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Archiv: Highlights at the MBI
Highlights 2011
 
Highlights from 2011
 

The onset of electrical resistance

16th December 2011

Researchers at the Max-Born-Institute, Berlin, Germany, observed the extremely fast onset of electrical resistance in a semiconductor by following electron motions in real-time.

When you first learned about electric currents, you may have asked how the electrons in a solid material move from the negative to the positive terminal. In principle, they could move ballistically or ‘fly’ through the solid, without being affected by the atoms or other charges of the material. But this actually never happens under normal conditions because the electrons interact with the vibrating atoms or with impurities. These collisions typically occur within an extremely short time, usually about 100 femtoseconds (10-13 seconds, or a tenth of a trillionth of a second). So the electron motion along the material, rather than being like running down an empty street, is more like trying to walk through a very dense crowd. Typically, electrons move only with a speed of 1m per hour, they are slower than snails.

Though the electrons collide with something very frequently in the material, these collisions do take a finite time to occur. Just like if you are walking through a crowd, sometimes there are small empty spaces where you can walk a little faster for a short distance. If it were possible to follow the electrons on an extremely fast (femtosecond) time scale, then you would expect to see that when the battery is first turned on, for a very short time, the electrons really do fly unperturbed through the material before they bump into anything. This is exactly what scientists at the Max-Born-Institute in Berlin recently did in a semiconductor material and report in the current issue of the journal Physical Review Letters [volume 107, 256602 (2011)]. Extremely short bursts of terahertz light (1 terahertz = 1012 Hz, 1 trillion oscillations per second) were used instead of the battery (light has an electric field, just like a battery) to accelerate optically generated free electrons in a piece of gallium arsenide. The accelerated electrons generate another electric field, which, if measured with femtosecond time resolution, indicates exactly what they are doing. The researchers saw that the electrons travelled unperturbed in the direction of the electric field when the battery was first turned on. About 300 femtoseconds later, their velocity slowed down due to collisions.

In the attached movie, we show a cartoon of what is happening in the gallium arsenide crystal. Electrons (blue balls) and holes (red balls) show random thermal motion before the terahertz pulse hits the sample. The electric field (green arrow) accelerates electrons and holes in opposite directions. After onset of scattering this motion is slowed down and results in a heated electron-hole gas, i.e., in faster thermal motion.
 
The present experiments allowed the researchers to determine which type of collision is mainly responsible for the velocity loss. Interestingly, they found that the main collision partners were not atomic vibrations but positively charged particles called holes. A hole is just a missing electron in the valence band of the semiconductor, which can itself be viewed as a positively charged particle with a mass 6 times higher than the electron. Optical excitation of the semiconductor generates both free electrons and holes which the terahertz bursts, our battery, move in opposite directions. Because the holes have such a large mass, they do not move very fast, but they do get in the way of the electrons, making them slower.
Such a direct understanding of electric friction will be useful in the future for designing more efficient and faster electronics, and perhaps for finding new tricks to reduce electrical resistance.

Contact:

Dr. Michael Wörner, Tel.: +49-30 6392 1470

Prof. Dr. Klaus Reimann, Tel. +49-30 6392 1476

Prof. Dr. Thomas Elsässer, Tel. +49-30 6392 1400

     
 

Two former PhD students of the Max-Born-Institute receive the Carl Ramsauer Prize 2011

14th November 2011

ramsauer-smallDr. Christian Eickhoff and Dr. Wilhelm Kühn are among this year's winners of the Carl Ramsauer Prize of the Physikalische Gesellschaft zu Berlin (PGzB), an award for outstanding PhD work. 

Christian Eickhoff (third from left in the picture) received his doctor degree at the Freie Universität Berlin and Wilhelm Kühn (second from left in the picture) is awarded for his doctoral thesis at Humboldt University. They did their research work at the Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie (MBI). The prizes will be awarded on November 17th, 2011, at the Physics Department of FU Berlin.

