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Nature / Physical science 590(7846), 401 - 404 (2021). doi:10.1038/s41586-021-03276-x, Coherent control of quantum dynamics is key to a multitude of fundamental studies and applications. In the visible or longer-wavelength domains, near-resonant light fields have become the primary tool with which to control electron dynamics. Recently, coherent control in the extreme-ultraviolet range was demonstrated, with a few-attosecond temporal resolution of the phase control. At hard-X-ray energies (above 5–10 kiloelectronvolts), Mössbauer nuclei feature narrow nuclear resonances due to their recoilless absorption and emission of light, and spectroscopy of these resonances is widely used to study the magnetic, structural and dynamical properties of matter. It has been shown that the power and scope of Mössbauer spectroscopy can be greatly improved using various control techniques. However, coherent control of atomic nuclei using suitably shaped near-resonant X-ray fields remains an open challenge. Here we demonstrate such control, and use the tunable phase between two X-ray pulses to switch the nuclear exciton dynamics between coherent enhanced excitation and coherent enhanced emission. We present a method of shaping single pulses delivered by state-of-the-art X-ray facilities into tunable double pulses, and demonstrate a temporal stability of the phase control on the few-zeptosecond timescale. Our results unlock coherent optical control for nuclei, and pave the way for nuclear Ramsey spectroscopy and spin-echo-like techniques, which should not only advance nuclear quantum optics, but also help to realize X-ray clocks and frequency standards. In the long term, we envision time-resolved studies of nuclear out-of-equilibrium dynamics, which is a long-standing challenge in Mössbauer science., Published by Macmillan28177, London

We develop two ab initio quantum approaches to thin-film x-ray cavity quantum electrodynamics with spectrally narrow x-ray resonances, such as those provided by M\"ossbauer nuclei. The first method is based on a few-mode description of the cavity, and promotes and extends existing phenomenological few-mode models to an ab initio theory. The second approach uses analytically-known Green's functions to model the system. The two approaches not only enable one to ab initio derive the effective few-level scheme representing the cavity and the nuclei in the low-excitation regime, but also provide a direct avenue for studies at higher excitation, involving non-linear or quantum phenomena. The ab initio character of our approaches further enables direct optimizations of the cavity structure and thus of the photonic environment of the nuclei, to tailor the effective quantum optical level scheme towards particular applications. To illustrate the power of the ab initio approaches, we extend the established quantum optical modeling to resonant cavity layers of arbitrary thickness, which is essential to achieve quantitative agreement for cavities used in recent experiments. Further, we consider multi-layer cavities featuring electromagnetically induced transparency, derive their quantum optical few-level systems ab initio, and identify the origin of discrepancies in the modeling found previously using phenomenological approaches as arising from cavity field gradients across the resonant layers., Comment: 41 pages, 20 figures, added clarifications and minor corrections

Physical review letters 123(15), 153902 (2019). doi:10.1103/PhysRevLett.123.153902, We introduce an analytical phase-reconstruction principle that retrieves atomic scale motion via timedomaininterferometry. The approach is based on a resonant interaction with high-frequency light and doesnot require temporal resolution on the time scale of the resonance period. It is thus applicable to hard x raysand γ rays for measurements of extremely small spatial displacements or relative-frequency changes. Here,it is applied to retrieve the temporal phase of a 14.4 keVemission line of an 57Fe sample, which correspondsto a spatial translation of this sample. The small wavelength of this transition (λ ¼ 0.86 Å) allows fordetermining the motion of the emitter on sub-Ångström length and nanosecond timescales., Published by APS, College Park, Md.

Science 357(6349), 375 - 378(2017). doi:10.1126/science.aan3512, Spectroscopy of nuclear resonances offers a wide range of applications due to the remarkable energy resolution afforded by their narrow linewidths. However, progress toward higher resolution is inhibited at modern x-ray sources because they deliver only a tiny fraction of the photons on resonance, with the remainder contributing to an off-resonant background. We devised an experimental setup that uses the fast mechanical motion of a resonant target to manipulate the spectrum of a given x-ray pulse and to redistribute off-resonant spectral intensity onto the resonance. As a consequence, the resonant pulse brilliance is increased while the off-resonant background is reduced. Because our method is compatible with existing and upcoming pulsed x-ray sources, we anticipate that this approach will find applications that require ultranarrow x-ray resonances., Published by AAAS, Washington, DC [u.a.]

Die Spektroskopie schmaler Resonanzen ist ein Schlusselbaustein vieler moderner Anwendungen. Pulse moderner Rontgenlichtquellen sind jedoch spektral viel breiter als die zu untersuchenden Resonanzen, so dass nur ein kleiner Teil des Lichts wechselwirkt und zum Signal beitragt. Kurzlich ist es unserem Team gelungen, solche Pulse so zu manipulieren, dass zuvor ungenutzte Photonen in Resonanz geschoben werden. Die „gescharften“ Rontgenpulse eroffnen eine Vielzahl von Anwendungen.

