56 results on '"Tobias Kampfrath"'
Search Results
2. Terahertz Spin‐to‐Charge Current Conversion in Stacks of Ferromagnets and the Transition‐Metal Dichalcogenide NbSe2
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Lukáš Nádvorník, Oliver Gueckstock, Lukas Braun, Chengwang Niu, Joachim Gräfe, Gunther Richter, Gisela Schütz, Hidenori Takagi, Mahmoud Zeer, Tom S. Seifert, Peter Kubaščík, Avanindra K. Pandeya, Abdelmadjid Anane, Heejun Yang, Amilcar Bedoya‐Pinto, Stuart S. P. Parkin, Martin Wolf, Yuriy Mokrousov, Hiroyuki Nakamura, and Tobias Kampfrath
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spin Hall angles ,spin‐to‐charge‐current conversion ,terahertz emission spectroscopy ,transition‐metal dichalcogenides (TMDCs) ,ultrafast spin current injections ,Physics ,QC1-999 ,Technology - Abstract
Abstract Transition‐metal dichalcogenides (TMDCs) are an aspiring class of materials with unique electronic and optical properties and potential applications in spin‐based electronics. Here, terahertz emission spectroscopy is used to study spin‐to‐charge current conversion (S2C) in the TMDC NbSe2 in ultra‐high‐vacuum‐grown F|NbSe2 thin‐film stacks, where F is a layer of ferromagnetic Fe or Ni. Ultrafast laser excitation triggers an ultrafast spin current that is converted into an in‐plane charge current and, thus, a measurable THz electromagnetic pulse. The THz signal amplitude as a function of the NbSe2 thickness shows that the measured signals are fully consistent with an ultrafast optically driven injection of an in‐plane‐polarized spin current into NbSe2. Modeling of the spin‐current dynamics reveals that a sizable fraction of the total S2C originates from the bulk of NbSe2 with the opposite, negative sign of the spin Hall angle as compared to Pt. By a quantitative comparison of the emitted THz radiation from F|NbSe2 to F|Pt reference samples and the results of ab initio calculations, it is estimated that the spin Hall angle of NbSe2 for an in‐plane polarized spin current lies between ‐0.2% and ‐1.1%, while the THz spin‐current relaxation length is of the order of a few nanometers.
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- 2022
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3. Broadband Terahertz Probes of Anisotropic Magnetoresistance Disentangle Extrinsic and Intrinsic Contributions
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Lukáš Nádvorník, Martin Borchert, Liane Brandt, Richard Schlitz, Koen A. de Mare, Karel Výborný, Ingrid Mertig, Gerhard Jakob, Matthias Kläui, Sebastian T. B. Goennenwein, Martin Wolf, Georg Woltersdorf, and Tobias Kampfrath
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Physics ,QC1-999 - Abstract
Anisotropic magnetoresistance (AMR) is a ubiquitous and versatile probe of magnetic order in contemporary spintronics research. Its origins are usually ascribed to extrinsic effects (i.e., spin-dependent electron scattering), whereas intrinsic (i.e., scattering-independent) contributions are neglected. Here, we measure AMR of polycrystalline thin films of the standard ferromagnets Co, Ni, Ni_{81}Fe_{19}, and Ni_{50}Fe_{50} over the frequency range from dc to 28 THz. The large bandwidth covers the regimes of both diffusive and ballistic intraband electron transport and, thus, allows us to separate extrinsic and intrinsic AMR components. Analysis of the THz response based on Boltzmann transport theory reveals that the AMR of the Ni, Ni_{81}Fe_{19}, and Ni_{50}Fe_{50} samples is of predominantly extrinsic nature. However, the Co thin film exhibits a sizable intrinsic AMR contribution, which is constant up to 28 THz and amounts to more than 2/3 of the dc AMR contrast of 1%. These features are attributed to the hexagonal structure of the Co crystallites. They are interesting for applications in terahertz spintronics and terahertz photonics. Our results show that broadband terahertz electromagnetic pulses provide new and contact-free insights into magnetotransport phenomena of standard magnetic thin films on ultrafast timescales.
