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arXiv:2406.01962 · Physical Review A

Theory of resonant x-ray scattering with ultrafast intense pulses

Akilesh Venkatesh, Phay J. Ho

Published Feb 5, 2025• 3 citations
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Abstract

We present a time-dependent Schr\"odinger equation approach within a nonrelativistic quantum electrodynamics framework to investigate resonant x-ray scattering driven by intense x-ray pulses. This method enables us to explore how coherent x-ray electron dynamics influence scattering signals from ${\mathrm{Ne}}^{+}$. We account for both resonance fluorescence and elastic scattering channels, while also considering competing photoionization and inner-shell decay processes. By computing the angular distribution and energy spectrum of scattered photons, we uncover interference effects between elastic scattering and resonance fluorescence pathways. Notably, this interference results in a small asymmetry in the energy spectrum. We discuss the experimental potential for detecting signatures of interference. Our findings demonstrate that the x-ray Rabi dynamics can be used to control scattering responses and provide insights into interference mechanisms and scattering efficiency in high-intensity x-ray regimes.

DOI
10.1103/physreva.111.023101

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We present a time-dependent Schr"odinger equation approach within a nonrelativistic quantum electrodynamics framework to investigate resonant x-ray scattering driven by intense x-ray pulses. This method enables us to explore how coherent x-ray electron dynamics influence scattering signals from Ne+{\mathrm{Ne}}^{+}Ne+. We account for both resonance fluorescence and elastic scattering channels, while also considering competing photoionization and inner-shell decay processes. By computing the angular distribution and energy spectrum of scattered photons, we uncover interference effects between elastic scattering and resonance fluorescence pathways. Notably, this interference results in a small asymmetry in the energy spectrum. We discuss the experimental potential for detecting signatures of interference. Our findings demonstrate that the x-ray Rabi dynamics can be used to control scattering responses and provide insights into interference mechanisms and scattering efficiency in high-intensity x-ray regimes.
The spectrum of resonance fluorescence is calculated for a two-level system excited by an intense, ultrashort x-ray pulse made available, for instance, by free-electron lasers such as the Linac Coherent Light Source. We allow for inner-shell hole decay widths and destruction of the system by further photoionization. This two-level description is employed to model neon cations strongly driven by x rays tuned to the $1s2{p}^{\ensuremath{-}1}\ensuremath{\rightarrow}1{s}^{\ensuremath{-}1}2p$ transition at 848eV848\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{eV}848eV; the x rays induce Rabi oscillations which are so fast that they compete with Ne 1s1s1s-hole decay. We predict resonance fluorescence spectra for two different scenarios: first, chaotic pulses based on the self-amplified spontaneous emission principle, like those presently generated at x-ray free-electron-laser facilities and, second, Gaussian pulses which will become available in the foreseeable future with self-seeding techniques. As an example of the exciting opportunities derived from the use of seeding methods, we predict, in spite of the above obstacles, the possibility to distinguish at x-ray frequencies a clear signature of Rabi flopping in the spectrum of resonance fluorescence.
Both coherent pumping and energy relaxation play important roles in understanding physical processes of ultra-intense coherent light-matter interactions. Here, using a large-scale quantum master equation approach, we describe dynamical processes of practical open quantum systems driven by both coherent and stochastic interactions. As examples, two typical cases of light-matter interactions are studied. First, we investigate coherent dynamics of inner-shell electrons of a neon gas irradiated by a high-intensity X-ray laser along with vast number of decaying channels. In these single-photon dominated processes, we find that, due to coherence-induced Rabi oscillations and power broadening effects, the photon absorptions of a neon gas can be suppressed resulting in differences in ionization processes and final ion-stage distributions. Second, we take helium as an example of multiphoton and multichannel interference dominated electron dynamics, by investigating the transient absorption of an isolated attosecond pulse in the presence of a femtosecond infrared laser pulse.
