Theory Division

Theoretical Quantum Dynamics and Quantum Electrodynamics


Research topics - Division Christoph H. Keitel

Figure 1: Matter interacting with intense laser beams: key words describing various topics of interest of the division.

The theoretical investigation of the interaction of matter with laser pulses by now has reached a level at which fundamental aspects such as the quantum nature of both light and matter, relativity and correlations among the involved particles have become key issues and substantial challenges alike. In this overview, our efforts are summarized towards a detailed understanding of the quantum mechanical interplay of all constituents of atomic, ionic and nuclear systems as well as the quantum vacuum with strong laser fields. Emphasis is placed on various applications with strong connection to experiments at the Institute (see also fig. 1): High-precision calculations involving quantum electrodynamical and nuclear effects are employed for accurate determinations, e.g., of ionic spectra and g-factors. Coherent control of atomic and nuclear ensembles is investigated in the light of advanced synchrotron and x-ray free-electron laser sources. And finally our research on extreme field laser physics is directed towards carrying out quantum electrodynamics, nuclear, high-energy and astrophysics with the strongest laser pulses presently available or under construction.

Precision Studies with Ions and Nuclei

High-precision experiments with ions and nuclei enable a direct access to fundamental physics. In a highly charged ion, inner-shell electrons experience the strongest electromagnetic fields accessible nowadays, providing an ideal testing ground to prove weather quantum electrodynamics, the field theory of the electromagnetic interaction within the Standard Model, is valid in intense external fields. Precision measurements with these systems, when combined with sufficiently accurate theoretical calculations, also yield the values of fundamental constans or can test whether these vary in space and time. Furthermore, nuclei become also attractive in this direction being both increasingly accessible with advanced light sources and stable against external perturbations.

High-precision fundamental research with ions

An external static magnetic field gives rise to the Zeeman splitting of atomic energy levels, with a strength characterized by the dimensionless g-factor of the atomic state. The theory of the g-factor of an electron bound in the attractive potential of an atomic nucleus is investigated in the group around Zoltán Harman. These studies are paralleled with a quantum leap in the experimental accuracy in the investigation of the g-factor, especially in Penning trap measurements performed by the division headed by Klaus Blaum. Measuring the electron's g-factor in highly charged ions provide an exciting possibility for testing fundamental theories. Effects of strong-field quantum electrodynamics (QED) are increasingly relevant at higher and higher ionic charges. Bound-state QED effects are scrutinized to the highest precision in recent trapped-ion experiments, which have reached the 10-11 level in terms of relative precision with hydrogenlike carbon and silicon ions. From a combined analysis of experimental and theoretical data for carbon ions, an improved value of the atomic mass of the electron has been determined, representing an improvement in accuracy by more than an order of magnitude as compared to the previously established value.

Figure 2: An illustration of the physical effects appearing when a bound electron is orbiting the nucleus of a trapped ion. The electron (blue) interacts with an external magnetic field, the strength of which is described by the electron's g-factor. During its cycling around the nucleus, the electron may emit and reabsorb virtual photons (wave line), and may create virtual charged lepton or hadron pairs (closed loop), changing its wave function. The atomic nucleus (green) may be extended, deformed, and it may possess a nonzero spin.

These experiments are currently being extended to a range of ions along the periodic table, including the heaviest stable elements. An essential motivation of such studies is that g-factor measurements with highly charged ions are anticipated to yield a new value of the fine-structure constant, i.e. the fundamental constant defining the strength of any kind of electromagnetic interactions in the Universe. We have recently found that a combination of the experimental g-factors of light one- and three-electron ions allows one to substract detrimental nuclear uncertainties, and thus one can extract this constant to unprecedented precision. This necessitates also a continuous improvement in the theoretical description of radiative corrections. In recent studies, we calculated small corrections to the bound g-factor which arise from a virtual creation and annihilation of more exotic charged particles such as muons and hadrons. Furthermore, as with the increasing strength of the binding Coulomb field the electronic wave functions have a larger and larger overlap with the nucleus, accurate measurements with such systems may also deliver new insights into nuclear structural properties. As an example, we have considered the nuclear shape (or deformation) effect, i.e. the deviation of the nuclear shape from a perfectly spherical one.

