Correlated and X-Ray Quantum Dynamics

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Full inversion of nuclear ensembles with x-ray free electron lasers

Strong excitation of nclei with x-rays.

Dynamics of ensembles of nuclei at weak (i) and strong (ii) driving. The signatures for strong driving are population inversion or even Rabi oscillations.
Up to now, experiments involving Mössbauer nuclei driven by x-rays have been restricted to the low-excitation regime. To overcome this problem, we recently proposed a setup which promises significant excitation, ideally exceeding full inversion of the nuclear ensemble, at x-ray light sources under construction. We further introduced a method to experimentally verify such inversions, in which population inversions manifest themselves in symmetry flips of suitably recorded spectra. It neither requires per-shot spectra of the incoming x-ray pulses, nor absolute measurements of the scattered light intensity. We also estimated the effect of the pulse-to-pulse coherence in x-ray free electron laser oscillators, and showed that it could lead to orders of magnitude enhancement of the signal rate for ultra-narrow nuclear resonances. These are of primary significance for precision spectroscopy, metrology, and fundamental tests.

Tailoring superradiance to design artificial quantum systems

Phase-sensitive detection at x-ray energies.

The key idea is to tailor the collective properties of an ensemble of atoms in such a way that it acts as a designer artificial atom with tunable properties.
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. To overcome this issue, we developed an analytical framework for the engineering of single-photon superradiance in extended media. Our approach is applicable to a large class of model systems across the entire electromagnetic spectrum. The key idea is to use an ensemble of atoms with fixed properties. By controlling the cooperative dynamics of the ensemble, a tunable artificial quantum system is created. Our analytic approach establishes a one-to-one relation between artificial atom and ensemble. This way, superradiance can be reverse engineered, which provides an avenue towards non-linear and quantum mechanical phenomena at x-ray energies, and also leads to a unified view on and a better understanding of superradiance across different physical systems.

A new phase for x-ray quantum optics

Phase-sensitive detection at x-ray energies.

Experimental data showing different controllable Fano line shapes.
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. In this experiment, we demonstrated 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.

A handbrake for x-rays

X-ray pulse delay.

Experimental data showing the delay of x-ray pulses as function of the x-ray frequency.
We experimentally demonstrated group velocity control for x-ray photons of 14.4 keV energy via a direct measurement of the temporal delay imposed on spectrally narrow x-ray pulses. The subluminal light propagation was achieved by inducing a steep positive linear dispersion in the optical response of Fe Mössbauer nuclei embedded in a thin film planar x-ray cavity. To directly detect the temporal pulse delay, we developed a new method to generate frequency-tunable spectrally narrow x-ray pulses from broadband pulsed synchrotron radiation. Our theoretical model is in good agreement with the experimental data. This project is an important step towards the exploitation of non-linear phenomena with nuclei.

Quantum states out of nothing


Left: Illustration of the fundamental process leading to the formation of coherences. A virtual photon is emitted on one transition, and re-absorbed on another transition. This effectively couples the initial and the final state, leading to the formation of coherence. Right: Example for the recorded spectra. The deep minima are a signature for the appearance of the coherences. They arise due to destructive interference, enabled by the generated coherences. Black dots show experimental data, the red line the corresponding theoretical predictions.
Quantum mechanical superpositions are important resources for future quantum technologies, but extremely fragile: already the interaction with the vacuum alone can destroy them. A promising solution in theory is already known for more than 40 years. At that time it was predicted that the interaction with the vacuum may be manipulated in such a way that it produces the desired superpositions instead of destroying them. Unfortunately, this is linked to rigorous conditions which so far hindered the experimental realization. We have circumvented these constraints, and demonstrated the spontaneous generation of coherences between the quantum states of a large ensemble of nuclei. Probing the system using nuclear resonance scattering, we observed clear signatures of the formed coherences, controlled by a weak external magnetic field. This opens up a variety of future perspectives for quantum optics with novel X-ray light sources.

Theory of x-ray cavity quantum electrodynamics

X-ray cavity QED setup.

Schematic setup. X-ray light with arbitrary polarization impinges in grazing incidence onto an x-ray cavity. The cavity is a thin-film waveguide and contains a layer of resonant nuclei. The scattered light is calculated as the main observable.
Mössbauer nuclei embedded in thin-film cavities have proven to be a most promising platform for x-ray quantum optics, as evidenced by a number of recent experiments. We developed a comprehensive quantum optical framework for the description of experimentally relevant settings involving nuclei embedded in x-ray waveguides. For a large class of experimentally relevant conditions, we derived compact analytical expressions, and showed that the alignment of medium magnetization, as well as incident and detection polarization, enable the engineering of advanced quantum optical level schemes. The model encompasses nonlinear and quantum effects, and we have recently also extended it to encompass multiple nuclear ensembles and multiple cavity modes as used in some experiments. Our theoretical model has been successfully employed to design and quantitatively analyse several recent experiments.

Self-assembly of Rydberg aggregates

Number-resolved excitation density of Rydberg aggregates

Left panel: Rydberg excitation density versus position in an 1-dimensional atomic cloud. The different curves show results resolved into different excitation number subspaces. It can be seen that a coherent superposition of different Rydberg excitation aggregate structures is observed. The characteristic shapes of the different excitation number subspaces can be understood as illustrated in the right panel. Since the aggregates arise due to the interaction between the particles at off-resonant driving, they are essentially independent of the trap, and can form anywhere in the atom cloud. Averaging over all possible aggregate positions explains the predicted excitation densities.
In strongly interacting Rydberg gases, the atom-atom interactions induce level shifts for multi-particle excitation states. At off-resonant laser driving, the laser detuning can compensate these level shifts, leading to resonant excitation channels for multi-particle Rydberg aggregates. We study such off-resonant driving in a cloud of ultracold two-level atoms. 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 within an aggregate depend on the laser detuning and on the interaction potential. These properties lead to unique features in the spatial excitation density, the Mandel Q parameter, and the total number of excitations. We have also modeled recent related experiments in a strongly dissipative Rydberg system.

