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Correlated and X-Ray Quantum Dynamics

Quantum optical concepts based on coherence and interference have proven extremely successful for the study and manipulation of atoms and molecules. Recent improvements in modern x-ray light sources prompt the question, whether such techniques could also be applied in the hard x-ray regime. This could not only pave the way for new applications, but also is indispensable for taking advantage of the full potential of these new machines.

However, despite the new light sources, it remains challenging to exploit quantum optical phenomena in the x-ray domain, and it is typically not possible to directly transfer established concepts to the x-ray domain. We develop new approaches to establish quantum optical methods at x-ray energies, focusing in particular on the coupling of x-rays to nuclear resonances in large ensembles of Mössbauer nuclei. While we mainly work theoretically, we regularly conduct experiments at x-ray sources in collaboration with other groups to explore new regimes and to verify our predictions.

Interestingly, the relevant setups in x-ray quantum optics typically involve strong collective phenomena inducing correlations within the ensemble of nuclei, and the understanding or even control of these phenomena is a key requirement. Motivated by this, we also study correlations and collective phenomena in other related model systems, as well as fundamental coherence and interference effects.

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

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.

  1. K. P. Heeg, C. H. Keitel, and J. Evers, submitted (2016)

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. 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.

  1. P. Longo, C. H. Keitel, and J. Evers, Sci. Rep. 6, 23628 (2016)

A new phase for x-ray quantum optics

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.

  1. K. P. Heeg, C. Ott, D. Schumacher, H.-C. Wille, R. Röhlsberger, T. Pfeifer, and J. Evers, Phys. Rev. Lett. 114, 207401 (2015)
  2. C. Ott, A. Kaldun, P. Raith, K. Meyer, M. Laux, J. Evers, C. H. Keitel, C. H. Greene, and T. Pfeifer, Science 340, 716 (2013)

A handbrake for x-rays

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.

  1. K. P. Heeg, J. Haber, D. Schumacher, L. Bocklage, H.-C. Wille, K. S. Schulze, R. Loetzsch, I. Uschmann, G. G. Paulus, R. Rüffer, R. Röhlsberger, and J. Evers, Phys. Rev. Lett. 114, 203601 (2015)

Quantum states out of nothing

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.

  1. K. P. Heeg, H.-C. Wille, K. Schlage, T. Guryeva, D. Schumacher, I. Uschmann, K. S. Schulze, B. Marx, T. Kämpfer, G. G. Paulus, R. Röhlsberger, and J. Evers, Phys. Rev. Lett. 111, 073601 (2013)

Theory of x-ray cavity quantum electrodynamics

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.

  1. K. P. Heeg and J. Evers, Phys. Rev. A 88, 043828 (2013)
  2. K. P. Heeg and J. Evers, Phys. Rev. A 91, 063803 (2015)

Self-assembly of Rydberg aggregates

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.

  1. M. Gärttner, K. P. Heeg, T. Gasenzer, and J. Evers, Phys. Rev. A 88, 043410 (2013)
  2. H. Schempp, G. Günter, M. Robert-de-Saint-Vincent, C. S. Hofmann, D. Breyel, A. Komnik, D. W. Schönleber, M. Gärttner, J. Evers, S. Whitlock, M. Weidemüller, Phys. Rev. Lett. 112, 013002 (2014)
  3. K. Heeg, M. Gärttner, and J. Evers, Phys. Rev. A 86, 063421 (2012)

Rydberg electromagnetically induced transparency

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.

  1. C. S. Hofmann, G. Günter, H. Schempp, M. Robert-de-Saint-Vincent, M. Gärttner, J. Evers, S. Whitlock, M. Weidemüller, Phys. Rev. Lett. 110, 203601 (2013)
  2. M. Gärttner and J. Evers, Phys. Rev. A 88, 033417 (2013)

Single-photon entanglement in the hard x-ray regime

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.

  1. A. Pálffy, C. H. Keitel, and J. Evers, Phys. Rev. Lett. 103, 017401 (2009)
    (and July 2009 issue of Virtual Journal of Quantum Information)
    (and July 13, 2009 issue of Virtual Journal of Nanoscale Science & Technology)

Isomer triggering via nuclear excitation by electron capture

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.

  1. A. Pálffy, J. Evers and C. H. Keitel, Phys. Rev. Lett. 99, 172502 (2007)

Nuclear quantum optics with x-ray laser pulses

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.

  1. T. J. Bürvenich, J. Evers and C. H. Keitel, Phys. Rev. Lett. 96, 142501 (2006)
    (and May 2006 issue of Virtual Journal of Ultrafast Science)
  2. T. J. Bürvenich, J. Evers, and C. H. Keitel, Phys. Rev. C 74, 044601 (2006)
  3. A. Pálffy, J. Evers, and C. H. Keitel, Phys. Rev. C 77, 044602 (2008)