Resonant X-ray excitation of the nuclear clock isomer 45Sc.

Resonant oscillators with stable frequencies and large quality factors help us to keep track of time with high precision. Examples range from quartz crystal oscillators in wristwatches to atomic oscillators in atomic clocks, which are, at present, our most precise time measurement devices1. The search for more stable and convenient reference oscillators is continuing2-6. Nuclear oscillators are better than atomic oscillators because of their naturally higher quality factors and higher resilience against external perturbations7-9. One of the most promising cases is an ultra-narrow nuclear resonance transition in 45Sc between the ground state and the 12.4-keV isomeric state with a long lifetime of 0.47 s (ref. 10). The scientific potential of 45Sc was realized long ago, but applications require 45Sc resonant excitation, which in turn requires accelerator-driven, high-brightness X-ray sources11 that have become available only recently. Here we report on resonant X-ray excitation of the 45Sc isomeric state by irradiation of Sc-metal foil with 12.4-keV photon pulses from a state-of-the-art X-ray free-electron laser and subsequent detection of nuclear decay products. Simultaneously, the transition energy was determined as [Formula: see text] with an uncertainty that is two orders of magnitude smaller than the previously known values. These advancements enable the application of this isomer in extreme metrology, nuclear clock technology, ultra-high-precision spectroscopy and similar applications.

Certifying Multimode Light-Matter Interaction in Lossy Resonators.

Quantum models based on few-mode master equations have been a central tool in the study of resonator quantum electrodynamics, extending the seminal single-mode Jaynes-Cummings model to include loss and multiple modes. Despite their broad application range, previous approaches within this framework have either relied on a Markov approximation or a fitting procedure. By combining ideas from pseudomode and quasinormal mode theory, we develop a certification criterion for multi-mode effects in lossy resonators. It is based on a witness observable, and neither requires a fitting procedure nor a Markov approximation. Using the resulting criterion, we demonstrate that such multi-mode effects are important for understanding previous experiments in x-ray cavity QED with Mössbauer nuclei and that they allow one to tune the nuclear ensemble properties.

Coherent X-ray-optical control of nuclear excitons.

Coherent control of quantum dynamics is key to a multitude of fundamental studies and applications1. In the visible or longer-wavelength domains, near-resonant light fields have become the primary tool with which to control electron dynamics2. Recently, coherent control in the extreme-ultraviolet range was demonstrated3, 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 matter4,5. It has been shown that the power and scope of Mössbauer spectroscopy can be greatly improved using various control techniques6-16. 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 spectroscopy17 and spin-echo-like techniques, which should not only advance nuclear quantum optics18, but also help to realize X-ray clocks and frequency standards19. In the long term, we envision time-resolved studies of nuclear out-of-equilibrium dynamics, which is a long-standing challenge in Mössbauer science20.

Time-Resolved sub-Ångström Metrology by Temporal Phase Interferometry near X-Ray Resonances of Nuclei.

We introduce an analytical phase-reconstruction principle that retrieves atomic scale motion via time-domain interferometry. The approach is based on a resonant interaction with high-frequency light and does not require temporal resolution on the time scale of the resonance period. It is thus applicable to hard x rays and 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 keV emission line of an ^{57}Fe sample, which corresponds to a spatial translation of this sample. The small wavelength of this transition (λ=0.86 Å) allows for determining the motion of the emitter on sub-Ångström length and nanosecond timescales.

Probing Quantum Dynamical Couple Correlations with Time-Domain Interferometry.

Time-domain interferometry (TDI) is a promising method to characterize spatial and temporal correlations at x-ray energies, via the so-called intermediate scattering function and the related dynamical couple correlations. However, so far, it has only been analyzed for classical target systems. Here, we provide a quantum analysis, and suggest a scheme that allows us to access quantum dynamical correlations. We further show how TDI can be used to exclude classical models for the target dynamics, and illustrate our results using a single particle in a double well potential.

Tailoring superradiance to design artificial quantum systems.

Cooperative phenomena arising due to the coupling of individual atoms via the radiation field are a cornerstone of modern quantum and optical physics. Recent experiments on x-ray quantum optics added a new twist to this line of research by exploiting superradiance in order to construct artificial quantum systems. However, so far, systematic approaches to deliberately design superradiance properties are lacking, impeding the desired implementation of more advanced quantum optical schemes. Here, we develop an analytical framework for the engineering of single-photon superradiance in extended media applicable across the entire electromagnetic spectrum, and show how it can be used to tailor the properties of an artificial quantum system. This "reverse engineering" of superradiance not only provides an avenue towards non-linear and quantum mechanical phenomena at x-ray energies, but also leads to a unified view on and a better understanding of superradiance across different physical systems.

Tunable Subluminal Propagation of Narrow-band X-Ray Pulses.

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. Subluminal light propagation is achieved by inducing a steep positive linear dispersion in the optical response of 57Fe 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.

Collective excitation of Rydberg-atom ensembles beyond the superatom model.

In an ensemble of laser-driven atoms involving strongly interacting Rydberg states, the steady-state excitation probability is usually substantially suppressed. In contrast, here we identify a regime in which the Rydberg excited fraction is enhanced by the interaction. This effect is associated with the buildup of many-body coherences induced by coherent multiphoton excitations between collective states. The excitation enhancement should be observable under currently existing experimental conditions and may serve as a direct probe for the presence of coherent multiphoton dynamics involving collective quantum states.

Far-field signatures of a two-body bound state in collective emission from interacting two-level atoms on a lattice.