Dr. Christian Eickhoff's dissertation was devoted to “Time-resolved two-photon photoemission at the Si(001)-surface: Hot electron dynamics and two-dimensional Fano resonance.” He investigated the (100) surface of silicon, the basic material of the present semiconductor technology. The ongoing miniaturization and increasing efficiency of devices require a basic understanding of the electronic and and dynamic properties of carriers at the Si surface. Eickhoff designed a complex experiment consisting of a laser system which provides widely tunable photon energies, and a ultrahigh vacuum setup including a two-dimensional detector for photoelectrons. He observed the dynamics of optically excited electrons in surface states and in the conduction band of silicon with a time resolution of several tens of femtoseconds (1 fs = 1015 sec). He also investigated the influence of elastic and inelastic scattering processes on energy relaxation and surface recombination. He showed how optical excitation of carriers leads to complex two-dimensional interference phenomena which are accounted for by Fano resonances in the initial and intermediate state. His work explained why the elevated temperature of hot electrons in the conduction band is maintained over an unexpectedly long period of many picoseconds (1 ps = 1012 sec). The extraction of hot electrons may find application for increasing the efficiency of third-generation solar cells.

Dr. Wilhelm Kühn has developed a novel method of nonlinear spectroscopy in the THz frequency domain (1 THz = 1012 Hz) and applied it in basic solid state research. The nonlinear interaction of light and matter is measured in two independent dimensions in time to derive two-dimensional (2D) spectra in the frequency domain. Such spectra give insight into the couplings between different excitations of the system under study and their time evolution. THz oscillations are extremely slow compared to visible light, an oscillation period lasts approximately 250 fs. Focusing the THz beam allows for generating high electric fields (ca. 300 kV/cm) and applying them for the acceleration of charge carriers in solids. With this novel method, Kühn studied the transport properties of electrons in the semiconductor gallium arsenide (GaAs).  He observed that strongly accelerated electrons move without appreciable friction ('ballistic motion'). At very high kinetic energies, however, they slow down and are accelerated into the opposite direction, due to their negative effective mass. In this way, the resulting circular motion of electrons, the so-called Bloch oscillations, was observed for the first time in a bulk crystal.
In a second experiment, Kühn investigated a semiconductor model system displaying an extremely strong coupling of electrons and the crystal lattice. He was able to show the formation of a new particle, the polaron which consists of an electron and a cloud of phonons. His results which were confirmed by theoretical calculations, also demonstrate how and into which channels electron energy is transferred to the crystal lattice.

More Information:

Dr. Christian Eickhoff, Freie Universität Berlin, Tel.: 030 838-56047
Tutor: Prof. Martin Weinelt, Freie Universität Berlin, Tel.: 030 838-56060

Dr. Wilhelm Kühn, Tel.: 0163-7356544
Tutor: Prof. Thomas Elsässer, Max-Born-Institute, Tel.: 030 6392 1401

Physikalische Gesellschaft zu Berlin, Managing Director Prof. Dr. Holger Grahn
Tel.: 030 20377-318

     
 

Imaging the Kramers-Henneberger atom

15th September 2011

Today laser pulses with electric fields comparable to or higher than the electrostatic forces binding valence electrons in atoms and  molecules have become a routine tool with applications in laser acceleration of electrons  and ions, generation of short wavelength emission from plasmas  and clusters, laser fusion, etc. Intense fields are also naturally created during laser filamentation in the air  or due to local field enhancements in the vicinity of metal nanoparticles. One would expect that very intense fields would always lead to fast ionization of atoms or molecules. However, recently the experimental team at the MBI division B observed acceleration of neutral atoms at the rate of 1015 m/sec2 when exposing these atoms to very intense infrared (IR) laser pulses [1]. Thus, substantial fraction of atoms remained stable during the pulse. What is the structure of these exotic laser-dressed atoms surviving superatomic fields? Can it be directly imaged using modern experimental tools? Using ab-initio calculations for potassium atom, we show [2] how the electronic structure of these stable "laser-dressed" atoms can be unambiguously identified and imaged in the angle resolved photoelectron spectra obtained with standard femtosecond laser pulses and velocity map imaging techniques, see e.g. recent experiments [3,4]. We find that the electronic structure of these atoms follows the theoretical predictions made over 40 years ago by W. Henneberger [5], that have so far remained unconfirmed experimentally and thus not generally accepted. We also show that the so-called Kramers-Henneberger (KH) atom is formed and can be detected even before the onset of stabilization regime. Our findings open the way to visualizing and controlling bound electron dynamics in strong laser fields and reexamining its role in various strong field processes, including microscopic description of high order Kerr non linearities and their role in laser filamentation [6].

kh-atom

Fig. 1 Direct visualization of the exotic  Kramers-Henneberger  atom in the photoelectron spectra: Angle and energy-resolved photoelectron spectra for potassium interacting with a 800 nm, 1.4·1013 W/cm2, 65 fs laser pulse (pz and pρ are electron momenta along and perpendicular to the laser polarization).Click to enlarge.