Figure 3: a) Schematic transient-absorption-spectroscopy scenario: an atomic ensemble interacts with two pulses separated by a time delay τ, and the absorption spectrum of the transmitted probe pulse is recorded. The Rb atoms are modeled as a V-type three-level system where both transitions are coupled to broadband pulses. b) Theoretical absorption spectra of a delayed probe pulse exemplified for the 1↔3 transition, with the atoms driven by a pump pulse of lower (upper panel) and higher (lower panel) intensity. Spectra are displayed as a function of negative or positive time delays. The red dashed lines highlight the phase shift of time-delay-dependent oscillations. This shift is connected to the driving laser intensity and this again to the relative phase of the excited states.

Highly charged ions do not only allow the precision determination of the values of physical constants, but they have also been proposed as ideal systems for testing a potential variation of fundamental constants. Open-shell ions near level crossings have been predicted to be particularly sensitive to a variation of the fine-structure constant, and their optical spectra are being investigated by ion trap experiments by the group of José Crespo López-Urrutia. We perform large-scale calculations of the atomic structural properties of these ions to accompany the experiments, and put forward further ions and transition schemes for an efficient testing of the potential variation of the fine-structure constant and the electron-proton mass ratio.

As these trapped-ion experiments are reaching extreme precision in the microwave and optical range, it would be desirable to also achieve high accuracy in a broader regime of the electromagnetic spectrum up to x-ray frequencies. While research with new x-ray free electron lasers has already produced remarkable results, the spectral qualities of these light sources are still far from those of optical lasers. We have developed x-ray pulse shaping schemes which are anticipated to decrease the bandwidth and improve the temporal coherence of the x-ray light. In collaboration with the experimental group of Thomas Pfeifer at the Institute, projects have been started to devise optimal schemes towards the generation of x-ray frequency combs. Such a comb structure would enable precision comb techniques in a broader regime of wavelengths and would improve the precision of x-ray measurements by orders of magnitude. Towards an experimental realisation of such schemes, related line-shape manipulation techniques have already been experimentally investigated in the optical regime. In our collaboration, we have shown how atomic phases generated by an ultrashort pump pulse are encoded in the line shape of transient-absorption spectra, thereby providing a thus far missing link for spectral control. This was demonstrated experimentally, by using intense femtosecond pulses to excite optical transitions in rubidium atoms, and confirmed by comparison with our quantum-theory predictions (see fig. 3).

Nuclear transitions as accurate frequency standards

While usually ions and electrons are the typical candidates for precision studies, electromagnetic transitions in the atomic nucleus open new perspectives due to their increased stability and long decoherence time. For instance, the lowest transition in the 229Th nucleus with frequency in the vacuum ultraviolet range and very narrow linewidth promises enhanced precision and amazing stability. This could be used for instance to determine variations in the value of the fine structure constant or as the basis for incredibly precise nuclear clocks that may soon outperform and replace the present atomic clocks defining the global time standard. The low accuracy level on which the nuclear transition frequency has been determined so far is the main impediment on the way towards a new nuclear frequency standard.

The group led by Adriana Pálffy is investigating theoretically what are the most promising approaches to determine the nuclear transition on the required level of accuracy. A possible approach involves ion detection after the excited nucleus has undergone internal conversion and has ejected one electron from its electronic shell. Once the transition frequency is determined with sub-eV accuracy, coherence properties may be exploited to significantly enhance its precision up to the level required for a frequency standard. For instance, nuclear quantum optics calculations show that by driving the nuclear transition simultaneously with two vacuum ultraviolet laser fields, the precision of the measurement can be improved by up to thirteen orders of magnitude. Coherence effects may provide also an unmistakable signature for the nuclear excitation, which is so far an important unaccomplished goal. The determination of the 229Th transition frequency paves the way for a whole range of applications in the newly emerging field of nuclear quantum optics.

X-ray Quantum Dynamics with Atoms, Ions and Nuclei

High-precision research is increasingly enriched by advanced light sources, pushing the boundaries of physical research to shorter and shorter wavelengths. However, also in its own right x-ray free electron lasers and synchrotron sources allow for novel fundamental research on correlated relativistic quantum dynamics in ions as well as on x-ray quantum optics with nuclei, and on control of nuclear forward scattering.

Highly charged ions in x-ray fields

In highly charged atomic ions, inner-shell electrons experience extremely high nuclear binding fields. The dynamics of electrons becomes relativistic. Also, the electronic probability density has a considerate overlap with the nuclear matter. These properties render highly charged ions an ideal tool for basic research in relativistic atomic structure theory, quantum electrodynamics at extreme fields, and in the study of nuclear contributions. In many-electron ions, relativistic and nuclear effects are intertwined with electron correlation. Because of this complex interplay, accurate theoretical calculations, performed by the group around Zoltán Harman, are necessary to explain the physical phenomena observed in the increasingly accurate experimental spectra.

