Nuclear and atomic quantum dynamics
The borderline between atomic and nuclear physics offers a special playground for quantum dynamics effects. Here, novel high-frequency light sources such as the x-ray free electron laser (XFEL) or the Extreme Light Infrastructure (ELI) play a key role in transferring quantum control techniques known from atomic physics to nuclear systems. Our interest in x-ray quantum optics in nuclear systems is motivated by attractive applications that rely specifically on the interaction between high-frequency fields and nuclei such as nuclear batteries, the gamma-ray laser or a nuclear transition-based frequency standard. Furthermore, nuclear excitations can also be used to store and control single x-ray photons. This may allow forwarding optics and quantum information to shorter wavelengths and shrinking computing elements in future photonic devices past the present diffraction limit bottleneck.
Closer to atomic physics, one may explore the coupling between the atomic and nuclear degrees of freedom in nuclear processes that involve atomic electrons. Nuclear excitation by electron capture (NEEC) and nuclear excitation by electron transition (NEET) are such examples. These processes can be the most efficient nuclear excitation mechanisms for small transition energies and are expected to play an important role in dense plasmas. In particular, theoretical studies can shed light on the role NEEC and NEET play in laser-generated plasma environments where nuclear excitation might be used as diagnostics.
Group photo end of October 2016. Counterclockwise from lower right corner: Nikolay, Yuanbin, Gregor, Brenden, Jonas, Pavlo, Hyoyin and Adriana. Xiangjin was missing in action at the time.
Some recent and current projects:
Nuclear excitation mechanisms in plasmas
Figure 1: If the atomic and nuclear transition energies match, an electron can recombine into an ion (left panel) with the simultaneous excitation of the nucleus (right panel) from the ground state G to the excited state E .
Nuclei may couple to atomic shells if the recombination of a free electron into a highly charged ion leads to the excitation of the nucleus . Known as nuclear excitation by electron capture (NEEC), this process becomes increasingly efficient with rising electron density and degree of ionisation. Such conditions are predominant in dense astrophysical plasmas in the interior of stars and supernovae or might be produced by ultra-strong optical laser fields. In dense plasma environments, both nuclear excitation by photoabsorption as well as via coupling to the atomic shells is possible, populating higher nuclear states and in astrophysical plasmas potentially influencing the formation paths for heavy elements. Closer to laboratory conditions on Earth, it turns out that NEEC can be an important process also in experiments aiming to directy excite nuclei with XFEL photons. Our results unexpectedly show that secondary processes coupling nuclei to the atomic shell in the created cold high-density plasma when XFEL beams shine on a solid-state nuclear target can exceed direct photoexcitation [2,3]. Thus, experiments aiming at exciting nuclei with XFEL photons might be in fact dominated by secondary processes like NEEC in the created plasma. Optical lasers might also be directly used to create plasmas with tailored conditions for the occurence of NEEC . This calls for further theoretical studies for understanding nuclear excitation in plasma conditions.
Storing and manipulating single x-ray photons
Figure 2: Thin-film planar cavity setup with x-ray grazing incidence. The nuclei experience a hyperfine magnetic field B (red horizontal arrow). Inset panel: 57Fe level scheme with hyperfine splitting. This is equivalent with a V-like three-level scheme comprising the common ground state and the two excited states.
While in the future very strong x-ray fields may be used to control nuclei, one may turn the problem to see how x-ray light might be controlled by nuclei. Instead of mere pumping of a nuclear transition by strong high-frequency lasers such as the XFEL, one envisages the situation of a weak excitation - a single nucleus, in fact - that stores a single x-ray photon. A novel scenario to store, release and control the phase properties of such a photon by using iron nuclei as a "nuclear cage" has been developed in . This effect relies on the delocalized nature of the nuclear excitation which opens the possibility to control the re-emission of the single photon by switching the nuclear hyperfine magnetic field off and on. Furthermore, it turns out that storage could be even more robust and more flexible when using special layered structures that contain a nanometer-thick iron film. We have investigated theoretically how spectrally narrow x-ray pulses typically containing at most one photon can be mapped and stored as nuclear coherence in thin-film planar x-ray cavities . The storage mechanism relies on interference effects possible due to the occurrence of spontaneously generated coherences specific to the nuclear system. The role of the control field is played here by a hyperfine magnetic field which induces interference effects reminiscent of electromagnetically induced transparency. By switching off the control magnetic field, a narrow-band x-ray pulse resonant to the nuclear transition can be completely stored in the cavity for approximately 100 ns. In addition, we could experimentally demonstrate Rabi oscillations of x-ray radiation mimicking the strong coupling regime for thin-flim cavities with two iron layers . These are exciting prospects for future processing and control of x-ray qubits and quantum information applications for the first time in the x-ray regime.
Logical operations with single x-ray photons
Figure 3: Nuclear forward scattering setup. Sigma- (orange) or pi-polarized (blue) x-rays scatter off a nuclear target in the forward direction. A spatially separated control photon triggers a magnetic field rotation from the z- to the x-axis. This rotation implements logical operations for x-ray qubits. The hyperfine-split nuclear level scheme of 57Fe is illustrated in the inset.