1. Eichmann et al., “Acceleration of neutral atoms in strong short-pulse laser fields”, Nature, 461, 1261-1264 (2009).
2. Felipe Morales, Maria Richter, Serguei Patchkovskii and Olga Smirnova,
“Imaging the Kramers-Henneberger atom”, PNAS, doi:10.1073/pnas.1105916108.
3. Wollenhaupt M., Krug M., Köhler J., Bayer T., Sarpe-Tudoran C. & Baumert T., “Photoelectron angular distributions from strong-field coherent electronic excitation”, Appl. Phys. B, 95, 245  (2009).
4. Schuricke M., Zhu G., Steinmann J., Simeonidis K., Ivanov I., Kheifets A., Grum-Grzhimailo A. N., Bartschat K., Dorn A. & Ullrich J., “ Strong-field ionization of lithium”, Phys. Rev. A, 83, 023413 (2011).
5. W. Henneberger, “Perturbation method for atoms in intense laser fields”, Phys. Rev. Lett., 21,838 (1968).
6. Béjot et al., “Higher-Order Kerr Terms Allow Ionization-Free Filamentation in Gases”, Phys. Rev. Lett., 104, 103903 (2010).

 

Contact: F. Morales, M. Richter, O. Smirnova, Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie

     
 

Electrons and Lattice Vibrations—A Strong Team in the Nano World

4th August 2011

nanokosmos Semiconductor electronics generates, controls, and amplifies electrical current in devices like the transistor. The carriers of the electric current are mobile electrons, which move with high velocities through the crystal lattice of the semiconductor. Doing this, they lose part of their kinetic energy by causing atoms in the lattice to vibrate. In semiconductors like gallium arsenide the positively and negatively charged ions of the crystal lattice vibrate with an extremely short period of 100 fs (1 fs = 10-15 s = 1 billionth part of one millionth of a second). In the microcosm of electrons and ions such vibrations are quantized. This means that the vibrational energy can only be an integer multiple of a vibrational quantum, also known as a phonon. When an electron interacts with the crystal lattice (the so called electron-phonon interaction), energy is transferred from the electron to the lattice in the form of such vibrational quanta.

Berlin researchers report in the latest issue of the scientific journal Physical Review Letters that the strength of the electron-phonon interaction depends sensitively on the electron size, i.e., on the spatial extent of its charge cloud. Experiments in the time range of the lattice vibration show that reducing the electron size leads to an increase of the interaction by up to a factor of 50. This results in a strong coupling of the movements of electrons and ions. Electron and phonon together form a new quasi particle, a polaron.

To visualize this phenomenon, the researchers used a nanostructure made from gallium arsenide and gallium aluminum arsenide, in which the energies of the movements of electrons and ions were tuned to each other. The coupling of both movements was shown by a new optical technique. Several ultrashort light pulses in the infrared excite the system under study. The subsequent emission of light by the moving charge carriers is measured in real time. In this way two-dimensional nonlinear spectra (see Fig.) are generated, which allow the detailed investigation of coupled transitions and the determination of the electron-phonon coupling strength. From the coupling strength one finds the size of the electron cloud, which is just 3-4 nanometers (1 nanometer = 10-9 m = 1 billionth of one meter). Furthermore, this new method shows for the first time the importance of electron-phonon coupling for optical spectra of semiconductors. This is of interest for the development of optoelectronic devices with custom-tailored optical and electric properties.

More information:

Publications: W. Kuehn et al., Phys. Rev. Lett. 107 (6), 067401(5),(2011); J. Phys. Chem. B 115, 5448 (2011).

Contact: Klaus Reimann, M. Wörner, T. Elsässer, Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie, Tel.: +49 30 6392 1470

 
     
 

CRASY Spectroscopy Plays with Quantum Physics

Scientists at the Max-Born-Institute developed a novel spectroscopic method for the simultaneous measurement of molecular structure and composition. They reported their work in Science.