The knowledge of the structural and dynamical properties of highly charged ions is also necessary for the modeling and diagnostics of astrophysical and fusion plasmas. The spectra of inner-shell transitions are of great relevance for astrophysical line diagnostics of x-ray binaries and stars, aiming at determining physical parameters of the emitter medium such as element decomposition, density, temperature, and velocity. These transitions are predominantly in the x-ray range, therefore, their efficient radiative excitation has been rather challenging until the advent of modern x-ray sources such as free electron lasers and synchrotrons, providing high intensities in the appropriate wavelength range. Natalia Oreshkina and coworkers calculate ionic transition energies, probabilities and cross sections of excitation, photoionization and recombination processes which are scrutinized in electron beam ion trap experiments at the institute. In recent studies, we investigated nonlinear dynamical effects appearing when highly charged iron ions are excited by intense x-ray pulses. We found by time-dependent simulations that for strong x-ray sources, such dynamical effects give a possible resolution of discrepancies between theory and experiment, advocating the use of light-matter interaction models also valid for strong light fields in the quantitative analysis of astrophysical and laboratory spectra. Atomic systems with considerable dynamical effects are further investigated, facilitating an experimental confirmation of the importance of time-dependent simulations.

X-ray quantum optics

Recent advances in existing and upcoming light sources provide access to laser-like light in the x-ray and gamma-ray frequency domain, with a multitude of novel applications across all the natural sciences. Nevertheless, the implementation of advanced laser-coupled quantum systems in the x-ray domain remains a challenge due to basic experimental limitations. We develop methods to overcome these limitations, and to establish x-ray quantum optics. This on the one hand will be required to unleash the full potential of the new x-ray light sources, and on the other hand provides a new platform for quantum optics as a whole.

X-ray slow light with nuclei.

Figure 4: X-ray slow light with nuclei. (a) Schematic setup. A narrow-band absorber imprints echo-like signatures in time onto the x-ray pulse (b). The nuclei embedded in a thin film cavity sample slow down the propagation of the x-ray pulse, inducing a temporal shift. (c) At the detector, the echo-like structures clearly reveal this shift. (d) The delay can be controlled by a detuning of the cavity with respect to the x-ray pulse and reaches almost up to 40ns.

In the group of Jörg Evers, currently the emphasis is on atomic Mössbauer nuclei, which have proven successful in first experiments on x-ray quantum optics. A particularly promising setup is x-ray cavity quantum electrodynamics with Mössbauer nuclei embedded in thin-film cavities probed by near-resonant x-ray light. Over the last years, we developed a sophisticated quantum optical framework for the description of this setting. It allows identifying and separating all physical processes contributing to the recorded signal, and encompasses nonlinear and quantum effects. Based on this model, advanced quantum optical setups can be engineered, exploiting the light polarization and an external magnetic field to control the nuclear level structure.

Recently, we demonstrated electromagnetically induced transparency-based group velocity control of spectrally narrow x-ray pulses (see Fig. 4). In the experiment, subluminal light propagation was achieved by inducing a steep positive linear material dispersion, and verified by direct measurements of the temporal delay imposed on the x-ray pulse. As a result, the experiment demonstrated coherent control, as well as cooperative and cavity enhancements of light-matter interaction in a single setup. It was performed at the nuclear resonance beam line (ID18) of the European Synchrotron Radiation Source (ESRF, Grenoble) in collaboration with an experimental team around Ralf Röhlsberger (DESY, Hamburg). To realize the required material dispersion, a large ensemble of 57Fe nuclei embedded in a thin film planar x-ray cavity was manipulated in such a way that the required multi-level setup was achieved. To enable the direct detection of the temporal pulse delay, we further proposed and implemented a flexible scheme to generate frequency-tunable spectrally narrow x-ray pulses from broadband synchrotron radiation, which will also find other applications in x-ray quantum optics. This method crucially relies on a high-purity x-ray polarimetry setup developed in the group around G. G. Paulus (University and Helmholtz Institute Jena). The experimental results obtained are in good agreement with our quantum optical theory (see Fig. 4), and form an important step towards the exploitation of nonlinear effects with nuclei.

Figure 5: 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 the x-ray qubits. The hyperfine-split nuclear level scheme of 57Fe is illustrated in the inset.

