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X-ray Quantum Dynamics with Atoms, Ions and Nuclei

High-precision research is increasingly enriched by advanced light sources, pushing the boundaries of physical research to shorter and shorter wavelengths. However, also in its own right x-ray free electron lasers and synchrotron sources allow for novel fundamental research on correlated relativistic quantum dynamics in ions as well as on x-ray quantum optics with nuclei, and on control of nuclear forward scattering.

Highly charged ions in x-ray fields

In highly charged atomic ions, inner-shell electrons experience extremely high nuclear binding fields. The dynamics of electrons becomes relativistic. Also, the electronic probability density has a considerate overlap with the nuclear matter. These properties render these atomic systems an ideal tool for basic research in relativistic atomic structure theory, quantum electrodynamics at extreme fields, and in the study of nuclear effects. In many-electron ions, relativistic and nuclear contributions are intertwined with electron correlation. Because of this complex interplay, accurate large-scale theoretical calculations, performed by the group around Zoltán Harman, are necessary to decipher the physical phenomena from the increasingly accurate experimental spectra.

The knowledge of the structural and dynamical properties of highly charged ions is also necessary for the modeling and diagnostics of astrophysical and fusion plasmas. The spectra of inner-shell transitions are of great relevance for astrophysical line diagnostics of x-ray binaries and stars, aiming at determining physical parameters of the emitter medium such as element decomposition, density, temperature, and velocity. These transitions are predominantly in the x-ray range, therefore, their efficient radiative excitation has been rather challenging until the advent of modern x-ray sources such as free electron lasers and synchrotrons, providing high intensities in the appropriate wavelength range. We calculate transition energies and probabilities of excitation processes and fluorescence which are scrutinized in electron beam ion trap experiments at the Institute.

X-ray quantum optics

Recent advances in existing and upcoming light sources provide access to laser-like light in the x-ray and gamma-ray frequency domain, with a multitude of novel applications across all the natural sciences. Nevertheless, the implementation of advanced laser-coupled quantum systems in the x-ray domain remains a challenge due to basic experimental limitations. We develop methods to overcome these limitations, and to establish x-ray quantum optics. This on the one hand will be required to unleash the full potential of the new x-ray light sources, and on the other hand provides a new platform for quantum optics as a whole.

In the group of Jörg Evers, currently the emphasis is on atomic Mössbauer nuclei, which have proven successful in ground-breaking experiments on x-ray quantum optics. A particularly promising setup is x-ray cavity quantum electrodynamics with Mössbauer nuclei embedded in thin-film cavities probed by near-resonant x-ray light. Over the last years, we developed a sophisticated quantum optical framework for the description of this setting. It allows identifying and separating all physical processes contributing to the recorded signal, and encompasses nonlinear and quantum effects. Based on this model, we engineer advanced quantum optical setups, and we verified a number of predictions of this model experimentally in collaboration with experimental teams around Ralf Röhlsberger (DESY, Hamburg), Thomas Pfeifer at the Institute, and G. G. Paulus (University and Helmholtz Institute Jena) at the Dynamics Beamline P01 of the synchrotron source PETRA III (DESY) and the Nuclear Resonance Beamline (ID18) of the European Synchrotron Radiation Facility (ESRF, Grenoble).

However, x-ray cavities typically have spectrally overlapping cavity modes. It has been debated in the literature whether the standard quantum optical methods apply in this case. Indeed, we found significant deviations between the standard quantum optical models and the actual cavity properties, and these deviations not only question the theoretical understanding, but also hinder the design of future x-ray cavity setups. To overcome this issue, we recently developed an ab-initio method to derive few-mode models for quantum potential scattering problems. It rigorously connects quantum optical few-mode approaches to ab-initio scattering theory, and extends their applicability range to extreme conditions such as in x-ray cavities. Our first analysis shows that this new ab-initio approach indeed resolves the deviations previously found in the modeling of the x-ray cavities. Furthermore, for extreme parameter regimes as found in the x-ray cavities, the ab-initio approach predicts qualitative new features as compared to standard quantum optical approaches such as frequency-dependent couplings (see Fig. 5) and cross-mode decay terms, and we expect that these features will lead to new applications of x-ray cavities.

The group of Adriana Pálffy is investigating how strong radiation from x-ray Free Electron Lasers can be used to drive nuclear transitions of keV energy. The interaction of x-ray radiation with matter occurs predominantly via the atomic shell, resulting in a cold dense plasma being generated. In this environment, nuclear excitation may occur also via secondary channels, such as nuclear excitation by electron capture (see Fig. 6). For certain nuclear transitions, we could show that the secondary nuclear excitation in the plasma environment can exceed by orders of magnitude the direct photoexcitation that can be achieved by the x-ray Free Electron Laser. Using our combined atomic, nuclear and plasma physics expertise we are working on optimizing the nuclear excitation by controlling the plasma conditions by strong optical lasers. Controlling the nuclear state population with x-ray and optical lasers is appealing also for possible nuclear physics applications to store energy in nuclear isomers (see Fig. 6).