Rydberg electromagnetically induced transparency

Illustration of Rydberg-EIT

Naive illustration of the effect of Rydberg-Rydberg interactions on the light propagation through the atomic ensemble. In the left panel, the atom density is low enough such that interactions can be neglected. Red dots are Rydberg-excited atoms, and their interaction range is indicated by the shaded red disc. In this case, electromagnetically induced transparency is unperturbed, which leads to low absorption on resonance. In the right panel, the density is higher, such that a single Rydberg-excited atom blockades the excitation of nearby atoms within the interaction range. The interaction-induced level shifts break the transparency, leading to much higher absorption.
Highly excited Rydberg atoms have extreme properties, which make them promising candidates for a number of fascinating applications. Most importantly, they feature long-range interactions, which lead to correlated dynamics of the ensemble of atoms. One application is to achieve strong interactions between photons by interfacing them with interacting states of matter. Recently, electromagnetically induced transparency was implemented in a cold gas of Rydberg atoms. The strong interaction of the Rydberg atoms leads to nonlinear optical effects such as a nontrivial dependence of the degree of probe-beam attenuation on the medium density and on its initial intensity. Furthermore, so-called dark-state polaritons form, which are combined excitation of the photon field and the atoms. Due to the atom-atom interactions, the polariton number statistics is modified to non-classical values. We have developed a Monte Carlo rate equation model to describe this setting, which self-consistently includes the effect of the probe-beam attenuation to investigate the steady state of the Rydberg medium driven by two laser fields. This model successfully describes the optical response observed in a recent experiment.

Single-photon entanglement in the hard x-ray regime

Setup for keV entanglement generation

Sketch of the setup for coherent control of nuclear forward scattering. A synchrotron radiation pulse is monochromatized (M) before it reaches the sample (S). One polarization component of the pulse is selected from the forward response by a polarizer (P), and the other component is extracted from the background with the help of a piezoelectric fast steering mirror (PSM). D are detectors.
Quantum entanglement is one of the most intriguing properties of quantum mechanics, and is commonly visualized as a correlation of two or more quantum particles that form a single quantum object. But entanglement does not necessarily involve two quantum particles. Possibly even more fascinating, a single photon can entangle two modes of the vacuum. Here we show that this single-particle entanglement can also be generated by coherently controlling the quantum dynamics of nuclei. First, the nuclei are excited with a synchrotron radiation pulse. Then, by applying a sequence of weak magnetic fields to the nuclei, they are forced to emit a single photon in the x-ray regime such that it entangles field modes at energies about 10000 times higher than usual. This could pave the way for entanglement research in nuclear physics, based on experiments exploiting nuclear complexity with synchrotron radiation sources and free-electron lasers in an as-yet unexplored energy regime.

Isomer triggering via nuclear excitation by electron capture

Level scheme isomer triggering

Schematic depiction of isomer triggering for the case of 93Mo. Triggering can occur via a number of nuclear excitation mechanisms such as photoexcitation, Coulomb excitation or coupling to the atomic shells.
The search for practical methods to change the internal state of atomic nuclei has been the subject of a number of investigation in the last years. In particular, isomer triggering refers to the possibility to excite the long-lived excited isomeric nuclear state to a higher level which is associated with freely radiating states and therefore releases the energy of the metastable state. Isomers are of interest in different contexts, for example, due to fascinating potential applications related to the controlled release of nuclear energy on demand, such as in nuclear batteries, or motivated by the fundamental challenge to understand the formation of isomers and their role in the evolution of the universe.
We have compared isomer triggering via photoabsorption to low-lying triggering levels with alternative mechanisms. We show that x-ray triggering is possible, but it turns out that among the possible isomer triggering mechanisms, the coupling to the atomic shell via the process of nuclear excitation by electron capture is the most efficient one. An experimental verification of our findings at the borderline of atomic and nuclear physics may be provided by upcoming ion storage ring facilities and ion beam traps which will commence operation in the near future.

Nuclear quantum optics with x-ray laser pulses

Nuclear Rabi flopping

Population inversion W on the 3/2- to 3/2+ E1 transition in 223Ra accelerated in a storage ring and under the influence of a 30fs FWHM Gaussian laser pulse with intensity I=10^24 W/cm^2 (nuclear rest frame parameters). The different curves correspond to different decoherence times of the system, i.e., driving x-ray field pulses with limited coherence lengths. It can be seen that with decreasing coherence length, the coherent Rabi oscillations are damped until the upper state population does no longer exceed the incoherent driving limit of half the population in the excited state.
The direct interaction of nuclei with super-intense laser fields is studied. We show that present and upcoming high-frequency laser facilities, especially together with a moderate acceleration of the target nuclei to match photon and transition frequency, do allow for resonant laser-nucleus interaction. These direct interactions may be utilized for the model-independent optical measurement of nuclear properties such as the transition frequency and the dipole moment, thus opening the field of nuclear quantum optics. As ultimate goal, one may hope that direct laser-nucleus interactions could become a versatile tool to enhance preparation, control and detection in nuclear physics.