Compared to optical photons, x rays are not plagued by the diffraction limit and can be much better focused. Thus, forwarding optics and quantum information to shorter wavelengths in the x-ray region has the potential of shrinking computing elements in future photonic devices using photons as the information carriers. Prior to the realization of short-wavelength quantum photonic circuits, mastery of x-ray optics and powerful control tools of single-photon wave packet amplitude, frequency, polarization and phase are required. In particular, efficient phase-sensitive photon storage and phase modulation, preferably even for single-photon wave packets, are desirable but so far very challenging. Potentially successful schemes using nuclei as the "cage" to store single x-ray photons were designed theoretically by the group around Adriana Pálffy exploiting a nuclear forward scattering setup together with a time-dependent magnetic field.

Such progress in control of single x-ray quanta would open 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, x-rays are resonant to nuclear transitions, which are very well isolated from the environment and present long coherence times. As a first application, it was theoretically shown that x-ray polarization qubits can be dynamically controlled by nuclear Mössbauer resonances. The control knob is played by nuclear hyperfine magnetic fields, that allow via fast rotations precise processing of single x-ray quanta polarization (see Fig. 5). 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.

Correlated quantum dynamics and laser control

X-ray cavity as an interferometer

Figure 6: (a) X-ray cavity as an interferometer for quantum state tomography. (a) Photons which interact with the nuclei form one virtual arm of the cavity, all other photons the second. (b) The interference between the two arms with very different spectral characteristics gives rise to Fano lineshapes, which enable one to recover the quantum state of the nuclei by recording the spectra as function of the relative phase between the two arms.

A key method to investigate structure and dynamics of physical systems is spectroscopy. Archetype signatures are Fano line shapes, which indicate the presence of different interfering quantum evolution pathways. Over the last years, in a collaboration with the experimental group of Thomas Pfeifer at the institute, we have established Fano resonances and in particular the interplay of its energy- and time domain interpretation as a powerful tool to investigate and also control quantum dynamics. Recently, the group of Jörg Evers has continued this effort in an experiment involving nuclei. In the experiment, a nuclear two-level system was prepared into a tunable superposition of its states, and subsequently the relative phase of this superposition was reconstructed from the emitted x-rays. The two-level system was realized using an ensemble of 57Fe nuclei embedded in a nanoscale planar cavity. We operated the system in such a way that the incident x-rays couple the nuclear ground state to a single collectively excited state of the large ensemble of nuclei, effectively forming a two-level system. The incident x-ray pulses were nearly instantaneous on the nuclear life time scale and prepared the two-level system in a superposition state with variable relative phase. On the much slower time scale of the nuclear life time, the two-level system then emitted its excitation as x-ray light, which enabled us to characterize the initial state prepared by the x-ray pulse. We achieved phase sensitive measurements by interpreting our cavity as an x-ray interferometer, see Fig. 6. The first arm of the interferometer is formed by all possible x-ray pathways through the cavity which do not involve interactions with the nuclei. The second arm comprises all other contributions with one or more interactions with the nuclei. Interference between the two pathways induces Fano lineshapes, which renders the phase of the emitted x-rays accessible. The experiment was performed in a joint collaboration between theoretical and experimental groups at the institute, together with the team of Ralf Röhlsberger (DESY, Hamburg) at the Dynamics Beamline P01 of the synchrotron source PETRA III at DESY. It not only is a first step towards x-ray quantum state tomography. But also, the capability to detect tiny phase changes with high precision, assisted by a precise theoretical model for the different observed line shapes, invites for applications in precision spectroscopy and metrology.

Tunable artificial atoms via

Figure 7: Ensembles of identical atoms arranged in lattices of variable dimension are embedded into an electromagnetic bath which mediates an atom-atom coupling Vr∝1/rα . The resulting collective eigenstates can be utilised for the implementation of an artificial two-level system with tunable decay rate and transition frequency.

An essential feature of our work on x-ray quantum optics is correlated quantum dynamics in large ensembles of nuclei. In order to be able to implement more advanced quantum optical level schemes with nuclei, we have recently proposed a systematic approach to design artificial quantum optical systems in the x-ray regime with limited resources (see Fig. 7). The basic idea is to tailor cooperative effects in large ensembles of nuclei in such a way that effectively, a single artificial quantum system is simulated with collective properties going beyond those of the basic two-level constituents. This way, a single nuclear species can be employed to engineer different quantum optical systems, by controlling cooperative effects. Combining several of such tailored ensembles could enable the realization of tunable multi-level setups. The key step for our results was the development of a comprehensive theoretical framework for single-photon superradiance, which enables us to “reverse engineer” cooperative effects in the sense that we can determine the necessary ensemble properties to achieve a desired artificial quantum system. From a broader perspective, this framework also provides a bridge between the various theoretical and experimental approaches currently pursued to explore cooperative effects in extended media.