 
In our daily experience, the observation of multiple material properties is a trivial task: Even a small kid will have no trouble to sort his building blocks according to shape and color simultaneously. But in the world of atoms and molecules, every observation must conform to the laws of quantum physics, which state that an observation always changes the observed system. Therefore, simultaneous observation of multiple molecular properties is a tricky proposition.

Scientists can play with a large set of spectroscopic tools when they wish to analyze specific properties of molecules. Rotational spectroscopy, for example, can resolve different molecular structures, because each molecule rotates with a characteristic set of frequencies. Mass spectrometry can determine the mass of a molecule and its fragments, and therefore offers information about the atomic composition of the sample. To date, experiments such as rotational spectroscopy or mass spectrometry were only performed separately. The method of Correlated Rotational Alignment Spectroscopy (CRASY) now allows the simultaneous (“correlated”) measurement of both, atomic composition and molecular structure.

crasy-waage
CRASY experiments resolve mass and structure
of inseparable compounds, such as the depicted CS2 isotopes.

To perform this experiment, the scientists used an experimental trick: They first used an ultra-short laser pulse to initiate a rotational motion in each molecule of a molecular ensemble. After a short time, a second laser pulse was used to remove an electron, i.e., to ionize the molecules. The mass of all molecular ions was then determined in a mass spectrometer. The rotational motion turns the molecules in space (“rotational alignment”), and thereby affects the probability to ionize. When the molecules are allowed to rotate for different amounts of time, the rotational motion is directly reflected in the number of detected molecular ions and the rotational frequencies can be calculated. With the simultaneous determination of rotational frequencies and masses, the researchers overcame the limits of the individual spectroscopic methods and obtained correlated information on molecular structure and atomic composition.

„CRASY experiments contain much more information than conventional spectroscopic experiments, because the information content scales as the product of that in individual experiments”, claims Thomas Schultz from the MBI. This should permit the investigation of increasingly complex systems. The researchers first demonstrated their technique with the analysis of rotational constants for ten isotopes in a natural carbon disulfide sample. In a single experiment, they were able to reproduce all rotational constants in the literature and to determine three additional constants, which were previously inaccessible by spectroscopic measurements. “As compared to conventional rotational spectroscopy, we only require minute amounts of sample and the sample can be highly impure”, continues Schultz. In the future, the researchers plan to use CRASY experiments for the analysis of photochemical reactions in DNA bases.

More information:

Contact: Dr. Thomas Schultz, Max-Born-Institute for Nonlinear Optics and Short Pulse Spectroscopy

 
     
 

Electron Ping Pong in the Nano-world

5th May 2011

PingPong figure1 An international team of researchers succeeded to control and monitor strongly accelerated electrons from nano-spheres with extremely short and intense laser pulses.
When intense laser light interacts with electrons in nanoparticles that consist of many million individual atoms, these electrons can be released and strongly accelerated. Such an effect in nano-spheres of silica was recently observed by an international team of researchers in the Laboratory for Attosecond Physics (LAP) at the Max Planck Institute of Quantum Optics. The researchers report how strong electrical fields (near-fields) build up in the vicinity of the nanoparticles and release electrons. Driven by the near-fields and collective interactions of the charges resulting from ionization by the laser light, the released electrons are accelerated, such that they can by far exceed the limits in acceleration that were observed so far for single atoms. The exact movement of the electrons can be precisely controlled via the electric field of the laser light. The new insights into this light-controlled process can help to generate energetic extreme ultraviolet (XUV) radiation. The experiments and their theoretical modeling, which are described by the scientists in the journal “Nature Physics,” open up new perspectives for the development of ultrafast, light-controlled nano-electronics, which could potentially operate up to one million times faster than current electronics.