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- 2021
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4. Electric and magnetic terahertz nonlinearities resolved on the sub-cycle scale
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Alexej Pashkin, Alexander Sell, Tobias Kampfrath, and Rupert Huber
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Science ,Physics ,QC1-999 - Abstract
Table-top sources of intense multi-terahertz (THz) pulses have opened the door to studies of extreme nonlinearities in the previously elusive mid- to far-infrared spectral regime. We discuss two concepts of fully coherent coupling of phase-locked THz pulses with condensed matter. The first approach demonstrates two-dimensional multi-THz spectroscopy of the semiconductor material InSb. By phase- and amplitude-sensitive detection of the nonlinear optical response, we are able to separate incoherent pump–probe signals from coherent four-wave mixing and reveal extremely non-perturbative nonlinearities. While this class of interactions is mediated by the electric field component of the THz pulse, the second approach is complementary, as it demonstrates that, alternatively, the magnetic THz field may be exploited to selectively control the spin degree of freedom in antiferromagnetic NiO.
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- 2013
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5. Theory of spin-Hall magnetoresistance in the ac terahertz regime
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Piet W. Brouwer, D. A. Reiss, and Tobias Kampfrath
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Coupling ,Physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,500 Naturwissenschaften und Mathematik::530 Physik::539 Moderne Physik ,Magnetoresistance ,Condensed matter physics ,Terahertz radiation ,Magnon ,Magnons ,FOS: Physical sciences ,Conductivity ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,Spin Hall magnetoresistance ,Ferromagnetism ,Ultrafast magnetic effects ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Condensed Matter::Strongly Correlated Electrons ,Spectroscopy ,Spin waves ,Spin-½ - Abstract
In bilayers consisting of a normal metal (N) with spin-orbit coupling and a ferromagnet (F), the combination of the spin-Hall effect, the spin-transfer torque, and the inverse spin-Hall effect gives a small correction to the in-plane conductivity of N, which is referred to as spin-Hall magnetoresistance (SMR). We here present a theory of the SMR and the associated off-diagonal conductivity corrections for frequencies up to the terahertz regime. We show that the SMR signal has pronounced singularities at the spin-wave frequencies of F, which identifies it as a potential tool for all-electric spectroscopy of magnon modes. A systematic change of the magnitude of the SMR at lower frequencies is associated with the onset of a longitudinal magnonic contribution to spin transport across the F-N interface., Comment: 21 pages, 9 figures
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- 2021
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6. High-Throughput Techniques for Measuring the Spin Hall Effect
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Björn Gliniors, Sebastian Wimmer, Lukas Liensberger, Tom Seifert, Mathias Weiler, Oliver Gueckstock, Tobias Kampfrath, Hubert Ebert, and Markus Meinert
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Spin torque ,Terahertz radiation ,FOS: Physical sciences ,General Physics and Astronomy ,Inverse ,Spin Hall effect ,02 engineering and technology ,Metrology ,01 natural sciences ,7. Clean energy ,Ferromagnetic resonance ,Spin generation ,Magnetization ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,0103 physical sciences ,Hall bar ,Spin-orbit coupling ,010306 general physics ,Spin-½ ,Physics ,Condensed Matter - Materials Science ,Condensed Matter - Mesoscale and Nanoscale Physics ,Condensed matter physics ,Spintronics ,Materials Science (cond-mat.mtrl-sci) ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,021001 nanoscience & nanotechnology ,Ferromagnetism ,Terahertz spectroscopy ,Condensed Matter::Strongly Correlated Electrons ,0210 nano-technology - Abstract