Next to our work on x-ray quantum optics, we also studied related cooperative effects in other systems. A particularly interesting platform of much current interest is Rydberg atoms, which feature a controllable long-range interaction between excited atoms. A key effect is the Rydberg blockade, which usually suppresses the fraction of Rydberg excited atoms as compared to the noninteracting case. However, in collaboration with Shannon Whitlock (University of Heidelberg), we could recently identify a parameter regime in which the Rydberg excitation in contrast is enhanced by the interaction. This counter-intuitive enhancement is directly associated to the buildup of many-body coherences. Therefore, more complex theoretical methods taking these many-body correlations into account are required to model the effect. Interestingly, similar challenges will arise in nuclear quantum optics, once x-ray free electron lasers will enable the transition from synchrotron-based experiments with single excitations to strongly correlated nuclear ensembles with many excitations.

Extremely Intense Laser Interactions with Fundamental Quantum Systems

Recent sustained technological progress such as the construction of the Extreme Light Infrastructure (ELI) is opening up the possibility of employing intense laser radiation to trigger or substantially influence physical processes beyond atomic-physics energy scales. Various topics in our division are devoted to laser-driven relativistic quantum dynamics and investigations on high-energy processes within the realm of quantum electrodynamics, nuclear and particle physics in extremely intense laser fields.

Relativistic quantum dynamics in intense laser fields

Figure 8: Schematic description of tunnel ionization of highly charged ions at relativistic laser intensities. The superposition of the Coulomb potential of the atomic core and the electric field of the laser forms a potential barrier (in blue) that the electronic wave packet (in green) may tunnel through into the direction of the laser's electric component. Unlike in nonrelativistic tunneling the ionization potential (in red) becomes position-dependent as a consequence of the laser's magnetic field. Furthermore, while tunneling the wave packet gets shifted under the influence of light pressure into the propagation direction fields (solid green line).

Quantum effects such as wave packet spreading, interference, vacuum fluctuations, spin oscillations and tunneling may be relevant when extremely intense laser pulses are impinging on atomic systems. In particular, a quantum tunneling barrier may be built up in an atom or a hydrogen-like ion by the attractive Coulomb forces that attach the electron to the atomic core and the electric field of a strong laser that pulls the electron away from the core. For highly charged hydrogen-like ions, i.e., an atomic core with a single electron, however, ultra-strong lasers with intensities of the order of 1018 W/cm2 and above are required to achieve measurable ionization probabilities. Such ultra-strong lasers can no longer be treated as pure electric fields; the laser's magnetic field component has to be taken into account, too. Magnetic fields, however, do not fit into the conventional picture of a tunneling barrier. Therefore, it has been argued that the whole tunneling concept may break down in the presence of magnetic fields. In the group around Karen Hatsagortsyan it has been shown, however, that the notion of a tunneling barrier can also be applied in the presence of magnetic fields of ultra-strong lasers via reshaping the potential barrier (see fig. 8). A question that has caused many controversial discussions among physicists and is still debated is how long an electron needs to tunnel through a barrier. Our calculations beyond the conventional quasiclassical approach show that the under-the-barrier dynamics can be represented via, so-called, Wigner trajectories, which answers the fundamental question how the transition occurs from the intrinsically quantum mechanical tunnel barrier to free space classical evolution of the ejected electron. We collaborate on this issue with the local experimental groups around Thomas Pfeifer and Robert Moshammer on a possible experimental proof of the theory based on the Wigner approach.

Figure 9: In the intermediate nonadiabatic regime, i.e. when the laser field varies during tunneling, the electron energy may increase during tunneling yielding a reduced barrier width due to simulatenous multiphoton absorption of laser photons.