The collective emission from a one-dimensional chain of interacting two-level atoms is investigated. We calculate the light scattered by dissipative few-excitation eigenstates in the far field, and, in particular, focus on signatures of a lattice two-body bound state. We present analytical results for the angle-resolved, temporal decay of the scattered light intensity. Moreover, we find that the steady-state emission spectrum that emerges when the system is probed by a weak, incoherent driving field exhibits a distinct signature for the existence of a bound state, and allows us to determine the momentum distribution of the two-body relative wave function. Intriguingly, our study does not rely on single-atom addressability and/or manipulation techniques.

Vacuum-assisted generation and control of atomic coherences at x-ray energies.

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.

Lorentz meets Fano in spectral line shapes: a universal phase and its laser control.

Symmetric Lorentzian and asymmetric Fano line shapes are fundamental spectroscopic signatures that quantify the structural and dynamical properties of nuclei, atoms, molecules, and solids. This study introduces a universal temporal-phase formalism, mapping the Fano asymmetry parameter q to a phase φ of the time-dependent dipole response function. The formalism is confirmed experimentally by laser-transforming Fano absorption lines of autoionizing helium into Lorentzian lines after attosecond-pulsed excitation. We also demonstrate the inverse, the transformation of a naturally Lorentzian line into a Fano profile. A further application of this formalism uses quantum-phase control to amplify extreme-ultraviolet light resonantly interacting with He atoms. The quantum phase of excited states and its response to interactions can thus be extracted from line-shape analysis, with applications in many branches of spectroscopy.

Optical diode made from a moving photonic crystal.

Optical diodes controlling the flow of light are of principal significance for optical information processing. They transmit light from an input to an output, but not in the reverse direction. This breaking of time reversal symmetry is conventionally achieved via Faraday or nonlinear effects. For applications in a quantum network, features such as the abilities of all-optical control, on-chip integration, and single-photon operation are important. Here we propose an all-optical optical diode which requires neither magnetic fields nor strong input fields. It is based on a "moving" photonic crystal generated in a three-level electromagnetically induced transparency medium in which the refractive index of a weak probe is modulated by the moving periodic intensity of a strong standing coupling field with two detuned counterpropagating components. Because of the Doppler effect, the frequency range of the crystal's band gap for the probe copropagating with the moving crystal is shifted from that for the counterpropagating probe. This mechanism is experimentally demonstrated in a room temperature Cs vapor cell.

Dressed-atom multiphoton analysis of anomalous electromagnetically induced absorption.

A method to interpret probe spectra of driven degenerate atomic systems is discussed. The dressed-atom multiphoton spectroscopy (DAMS) is based on a dressing of the atomic system with the strong coupling field, followed by a perturbative treatment of the probe field interaction. As an example, we apply the DAMS to provide a clear interpretation for anomalous electromagnetically induced absorption (EIA), which cannot be explained by spontaneous transfer of coherence. We show that anomalous EIA arises from quantum interference among competing two-photon transitions and explain the different dependences on the coupling field strength observed for various angular momentum setups.

Yoctosecond photon pulses from quark-gluon plasmas.

Present ultrafast laser optics is at the frontier between atto- and zeptosecond photon pulses, giving rise to unprecedented applications. We show that high-energetic photon pulses down to the yoctosecond time scale can be produced in heavy-ion collisions. We focus on photons produced during the initial phase of the expanding quark-gluon plasma. We study how the time evolution and properties of the plasma may influence the duration and shape of the photon pulse. Prospects for achieving double-peak structures suitable for pump-probe experiments at the yoctosecond time scale are discussed.

Single-photon entanglement in the keV regime via coherent control of nuclear forward scattering.

Generation of single-photon entanglement is discussed in nuclear forward scattering. Using successive switchings of the direction of the nuclear hyperfine magnetic field, the coherent scattering of photons on nuclei is controlled such that two signal pulses are generated out of one initial pump pulse. The two time-resolved correlated signal pulses have different polarizations and energy in the keV regime. Spatial separation of the entangled field modes and extraction of the signal from the background can be achieved with the help of state-of-the-art x-ray polarizers and piezoelectric fast steering mirrors.

Ground state cooling of a nanomechanical resonator in the nonresolved regime via quantum interference.

Ground state cooling of a nanomechanical resonator coupled to a superconducting flux qubit is discussed. By inducing quantum interference to cancel unwanted heating excitations, ground state cooling becomes possible in the nonresolved regime. The qubit is modeled as a three-level system in Lambda configuration, and the driving fluxes are applied such that the qubit absorption spectrum exhibits electromagnetically induced transparency, thereby canceling the unwanted excitations. As our scheme allows the application of strong cooling fields, fast and efficient cooling can be achieved.

Isomer triggering via nuclear excitation by electron capture.

Triggering of long-lived nuclear isomeric states via coupling to the atomic shells in the process of nuclear excitation by electron capture (NEEC) is studied. NEEC occurring in highly charged ions can excite the isomeric state to a triggering level that subsequently decays to the ground state. We present total cross sections for NEEC isomer triggering considering experimentally confirmed low-lying triggering levels and reaction rates based on realistic experimental parameters in ion storage rings. A comparison with other isomer triggering mechanisms shows that, among these, NEEC is the most efficient.

Strong-field spatial interference in a tailored electromagnetic bath.

Light scattered by a regular structure of atoms can exhibit interference signatures, similar to the classical double-slit. These first-order interferences, however, vanish for strong light intensities, restricting potential applications. Here, we show how to overcome these limitations to quantum interference in strong fields. First, we recover the first-order interference in strong fields via a tailored electromagnetic bath with a suitable frequency dependence. At strong driving, the optical properties for different spectral bands are distinct, thus extending the set of observables. We further show that for a two-photon detector as, e.g., in lithography, increasing the field intensity leads to twice the spatial resolution of the second-order interference pattern compared to the weak-field case.