We develop a large scale quantum master equation approach to describe dynamical processes of practical open quantum systems driven by both coherent and stochastic interactions by including more than one thousand true states of the systems, motivated by the development of highly bright and fully coherent lasers in the X-ray wavelength regime. The method combines the processes of coherent dynamics induced by the X-ray laser and incoherent relaxations due to spontaneous emissions, Auger decays, and electronic collisions. As examples, theoretical investigation of {\it real} coherent dynamics of inner-shell electrons of a neon gas, irradiated by a high-intensity X-ray laser with a full temporal coherence, is carried out with the approach. In contrast to the rate equation treatment, we find that coherence can suppress the multiphoton absorptions of a neon gas in the ultra-intense X-ray pulse, due to coherence-induced Rabi oscillations and power broadening effects. We study the influence of coherence on ionization processes of neon, and directly prove that sequential single-photon processes for both outer- and inner-shell electrons dominate the ionizations for the recently typical experiments with a laser intensity of ≈1018\approx10^{18}≈1018 W/cm2{\rm W/cm^2}W/cm2. We discuss possible experimental implementations such as signatures for coherent evolution of inner-shell electrons via resonance fluorescence processes. The approach can also be applied to many different practical open quantum systems in atomic, quantum optical, and cold matter systems, which are treated qualitatively by a few-level master equation model before.
The direct and optical control of x-ray transitions is studied theoretically by investigating the spectra of resonance fluorescence and absorption. The work is motivated by the rapid advances in x-ray science, enabling the application of quantum-control schemes at short wavelengths. In a two-level system we study Rabi oscillations of atomic inner-shell electrons, induced by intense x-ray pulses and competing with Auger decay, and their signature in the spectrum of resonance fluorescence. Subsequently, optical manipulation of x-ray transitions is examined, by employing an optical frequency comb coupling nearby excited levels to control their spontaneous decay. First, narrow-bandwidth x rays are adopted, giving rise to the periodic shaping of the atomic dynamic variables and the imprinting of a comb onto the x-ray resonance fluorescence spectrum. A more realistic model for an immediate experimental implementation is then provided, by developing a scheme to imprint a comb onto the absorption spectrum of an ultrashort x-ray pulse. An experimental realization of the predicted comb structures is anticipated to transfer the accuracy of optical frequency combs into the x-ray regime
Improving our understanding of electron dynamics is essential for advancing energy transfer, optoelectronics, light harvesting systems and quantum computing. Recent developments in attosecond x-ray sources provide the fundamental possibility of observing these dynamics with atomic-scale resolution. However, connecting a time-resolved signal to dynamics is challenging due to the broad bandwidth of an attosecond probe pulse. This makes exploring the capabilities of different attosecond imaging techniques crucial. Here, we propose attosecond momentum-resolved resonant inelastic x-ray scattering as a prominent technique for tracking ultrafast dynamics. We demonstrate that the scattering signal contains an information about the instantaneous distribution of charge density across the scattering atoms. To illustrate this, we consider scattering from an ααα-sexithiophene molecule, in which coupled electron-hole dynamics are excited.
This work aims at development of new dynamical methods to control a resonant light-matter interaction as well as at their application for producing new sources of coherent intense sub-fs radiation in x-ray range. The dynamical control is based on modulation in time and in space of the parameters of the atomic transition (coupled to the resonant high-frequency field) by means of sufficiently strong off-resonant low-frequency control field. In particular, it may result in efficient transfer of quasi-monochromatic VUV or XUV radiation into ultrashort pulses via its resonant interaction with atomic hydrogen gas or plasma of hydrogen-like ions respectively by means of two different techniques: time and space dependent linear Stark effect or interruption of resonant interaction by the tunneling ionization, as shown in previous works of our group. \n\nIn this thesis, I further develop these ideas and demonstrate their important potential applications. First of all, both techniques are extended to arbitrary (non-hydrogen-like) atomic medium. Furthermore, advanced analytical and numerical solutions describing a process of pulses formation are found and shown to be in excellent agreement with each other. A deep physical analogy between the processes of coherent forward scattering of γ-ray radiation in the vibrated quasi-resonant nuclear absorber and the XUV field propagation in the quasi-resonant atomic medium in the presence of the moderately strong IR field is established. \n\nFinally, the application of the developed techniques for production of intense coherent attosecond sources of soft X-ray radiation, including so-called “water window” range (2.2-4.3nm) (especially promising for dynamical imaging of the proteins in a living cell) is proposed. Two different paths towards production of intense coherent attosecond pulses in a soft X-ray range are suggested: (i) via efficient transformation of the picosecond radiation of the high energy pulses of the existing x-ray plasma lasers into the trains of attosecond pulses in the resonant passive plasma, and (ii) via amplification of the low energy pulses of the existing high harmonic sources in the resonant active plasma of x-ray lasers.