While extending the tunneling picture into the regime of ultra-strong lasers, we demonstrated that tunnel ionization of hydrogen-like ions via ultra-strong lasers features two time scales which may be measured indirectly. In particular, a small shift of the point of exit where the electron leaves the tunneling barrier is caused by the presence of a magnetic field. This shift is proportional to the Wigner tunneling time. Furthermore, the magnetic field changes the velocity distribution of the ionized electrons. Ionized electrons escape with a non-zero velocity along the propagation direction of the laser that is proportional to the so-called Keldysh tunneling time. Thus, one can relate these two tunneling times to quantities that are accessible to direct measurements in laboratory experiments. For tunnel ionization of hydrogen-like ions with small atomic numbers lasers of moderate intensities and, therefore, weak magnetic components are sufficient and the consequences of the two tunneling time scales become small. By increasing the laser's intensity the height of the tunneling barrier decreases and the shape of the barrier changes qualitatively. First calculations have given hints that in this regime the tunneling times become relevant again and may be determined experimentally.

We have shown also that the tunneling picture still can be valid in the intermediate domain of strong-field ionization when the laser field varies significantly during the electron´s release from the bound state. We developed an intuitive model for the dynamics in this case which describes the ionization process within a nonadiabatic tunneling picture with a coordinate dependent electron energy due to absorption of photons during tunneling, see fig. 9. The nonadiabatic effects in the elliptically polarized laser field induce a transversal momentum shift of the tunneled electron wave packet at the tunnel exit and a delayed appearance in the continuum. The latter complicates the experimental determination of the pure tunneling delay time.

Figure 10: A relativistic electron is scattered at a counter-propagating tightly focused laser pulse due to ponderomotive forces. The scattering angle depends also on the electron's initial spin orientation. Final momenta of spin-up and and spin-down electrons differ by the angle Δθ, which depends on the applied classical model.

Furthermore, the role of the spin may become essential in intense laser-matter interaction as investigated in the teams around Heiko Bauke and Karen Hatsagortsyan. In a recent study, it has been investigated how the electron's spin influences the motion of a bunch of electrons during the interaction with an intense laser field (see fig. 10). According to classical electrodynamics the motion of an electron is determined by the Lorentz force. This force is induced via an interaction of the electron's charge to the electromagnetic fields. The Lorentz force (in its standard form) does not account for the electron's spin degree of freedom which naturally emerges within the framework of relativistic quantum mechanics and the Dirac equation. Therefore, different classical theories have been put forward and are commonly applied in various branches of physics to describe the relativistic dynamics of electrons by coupled equations for the orbital motion and spin precession. Little, however, is known how well these classical models agree with the more fundamental Dirac theory. The Frenkel model and the classical Foldy-Wouthuysen model with spin-dependent forces (Stern-Gerlach forces) are exemplary benchmarked to the Dirac equation. Both classical theories can lead to different or even contradicting predictions how the Stern-Gerlach forces modify the electron's orbital motion, when the electron moves in strong electromagnetic field configurations of emerging high-intensity laser facilities. In this way, one may evaluate the validity and identify the limits of these classical theories via a comparison with possible experiments to provide a proper description of spin-induced dynamics. Our results indicate that the Foldy-Wouthuysen model is qualitatively in better agreement with the Dirac theory than the widely used Frenkel model.

Next to spin effects during the tunneling ionization process, we have also investigated the spin-resolved ionization dynamics employing the relativistic Coulomb corrected dressed strong field approximation, involving the laser field driven electron spin dynamics in the bound state. Even if an electron is very tightly bound to an ionic core, it may still be crucially affected by a laser field of moderate intensity. The magnitude and scaling of the spin-flip and spin-asymmetry effects at ionization are reduced when the electron spin dynamics in the bound state is taken into account. However, with super-strong laser fields a large spin-flip effect is measurable when employing highly charged ions, initially polarized along the laser propagation direction. The anticipated spin-flip effect is expected to be measurable with modern laser techniques combined with an ion storage facility.

QED and high-energy processes in strong laser fields

The success of QED in vacuum calls for testing this theory under more extreme conditions as those provided, for example, by strong electromagnetic background fields. The typical fields scale of QED is provided by the so-called Schwinger or critical fields of QED: Ecr=1.3×1016 V/cm and Bcr=4.4×1013 G. The team led by Antonino Di Piazza investigates theoretically the possibility of testing QED by means of ultra-intense laser beams in these rather unexplored areas, where processes occur effectively in the presence of strong background fields of the order of the critical ones. A linearly polarized laser field with an amplitude of the order of Ecr, would have a peak intensity Icr of about 4.6×1029W/cm2. Present laser systems are able to produce electromagnetic fields of intensities of the order of 1022 W/cm2 and future facilities like ELI and the Exawatt Center for Extreme Light Studies (XCELS) aim at laser intensities exceeding 1024 W/cm2. Although the intensity Icr seems to be out of reach in the near future, the experimental investigation of strong-field QED, i.e., of QED in the presence of background fields effectively of the order of the critical ones, is still possible. In fact, if an ultra-relativistic electron with energy ε collides head-on with a strong laser beam with electric field amplitude E, the strong-field QED effects depend on the parameter χ≈2(ε/mc2) (E/Ecr), where mc2 is the electron rest energy. Therefore, by employing ultra-relativistic electron beams and intense laser fields, it is possible to render the parameter χ of the order of unity or larger, enter the strong-field QED regime, and test the predictions of QED under such extreme conditions.

