defined as the standard deviation of transmission at the pulse rear divided by the transmission jump (see Figure 3a), at the intensity of 1.9 \(\times\) 10\({}^{18}\) cm\({}^{2}\), is expected to be around 6% for 50 incident SASE pulses. Based on the known XFEL performances and published THz streaking data, one can thus estimate that the X-ray chronoscopy experiment should be accomplished with good quality within a few hours by means of the proposed X-ray chronoscopy setup. Worth noting is the ongoing development of time diagnostics methods at XFELs, providing higher precision in temporal characterization of X-ray pulses and bringing X-ray chronoscopy closer to realization at XFELs. For instance, a pulse profile determination using a velocity map imaging (VMI) spectrometer has been demonstrated for attosecond soft X-ray pulses [10]. The fast, robust and simple derivation of pulse duration based on the center-of-energy shifts in the THz-streaked ionized electron spectra is also promising [21]. Precise pulse duration measurement before and after the target sample could be a prelude to realization of X-ray chronoscopy at XFELs. Conceptualization, [PERSON], [PERSON] ([PERSON]), [PERSON] and P.J. ; methodology, [PERSON] and [PERSON]. ([PERSON]); software, [PERSON], [PERSON] ([PERSON]), M.D., M.L. and J.S. ([PERSON]); validation, [PERSON], [PERSON] ([PERSON]), [PERSON] and P.J. ; formal analysis, [PERSON] and [PERSON]. ([PERSON]). investigation, [PERSON] and [PERSON]. ([PERSON]); resources, all authors; data curation, [PERSON] and [PERSON].