Electron acceleration in a laser field is similar to a short rally in a ping pongmatch: a serve, a return and a smash securing the point. A similar scenario occurs when electrons in nanoparticles are hit by light pulses. An international team, in which Prof. Marc Vrakking from the Max-Born-Instiute in Berlin participates, was now successful in observing the mechanisms and aftermath of such a ping pong play of electrons in nanoparticles interacting with strong laser light-fields.
The researchers illuminated silica nanoparticles with a size of around 100 nm with very intense light pulses, lasting around five femtoseconds (one femtosecond is a millionth of a billionth of a second). Such short laser pulses consist of only a few wave cycles. The nanoparticles contained around 50 million atoms each. The electrons are ionized within a fraction of a femtosecond and accelerated by the electric field of the remaining laser pulse. After travelling less than one nanometer away from the surface of the nano-spheres, some of the electrons can be returned to the surface by the laser field to the surface, where they were smashed right back (such as the ping pong ball being hit by the paddle). The resulting energy gain of the electrons can reach very high values. In the experiment electron energies of ca. 60 times the energy of a 700 nm wavelength laser photon (in the red spectral region of light) have been found.
PingPong figure2 For the first time, the researchers could observe and record the direct elastic recollision phenomenon from a nanosystem in detail. The scientists used polarized light for their experiments. With polarized light, the light waves are oscillating only along one axis and not, as with normal light, in all directions. “Intense radiation pulses can deform or destroy nanoparticles. We have thus prepared the nanoparticles in a beam, such that fresh nanoparticles were used for every laser pulse. This was of paramount importance for the observation of the highly energetic electrons”, explains Prof. Eckart Rühl from the Free University of Berlin. The accelerated electrons left the atoms with different directions and different energies. The flight trajectories were recorded by the scientists in a three-dimensional picture, which they used to determine the energies and emission directions of the electrons. “The electrons were not only accelerated by the laser-induced near-field, which by itself was already stronger than the laser field, but also by the interactions with other electrons, which were released from the nanoparticles,” describes Prof. Matthias Kling from the Max Planck Institute of Quantum Optics in Garching about the experiment. Finally, the positive charging of the nanoparticle-surface also plays a role. Since all contributions add up, the energy of the electrons can be very high. “The process is complex, but shows that there is much to explore in the interaction of nanoparticles with strong laser fields,” adds Kling. The electron movements can also produce pulses of extreme ultraviolet light when electrons that hit the surface do not bounce back, but are absorbed releasing photons with wavelengths in the XUV. XUV light is of particular interest for biological and medical research. “According to our findings, the recombination of electrons on the nanoparticles can lead to energies of the generated photons, which are up to seven-times higher than the limit that was so far observed for single atoms,” explains Prof. Thomas Fennel from the University of Rostock. The evidence of collective acceleration of electrons with nanoparticles offers great potential. Matthias Kling believes that “From this may arise new, promising applications in future, light-controlled ultrafast electronics, which may work up to one million times faster than conventional electronics.”

More information:

Contact: Prof. Dr. Marc Vrakking, Max-Born-Institute for Nonlinear Optics and Short Pulse Spectroscopy

Original Publication:

Controlled near-field enhanced electron acceleration from dielectric nanospheres with intense few-cycle laser fields
Sergey Zherebtsov, Thomas Fennel, Jürgen Plenge, Egill Antonsson, Irina Znakovskaya, Adrian Wirth, Oliver Herrwerth, Frederik Süßmann, Christian Peltz, Izhar Ahmad, Sergei A. Trushin, Vladimir Pervak, Stefan Karsch1, Marc J.J. Vrakking, Burkhard Langer, Christina Graf, Mark I. Stockman, Ferenc Krausz, Eckart Rühl, Matthias F. Kling
Nature Physics, 24. April, doi: 10.1038/NPHYS1983


Figure 1:
Mechanism of the acceleration of electrons near silica nanospheres. Electrons (depicted as green particles) are released by the laser field (red wave). These electrons are first accelerated away from the particle surface and then driven back to it by the laser field. After an elastic collision with the surface, they are accelerated away again and reach very high kinetic energies. The figure shows three fsnapshots of the acceleration (from left to right): 1) the electrons are stopped and forced to return to the surface , 2) when reaching the surface, they elastically bounce right back 3) the electrons are accelerated away from the surface of the particle reaching high kinetic energies.

