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.

The setting of Mössbauer 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 Röhlsberger 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.

A promising platform for the emerging field of x-ray quantum optics are Mössbauer 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 Mössbauer 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

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.

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 Mössbauer 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.Strong nonlinear interaction of light with matter is a key requirement for fundamental and applied quantum optical technologies alike. Since conventional materials typically exhibit weak nonlinearities, the ultimate quest for strong nonlinear interactions of individual quanta has led to the development of a number of methods to significantly enhance nonlinear light-matter interactions. Among the most prominent ones are coherently prepared media based on electromagnetically induced transparency, sub-luminal light and related effects [1,2], as well as cavity-enhanced light matter interactions [3].Recently, nuclear quantum optics featuring the interaction of x-ray light with Mössbauer nuclei in the few keV transition energy range has gained considerable momentum, both theoretically [4-9] and experimentally [10][11][12][13][14][15][16][17][18][19]. Interestingly, these experiments operate with less than one resonant x-ray photon per pulse on average due to restrictions in the available x-ray light sources. This raises the question, whether coherent or cavity-based enhancement techniques could be utilized to realize nonlinear light-matter interactions in nuclear quantum optics despite the low number of resonant photons.Here, we report a first step towards this goal, and demonstrate group velocity control of spectrally narrow x-ray pulses (SNXP). Sub-luminal light propagation is achieved by inducing a steep positive linear material dispersion, and verified by direct measurements of the temporal delay imposed on the SNXP. For this, we suitably manipulate the optical response of the ω 0 = 14.4 keV Mössbauer resonance (single nucleus linewidth γ = 4.7 neV) of a large ensemble of 57 Fe nuclei embedded in a thin film planar x-ray cavity. Our approach thereby combines coherent control, as well as cooperative and cavity enhancements of light-matter interaction in a single setup. To enable the direct detection of the temporal pulse delay, we further propose and implement a flexible scheme to generate frequency-tunable SNXP from broadband synchrotron radiation for applications in xray quantum optics. Our theoretical model is in good agreement with the experimental data.Sub-luminal light was first demonstrated in the visible frequency range [20][21][22], and by now has been implemented in a number of platforms [2], particularly also in cavity settings [23,24]. Manipulation of light propagation has also been reported in the x-ray regime. In Ref.[12], a...

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.

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 Mössbauer 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 nonlinear 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 multilayer 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.

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.