The above mentioned ultra-high intensities are obtained experimentally by tightly focusing the laser energy in space and time. However, so far systematic analytical methods to investigate theoretically strong-field QED processes have relied on approximating the background laser field as a plane wave, which allows to solve exactly the corresponding Dirac equation. However, the plane-wave model can only account for the focusing effects in time. In order to describe QED processes in the presence of strong background electromagnetic fields of more complicated spacetime structure also including tight focusing in space, we have developed an efficient method based on the WKB approximation, which has allowed us to determine analytically the electron wave functions and their Feynman propagator in the corresponding fields. These wave functions and the propagator represent the basic tools for a systematic investigation of strong-field QED processes in tightly focused laser beams.

The advent of petawatt-class lasers enables GeV electron beams in strong electromagnetic fields to be studied experimentally using all-optical systems. We have studied several promising configurations that explore previously untested regimes, where the radiation emitted by an electron plays a major role in shaping its dynamics. Generally, detection of various modifications of the radiation spectrum due to radiation reaction requires accurate quantitative measurements. However, we were able to identify signatures of quantum radiation reaction for Compton radiation spectra which are easily detectable in an experiment due to distinct qualitative characteristics of the angle-resolved spectra (angular and spectral bandwidths) in ultrashort laser pulses of variable duration. The quantum radiation reaction can also be harnessed for the generation of ultrashort gamma-ray pulses, which are aspired for time resolved nuclear spectroscopy. We demonstrated the feasibility of brilliant multi-MeV gamma rays of several hundreds of attoseconds duration via nonlinear Compton scattering of an intense laser pulse by a counterpropagating electron beam of much longer duration in the so-called reflection regime. The scheme relies on the nonlinear regime of interaction, the tightly focused driving laser pulse, and the crucial effect of the radiation reaction. The ultrashort duration of the emitted gamma rays determined solely by the intrinsic interaction mechanism.

Figure 11: Unlike typical vacuum flucutations, where virtual electron-positron pair covers a microscopic distance of the order of λC before annihilating, in a high-energy recollision process a virtual electron-positron pair can propagate along a distance of the order of the laser wavelength λL absorbing a relatively large amount of energy from the laser field.

The understanding of the structure of QED in the presence of strong background fields cannot be fully accomplished without a thorough investigation of radiative corrections. Among these we have studied the self-interaction of the electron with its own electromagnetic field (mass operator) and the temporary transformation of a photon into a virtual electron-positron pair (polarization operator). Both analyses have shown qualitatively new effects with respect to the vacuum case. On the one hand, the structure of the mass operator has indicated that, unlike in vacuum, the electron spin dynamics can be substantially altered by the electron self-field. On the other hand, the investigation of the polarization operator has even shown that in the presence of a strong laser beam, virtual electron-positron pairs can propagate along distances which exceed by orders of magnitude the typical microscopic QED lengths of the order of the Compton wavelength λC=3.9×10-11 cm and are comparable with the laser wavelength (of the order of micrometers for optical lasers). As a consequence, the electron and the positron can absorb a very large number of laser photons (of the order of a million for an optical laser of intensity 1022 W/cm2) and the corresponding energy can be potentially exploited to prime high-energy reactions once the virtual pair again annihilates (see Fig. 11). A thorough analysis shows that this process is the analogous in the high-energy domain of the well-known recollision processes in atomic and molecular physics responsible, for example, of high-harmonic generation. However, since the energy absorption from the laser field is mediated here by virtual electrons and positrons, which have the same mass and electric charge, the typical absorbed energies are not as severely bound as in the atomic and molecular scenarios. Thus, such high-energy recollision processes may represent a basic, key ingredient for an efficient, miniaturized version of a high-energy "vacuum" collider.