Figure 2:
Amplified near-fields at the poles of a silica nanosphere. The local field on the polar axis is plotted as function of time, where time within the few-cycle wave runs from the lower right to the upper left. The fields show a pronounced asymmetry along the polarization axis of the laser (i.e. along the rims and valleys of the wave). This asymmetry leads to higher energies gained by electrons on one side of the nanoparticle as compared to the other side. For the given example the most energetic electrons are emitted from the backside, where the highest peak field is reached. The energies of the electrons and their emission directions are determined from the experiment.
Courtesy of Christian Hackenberger/LMU

 
     
 

Wilhelm-Ostwald-Prize for Young Scientists 2010

16th February 2011

The Wilhelm-Ostwald-Gesellschaft Grossbothen e.V., the German Bunsen Society for Physical Chemistry, and the German Chemical Society have awarded the Wilhelm-Ostwald-Prize for Young Scientists 2010 to Dr. Ingo Barth (Max-Born-Institut Berlin) for his PhD thesis "Quantum control of electron and nuclear circulation, ring currents, and induced magnetic fields in atoms, ions and molecules by circularly polarized laser pulses".
Ingo Barth did his Ph.D. at the Free University of Berlin in the theoretical chemistry group of Prof. Dr. Jörn Manz. His thesis develops the quantum theoretical basis for excitations of ring currents and induced magnetic fields in molecules or molecular or atomic ions, by means of circularly polarized laser pulses. The main goal is to generate stationary electronic and nuclear ring currents in degenerate excited electronic or vibrational states. The advantage of Barth's new approach is that circularly polarized laser pulses are typically two orders of magnitude more efficient than traditional external magnetic fields. In addition, they allow to control the ring currents, e.g. to drive them along selective bonds. Barth also predicts that the magnetic fields in the center of the ring currents should be huge.
Following the example of the fundamental interdisciplinary work of Ostwald, Barth's PhD thesis provides new links between different fields, including theoretical chemistry, physical chemistry, theoretical physics, experimental physics, and mathematics. The results are also relevant for applications to special molecules of organic chemistry. Barth's thesis has already initiated new directions of research in organic chemistry, physical chemistry, and experimental physics.
It is worth noting that Ingo Barth was born deaf. In fact, among the community of the deaf, he is the first with a Ph.D. in chemistry in Germany. As a teacher of the German Sign Language, he has also built a new bridge to the humanities. Specifically, he has expanded the vocabulary of the German Sign Language by around 500 technical terms of theoretical and physical chemistry.
The prize is endowed with 2,500 Euros and will be awarded during a meeting of the Wilhelm-Ostwald-Gesellschaft in Grossbothen near Leipzig, the workplace of the Nobel Prize laureate for chemistry in 1909, Wilhelm Ostwald, on March 12, 2011. (Location: Wilhelm-Ostwald-Park, 04668 Grossbothen, Grimmaer Str. 25, Haus Werk)

More information:

Contact: Dr. Ingo Barth, Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie

 
     
 

BLiX – the Leibniz-Application Lab of the Max Born Institute at TU Berlin

4th February 2011

Opening BLiX laboratory On February, 4 the official grand opening of BLiX - the "Berlin Laboratory for innovative X-ray Technologies" www.blix.tu-berlin.de - was celebrated at TU (Technische Universität) Berlin. BLiX represents an Application Lab in the knowledge triangle university, research and enterprises and is jointly operated by the Institut für Optik und Atomare Physik of the TU Berlin and the Max-Born Institute. BLiX is a "Leibniz-Applikationslabor" of MBI.
BLiX is attached to the endowed professorship "Analytical X-ray Physics" held by Birgit Kanngießer. The laboratories of BLiX, completely renovated by TU cover an area of about 250 sqm and provide state of the art equipment for users from science and industry. A novel thin disk laser system as a driver laser for a plasma based highly brilliant x-ray source has been developed at MBI and transferred to BLiX. As a result of a BMBF joint research project a laboratory based x-ray microscope will be transferred from MBI to BLiX in the next months. The IOAP will provide a 3D micro XRF system for sensitive samples like cultural heritage objects as well as a novel x-ray spectrometer. In addition BLiX will provide lecture rooms for training and education in the field of x-ray physics. The current BLiX staff consists of 10 employee. It is managed by Dr. W. Malzer (TU) und Dr. H. Stiel (MBI).

More information:

Contact: Dr. Wolfgang Malzer, Technische Universität Berlin
Dr. Holger Stiel, Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie

 

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