The spin Hall effect in heavy-metal thin films is routinely employed to convert charge currents into transverse spin currents and can be used to exert torque on adjacent ferromagnets. Conversely, the inverse spin Hall effect is frequently used to detect spin currents by charge currents in spintronic devices up to the terahertz frequency range. Numerous techniques to measure the spin Hall effect or its inverse were introduced, most of which require extensive sample preparation by multi-step lithography. To enable rapid screening of materials in terms of charge-to-spin conversion, suitable high-throughput methods for measuring the spin Hall angle are required. Here, we compare two lithography-free techniques, terahertz emission spectroscopy and broadband ferromagnetic resonance, to standard harmonic Hall measurements and theoretical predictions using the binary-alloy series Au$_x$Pt$_{1-x}$ as benchmark system. Despite being highly complementary, we find that all three techniques yield a spin Hall angle with approximately the same $x$~dependence, which is also consistent with first-principles calculations. Quantitative discrepancies are discussed in terms of magnetization orientation and interfacial spin-memory loss., Comment: 9 pages, 3 figures
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- 2020
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7. The THz sum-frequency counterparts of stimulated Raman scattering
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Tobias Kampfrath, Dominik M. Juraschek, Alexander Paarmann, and Sebastian F. Maehrlein
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Physics ,Phonon ,02 engineering and technology ,021001 nanoscience & nanotechnology ,01 natural sciences ,Molecular physics ,Photon upconversion ,symbols.namesake ,Polarizability ,Excited state ,0103 physical sciences ,symbols ,010306 general physics ,0210 nano-technology ,Raman spectroscopy ,Excitation ,Raman scattering ,Light field - Abstract
Coherently excited phonons are unique tools to control material properties, drive phase transitions or even access hidden phases on ultrafast time scales. The increasing availability of high-field THz and mid-infrared sources facilitates targeting of specific resonantly driven phonon modes, while leaving the material in its electronic ground state. Nevertheless, this direct excitation is restricted to IR-active modes, whereas purely Ramanactive modes are symmetry protected against even intense resonant THz fields. Thus, for Raman-active modes, nonlinear excitation mechanisms must be employed, which are either mediated through modulation of the electric polarizability or through anharmonicities of the crystal lattice. Respectively, these difference-frequency processes are conventional impulsive stimulated Raman scattering (ISRS) and, more recently, ionic Raman scattering (IRS), which both lack the precise selectivity of resonant excitation. Here, we present the THz sum-frequency counterparts of these two mechanisms, which are more selective, nonimpulsive, and provide direct control over the phonon phase. We demonstrate THz sum-frequency excitation of the archetypal Raman-active phonon in diamond. This two-photon absorption process, the upconversion counter part of ISRS, directly imprints the carrier-envelope phase of the light field onto the coherent phonon’s phase. Additionally, our theoretical formalism based on first-principles calculations in combination with phenomenological modeling predicts an efficient sum-frequency counterpart for IRS, which was subsequently confirmed by other experimental research groups. In summary, we complete the map of photonic and ionic Raman excitation mechanisms with their sumfrequency counterparts, providing a comprehensive guide for selective excitation of coherent phonons and other Raman-active modes by strong THz fields.
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- 2019
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8. Femtosecond formation dynamics of the spin Seebeck effect revealed by terahertz spectroscopy
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Gerhard Jakob, Samridh Jaiswal, Baerbel Rethfeld, Sebastian T. Weber, Piet W. Brouwer, Martin Wolf, Alexey Melnikov, Sebastian F. Maehrlein, Georg Woltersdorf, Joel Cramer, Mathias Kläui, Ilya Razdolski, Markus Münzenberg, Shun Watanabe, Joseph Barker, Chiara Ciccarelli, Tobias Kampfrath, Sebastian T. B. Goennenwein, Lukas Nadvornik, Tom Seifert, Oliver Gueckstock, Barker, Joseph [0000-0003-4843-5516], Ciccarelli, Chiara [0000-0003-2299-3704], Goennenwein, Sebastian TB [0000-0002-5388-700X], Kläui, Mathias [0000-0002-4848-2569], and Apollo - University of Cambridge Repository