Progress in control of single x-ray quanta opens the possibility to use the latter as information carriers. Photonic qubits lie at the heart of quantum information technology, often encoding information in their polarization state. So far, only low-frequency optical and infrared photons have been employed as flying qubits, as the resources that are at present easiest to control. With their essentially different way of interacting with matter, x-ray qubits would bear however relevant advantages: they are extremely robust, penetrate deep through materials, and can be focused down to few-nm waveguides, allowing unprecedented miniaturization. Also, xrays are resonant to nuclear transitions, which are very well isolated from the environment and present long coherence times. We have shown theoretically that x-ray polarization qubits can be dynamically controlled by nuclear Möossbauer resonances . The control knob is played by nuclear hyperfine magnetic fields, that allow via fast rotations precise processing of single x-ray quanta polarization. With such rotations, single-qubit and binary logical operations such as a destructive C-NOT gate can be implemented. Apart from the realization of logical gates with x-rays, the polarization encoding can be used to design an x-ray quantum eraser scheme where the interference between scattering paths can be switched off and back on in a controlled manner . Such setups may advance time-energy complementarity tests to so far unexplored parameter regimes.
Nuclear excitation with zeptosecond gamma-ray pulses
Figure 4: Qualitative illustration of nuclear excitation regimes. The yrast line defines the minimum energy of a nuclear state with a certain angular momentum. Heavy-ion collisions preferentially excite states close to the yrast line (region depicted by hatched area). Absorption of coherent MeV photons on the other hand can produce high excitation with low angular momentum transfer, leading to compound nuclei several hundred MeV above yrast. The inset shows three angular-momentum distributions.
Going beyond the x-ray domain towards even higher frequencies will open unprecedented possibilities for high-energy nuclear physics experiments. The Extreme Light Infrastructure (ELI) holds promise to deliver coherent MeV gamma rays generated via Thompson scattering on a relativistic plasma mirror. Coherence strongly amplifies nuclear absorption potentially leading to the formation of a compound nucleus with remarkably high excitation energy. Since the total angular momentum transferred in the process is much smaller than in typical heavy-ion reactions, the excitation energy is several hundreds MeV above yrast. This opens a totally unexplored regime where the most basic physical properties of nuclei such as the density of states are not known. Standard theoretical methods fail for the high excitation energies and large particle numbers that play a role here. The approach developed in Refs. [1,2] yields approximate analytical expressions for the total and partial level densities and allows the semiquantitative study of the competition between photon absorption, photon-induced nucleon emission, and neutron evaporation. With neutron evaporation overtaking photon absorption at energies below the saturation of the latter for medium-weight and heavy nuclei, the process promises to yield neutron-poor nuclei far from the valley of stability [3,4]. Experiments planned at ELI thus promise to shed light on the structure of such nuclei and on the time scales involved. Altogether the field constitutes a totally novel domain of laser-matter interaction.
A nuclear frequency standard
Figure 5: (a) Thorium level scheme for the isomeric and ground states. (b,c) One-field and two-field setups for the optical determination of the nuclear transition. The presence of the second couple field (red arrow) produces interference effects that improve the nuclear level measurement precision.
Incredibly precise nuclear clocks may soon outperform and replace the present atomic clocks that define the global time standard. The lowest transition in the 229Th nucleus with frequency in the vacuum ultraviolet range and very narrow linewidth promises enhanced precision and amazing stability. The main impediment on the way is that this nuclear clock transition is as elusive in practice as it is attractive. The precise frequency could so far not be determined, and no experiment succeeded in directly exciting the nuclear transition. At the moment we are working on a new setup which would make use of internal conversion to determine more precisely energy of the nuclear transition. Once the transition energy is known to a certain precision, collective effects may help to increase that precision up to few Hz. Our results  show for instance that an unorthodox setup that relies on coherence effects offers an increase of several orders of magnitude in precision. The coherence trump comes into play when two laser fields instead of one are used to drive the nuclear transition . The two-field setup offers not only a significantly increased precision in the determination of the transition frequency, but also an unmistakable signature for the nuclear excitation, so far important unaccomplished goals. We note that this is particulary important as recent nuclear physics studies  reveal that the isomer width might be even narrower than so far expected. Once the nuclear transition frequency is determined, specific interrogation schemes for the nuclear frequency standard can be implemented. The determination of the 229Th transition frequency also paves the way for a whole range of applications in the newly emerging field of nuclear quantum optics.
Optomechanical coupling of x-rays and optical photons
Figure 6: Sketch of the optomechanical interface between optical and x-ray photons. The optical cavity is composed of a fixed mirror and a movable microlever. A layer containing Mössbauer nuclei that can resonantly interact with x-rays is embedded in the tip of the microlever.
Future photonic quantum networks will require interfaces between different photon frequency regimes. So far, conversion experiments bridged the visible with telecommunication bands in infrared. Going towards shorter wavelengths bears however certain advantages: x-rays are better focusable, are more robust and penetrate deeper through materials than visible or infrared photons. They also carry much larger momenta, potentially facilitating the entanglement of light and matter at a single-photon level. Unfortunately, a direct application of the conversion principles established so far is bound to fail, as the required high-performance cavities are not available for x-rays. In addition, x-rays are resonant to transitions in atomic nuclei rather than of valence electrons. We are at present working on an innovative solution for coupling x-ray quanta to an optomechanical device. So far we could demonstrate theoretically that using resonant interactions of x-rays with nuclear transitions, in conjunction with an optomechanical setup interacting with optical photons, an optical-x-ray interface can be achieved . Such a device would allow to tune x-ray absorption spectra and eventually to shape x-ray wavepackets for single photons by optomechanical control. The role of the x-ray cavity is here adopted by a nuclear transition with long coherence times. Our results show that optomechanically induced transparency of x-rays can be achieved in the optical-x-ray interface paving the way for both metrology and an unprecedentedly precise control of x-rays using optical photons. A metrology-relevant application would be an optomechanical coupling involving the nuclear clock transition of 229Th presented in the previous project.