This already hints to the fact that the fast development of laser technology is bringing two research fields closer, which have been far away from each other so far: laser physics and high-energy physics. Apart from the recent breakthrough about employing lasers to accelerate electrons via wake-field acceleration, we refer here to the possibility of altering high-energy processes directly by means of super-intense laser radiation. After studying how laser-based methods might bound the mass of hypothetical dark matter candidates as axions and their effective coupling constant with the electromagnetic field, more recently we have started investigating the feasibility to detect a possible interaction between neutrinos and intense light. In fact, the recent groundbreaking discovery of neutrinos being massive particles, has opened, among others, the possibility that neutrinos, although being electrically neutral, effectively possess a magnetic moment and may thus interact with electromagnetic radiation. Although we already expect such effects to be small, we find the idea tantalizing, for example, of affecting/controlling via intense laser light at least in principle such high-energy processes like neutrino oscillations and other physical phenomena even belonging to the physics beyond the Standard Model.

Many-body quantum plasmas and laboratory astrophysics with intense lasers

Figure 12: (a) Table-top experimental setup for the production of short, narrow, and ultra-relativistic lepton beams. (b) Possible pair-production mechanisms in the collision of an electron/positron with the solid target. (c) A typical example of positron signal as recorded by the image plate.

It has been recently realized that ultra-intense laser-matter interaction can create analogous physical conditions in Earth-based laboratories as those in violent astrophysical events like supernova explosions and gamma-ray bursts. "Laboratory astrophysics" is one of the youngest branches of astrophysics and one of the most promising, as it allows to investigate in a controlled and repeatable way extreme processes, which otherwise could be studied only indirectly. As an example, electron-positron bunches are emitted as ultra-relativistic jets in different astrophysical scenarios under extreme conditions, like during gamma-ray bursts. Thus, they represent a unique tool to test physics in so-far unexplored regimes also providing unique insights about the early stages of the Universe. In collaboration with the experimental group led by Dr. Gianluca Sarri and Prof. Matt Zepf at the Queen's University Belfast, the group around Antonino Di Piazza has studied both theoretically and experimentally the possibility of generating ultra-relativistic, highly-collimated positron beams (fig. 12c) and also electron-positron bunches having plasma features with a table-top laser facility (fig. 12a). An ultra-relativistic electron beam, generated in an all-optical setup via laser wake-field acceleration, hits a solid target. As a consequence of the complex interaction of the electron beam with the nuclei and the electrons in the target, an ultra-relativistic electron-positron bunch was observed on the rear side of the solid target, with a fraction of electrons and positrons depending on the target thickness. The density of the bunch was found to be sufficiently high that its skin-depth resulted smaller than the bunch transverse size, allowing for collective, i.e., plasma effects.

Figure 13: The presence of even a single electron at the focus of two colliding ultrastrong laser beams can prime an avalanche or cascade process in which abundant amounts of electron-positron pairs and photons are produced.

We have realized that among all possible interactions occurring inside the solid target, only two fundamental quantum electrodynamical processes essentially determine the dynamics: 1) bremsstrahlung of electrons and positrons, and 2) electron-positron photoproduction of photons (fig. 12b), both occurring in the presence of the screened electromagnetic field of the solid target atomic nuclei. Analytical estimations and numerical integrations of the corresponding kinetic equations agree extremely well with the experimental results on the relative population of electrons and positrons in the generated beam. Apart from their importance for astrophysics, the produced lepton beams are inherently synchronized with the strong laser beam, allowing for the possibility of electron-positron interactions with lasers, which, in turn, could be exploited for testing possible matter or antimatter asymmetries in a highly nonlinear regime.

In teams around Matteo Tamburini and Naveen Kumar we have also investigated numerous other dynamical plasma effects by including appropriate quantum features into established classical many-body codes. For example, large amounts of electron-positron pairs arise in the collision of ultrastrong laser pulses in the presence of seed electrons originating, e.g., from a residual gas which is unavoidably present in vacuum chambers (fig. 13). Even a single electron, in fact, accelerated at the focus of a superintense standing wave emits high-energy photons, which interacting again with the standing wave transform into electron-positron pairs, which again emit energetic photons and so on, priming in this way a so-called QED cascade. For this purpose we have developed an accurate numerical plasma code code to study the development of QED cascades and have in particular pointed out the crucial role played in the generation of the cascades by the focal volume of the laser and by the nature of the residual gas, resulting is some situations even more important than the laser intensity.

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