Modern x-ray light sources promise access to structure and dynamics of matter in largely unexplored spectral regions. However, the desired information is encoded in the light intensity and phase, whereas detectors register only the intensity. This phase problem is ubiquitous in crystallography and imaging, and impedes the exploration of quantum effects at x-ray energies. Here, we demonstrate phase-sensitive measurements characterizing the quantum state of a nuclear two-level system at hard x-ray energies. The nuclei are initially prepared in a superposition state. Subsequently, the relative phase of this superposition is interferometrically reconstructed from the emitted x-rays. Our results form a first step towards x-ray quantum state tomography, and provide new avenues for structure determination and precision metrology via x-ray Fano interference., 5 pages, 3 figures, plus supplementary information

The setting of Moessbauer nuclei embedded in thin-film cavities has facilitated an aspiring platform for x-ray quantum optics as shown in several recent experiments. Here, we generalize the theoretical model of this platform that we developed earlier [Phys. Rev. A 88, 043828 (2013)]. The theory description is extended to cover multiple nuclear ensembles and multiple modes in the cavity. While the extensions separately do not lead to qualitatively new features, their combination gives rise to cooperative effects between the different nuclear ensembles and distinct spectral signatures in the observables. A related experiment by Roehlsberger et al. [Nature 482, 199 (2012)] is successfully modeled, the scalings derived with semiclassical methods are reproduced, and a microscopic understanding of the setting is obtained with our quantum mechanical description., 18 pages, 6 figures

Group velocity control is demonstrated for x-ray photons of 14.4 keV energy via a direct measurement of the temporal delay imposed on spectrally narrow x-ray pulses. Sub-luminal light propagation is achieved by inducing a steep positive linear dispersion in the optical response of ${}^{57}$Fe M\"ossbauer nuclei embedded in a thin film planar x-ray cavity. The direct detection of the temporal pulse delay is enabled by generating frequency-tunable spectrally narrow x-ray pulses from broadband pulsed synchrotron radiation. Our theoretical model is in good agreement with the experimental data., Comment: 8 pages, 4 figures

A promising platform for the emerging field of x-ray quantum optics are M\"ossbauer nuclei embedded in thin film cavities probed by near-resonant x-ray light, as used in a number of recent experiments. Here, we develop a quantum optical framework for the description of experimentally relevant settings involving nuclei embedded in x-ray waveguides. We apply our formalism to two settings of current experimental interest based on the archetype M\"ossbauer isotope 57Fe. For present experimental conditions, we derive compact analytical expressions and show that the alignment of medium magnetization as well as incident and detection polarization enable the engineering advanced quantum optical level schemes. The model encompasses non-linear and quantum effects which could become accessible in future experiments., Comment: 13 pages, 6 figures

The control of light-matter interaction at the quantum level usually requires coherent laser fields. But already an exchange of virtual photons with the electromagnetic vacuum field alone can lead to quantum coherences, which subsequently suppress spontaneous emission. We demonstrate such spontaneously generated coherences (SGC) in a large ensemble of nuclei operating in the x-ray regime, resonantly coupled to a common cavity environment. The observed SGC originates from two fundamentally different mechanisms related to cooperative emission and magnetically controlled anisotropy of the cavity vacuum. This approach opens new perspectives for quantum control, quantum state engineering and simulation of quantum many-body physics in an essentially decoherence-free setting., Comment: 5 pages, 3 figures

The scaling of the number of Rydberg excitations in a laser-driven cloud of atoms with the interaction strength is found to be affected by the finite size of the system. The scaling predicted by a theoretical model is compared with results extracted from a numerical many-body simulation. We find that the numerically obtained scaling exponent in general does not agree with the analytical prediction. By individually testing the assumptions leading to the theoretical prediction using the results from the numerical analysis, we identify the origin of the deviations, and explain it as arising from the finite size of the system. Furthermore, finite-size effects in the pair correlation function $g^{(2)}$ are predicted. Finally, in larger ensembles, we find that the theoretical predictions and the numerical results agree, provided that the system is sufficiently homogeneous., 9 pages, 7 figures

The dynamics of a cloud of ultra-cold two-level atoms is studied at off-resonant laser driving to a Rydberg state. We find that resonant excitation channels lead to strongly peaked spatial correlations associated with the buildup of asymmetric excitation structures. These aggregates can extend over the entire ensemble volume, but are in general not localized relative to the system boundaries. The characteristic distances between neighboring excitations depend on the laser detuning and on the interaction potential. These properties lead to characteristic features in the spatial excitation density, the Mandel $Q$ parameter, and the total number of excitations. As an application an implementation of the three-atom CSWAP or Fredkin gate with Rydberg atoms is discussed. The gate not only exploits the Rydberg blockade, but also utilizes the special features of an asymmetric geometric arrangement of the three atoms. We show that continuous-wave off-resonant laser driving is sufficient to create the required spatial arrangement of atoms out of a homogeneous cloud., 8 pages, 7 figures

A model for the simulation of ensembles of laser-driven Rydberg-Rydberg interacting multi-level atoms is discussed. Our hybrid approach combines an exact two-body treatment of nearby atom pairs with an effective approximate treatment for spatially separated pairs. We propose an optimized evolution equation based only on the system steady state, and a time-independent Monte Carlo technique is used to efficiently determine this steady state. The hybrid model predicts features in the pair correlation function arising from multi-atom processes which existing models can only partially reproduce. Our interpretation of these features shows that higher-order correlations are relevant already at low densities. Finally, we analyze the performance of our model in the high-density case., Comment: significantly expanded and revised version (more observables, high-density regime); 9 pages, 8 figures