Correlated quantum dynamics and laser control

Mössbauer nuclei feature resonances with exceptionally narrow spectral line widths, which form the basis for a broad range of applications across the natural sciences. For x-ray quantum optics, the narrow line is favorable, because it translates into long lifetimes of the nuclear coherences. However, the narrow line width also accounts for a key challenge in nuclear quantum optics, namely, the lack of strong driving fields. The reason is that synchrotron and free-electron-laser x-ray sources deliver temporally short pulses with a broad spectrum, such that only a tiny fraction of the photons is resonant with the nuclei. To address this challenge, a group around Jörg Evers explores the possibility to simulate the effect of strong control fields using mechanical motion of a nuclear target, see Fig. 7. A short x-ray pulse impinging on a nuclear target may either pass without interaction, or interact with the nuclei. Because of the long lifetime, the interacting part of the x-ray pulse is delayed. By applying a suitable motion to the target immediately after the non-interacting part passed the target, an arbitrary time-dependent phase can be imprinted on the interacting part. While the overall phase of the x-rays varies randomly from pulse to pulse, the relative phase between the interacting and the non-interacting part can be controlled. As a first application, we demonstrated that the pulse shaping can be applied in such a way that the number of resonant x-ray photons in a given pulse can be significantly increased. Without mechanical motion, absorption reduces the number of resonant photons, because the relative phase is such that the two parts destructively interfere. Using a sudden displacement by half the x-ray wavelength, this destructive interference is turned into constructive interference, such that instead the number of resonant photons is increased. Energy is conserved, since this spectral gain on resonance is achieved by redistributing off-resonant photons onto the resonance. In the experiment with teams around Ralf Röhlsberger (DESY, Hamburg) and Thomas Pfeifer (MPIK) at the Nuclear Resonance Beamline (ID18) at ESRF, the nuclear sample was moved using a piezo film, and the sudden displacement was achieved within about 20 nanoseconds (1ns=10-9s) with a spatial precision better than one Angstrom (10-10 meter). As a result, we found an increase by more than a factor of 3, while our theoretical calculations predict a maximum possible enhancement by about one order of magnitude for the employed 57Fe nuclei. More generally, the dynamical control of the temporal phase enables one to tailor the frequency spectrum of the x-ray pulse. Sudden phase jumps lead to Fano resonances, which indicate the presence of different interfering quantum evolution pathways. This project therefore also continues a long-standing collaboration with the experimental group of Thomas Pfeifer at the Institute, in which we have established Fano resonances and in particular the interplay of its energy- and time domain interpretation as a powerful tool to investigate and also control quantum dynamics.

The shaping of the x-ray pulse spectrum using mechanical motion relies on a separation of an initial x-ray pulse into an interacting and a non-interacting part, and the motion enables one to dynamically control the relative phase between these two parts. The control possibility invites an interpretation as a tunable source of phase-coherent x-ray double-pulse sequences. This raises the question, if such double-pulses can be used to coherently control the dynamics of nuclei using suitably shaped x-ray fields. Recently, we demonstrated that this coherent x-ray-optical control indeed is possible. In the proof-of-principle experiment with teams around Ralf Röhlsberger (DESY, Hamburg) and Thomas Pfeifer (MPIK) at the Nuclear Resonance Beamline (ID18) at ESRF, we used the first part of the double-pulse sequence to excite an exciton within the nuclei, i.e., a single excitation coherently spread across many nuclei. The relative phase between the two parts of the double pulse then decides, how the second pulse continues the dynamics of the nuclear exciton. In particular, in the experiment, we demonstrated control over basic light-matter interactions between x-rays and nuclei, by switching between stimulated emission of the nuclear exciton, and further coherent excitation of the nuclei. These experimental results became possible using a powerful two-dimensional detection technique, which records the intensity of the x-ray light as function of time and energy. This multidimensional dataset contains rich interference patterns, which encode full holographic information of the complex-valued scattered x-ray field amplitude, allowing for the determination of the time-dependent complex dipole moment induced in the target nuclei. Our further analysis showed that the pulse shape control is exceptionally stable, opening perspectives such as multidimensional nuclear spectroscopy or nuclear pump-probe spectroscopy.

A key challenge in x-ray science is the characterization of spatial and temporal correlations on small scales. A promising method is time-domain interferometry (TDI), which promises access to correlations essentially background-free and over longer time scales than competing methods. In TDI, Mössbauer nuclei are used to split an incident x-ray pulse into two temporally separated parts (see Fig. 8). This double pulse probes the target system, which does not have to contain Mössbauer nuclei, at two different times. After the interaction, the two parts are overlapped in time, again using Mössbauer nuclei. The interference observed in the time-dependent intensity of the overlapped pulses then provides access to the correlations in the target. So far, TDI had only been analyzed for classical target systems and their classical correlations. However, quantum effects are expected to play a major role in strongly correlated and quantum materials, in and out of equilibrium. We therefore developed a TDI scheme that allows us to explore quantum dynamical correlations within the target, and to exclude classical models for the target dynamics. Quantum-TDI differs from the classical version by an additional phase control between the two interfering pathways, which can be realized by piezo-movements of the split unit. The quantum mechanical treatment shows that in TDI, a single photon is split into a time-bin entangled state, which subsequently provides information about the system at two different times, even though each realization of the experiment features only one interaction with the target. As a result, TDI allows for back-action free measurements of quantum mechanical correlation functions.