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Magnetism ,Terahertz radiation ,0299 Other Physical Sciences ,Science ,General Physics and Astronomy ,FOS: Physical sciences ,Physics::Optics ,02 engineering and technology ,01 natural sciences ,General Biochemistry, Genetics and Molecular Biology ,Article ,Condensed Matter::Materials Science ,Ferrimagnetism ,0103 physical sciences ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,ddc:530 ,010306 general physics ,Spin (physics) ,lcsh:Science ,Terahertz optics ,Physics ,Spin pumping ,Condensed Matter - Materials Science ,Multidisciplinary ,Condensed matter physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Magnon ,Far-infrared laser ,Materials Science (cond-mat.mtrl-sci) ,General Chemistry ,Spintronics ,021001 nanoscience & nanotechnology ,3. Good health ,Terahertz spectroscopy and technology ,lcsh:Q ,Condensed Matter::Strongly Correlated Electrons ,0210 nano-technology - Abstract
Understanding the transfer of spin angular momentum is essential in modern magnetism research. A model case is the generation of magnons in magnetic insulators by heating an adjacent metal film. Here, we reveal the initial steps of this spin Seebeck effect with, 14 pages, 5 figures
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- 2018
9. Complex Terahertz and Direct Current Inverse Spin Hall Effect in YIG/Cu1-xIrx Bilayers Across a Wide Concentration Range
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Martin Jourdan, Tom Seifert, Gerhard Jakob, Alexander Kronenberg, Felix Fuhrmann, Tobias Kampfrath, Joel Cramer, and Mathias Kläui
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Physics ,Spintronics ,Condensed matter physics ,Terahertz radiation ,Mechanical Engineering ,Direct current ,Yttrium iron garnet ,Bioengineering ,02 engineering and technology ,General Chemistry ,021001 nanoscience & nanotechnology ,Condensed Matter Physics ,01 natural sciences ,chemistry.chemical_compound ,chemistry ,0103 physical sciences ,Thermoelectric effect ,Spin Hall effect ,General Materials Science ,Thin film ,010306 general physics ,0210 nano-technology ,Spin-½ - Abstract
We measure the inverse spin Hall effect of Cu1-xIrx thin films on yttrium iron garnet over a wide range of Ir concentrations (0.05 ⩽ x ⩽ 0.7). Spin currents are triggered through the spin Seebeck effect, either by a continuous (dc) temperature gradient or by ultrafast optical heating of the metal layer. The spin Hall current is detected by electrical contacts or measurement of the emitted terahertz radiation. With both approaches, we reveal the same Ir concentration dependence that follows a novel complex, nonmonotonous behavior as compared to previous studies. For small Ir concentrations a signal minimum is observed, whereas a pronounced maximum appears near the equiatomic composition. We identify this behavior as originating from the interplay of different spin Hall mechanisms as well as a concentration-dependent variation of the integrated spin current density in Cu1-xIrx. The coinciding results obtained for dc and ultrafast stimuli provide further support that the spin Seebeck effect extends to terahertz frequencies, thus enabling a transfer of established spintronic measurement schemes into the terahertz regime. Our findings also show that the studied material allows for efficient spin-to-charge conversion even on ultrafast time scales.
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- 2018
10. Selective THz control of magnetic order : new opportunities from superradiant undulator sources
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Ilie Radu, Dmitry Turchinovich, Nilesh Awari, Alina M. Deac, Bertram Green, Sergey Kovalev, Jong Seok Lee, Jan-Christoph Deinert, Zhe Wang, Semyon Germanskiy, Stefano Bonetti, Nenad Stojanovic, Michael Gensch, Min Chen, Stefan Eisebitt, T. V. A. G. de Oliveira, Tobias Kampfrath, and Optical Physics of Condensed Matter
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magnetic order ,multicycle pulses ,terahertz ,THz control ,Electronic, Optical and Magnetic Materials ,Condensed Matter Physics ,Acoustics and Ultrasonics ,Surfaces, Coatings and Films ,Phonon ,Terahertz radiation ,Terahertz ,Physics::Optics ,02 engineering and technology ,7. Clean energy ,01 natural sciences ,Settore FIS/03 - Fisica della Materia ,Coatings and Films ,0103 physical sciences ,Electronic ,ddc:530 ,Optical and Magnetic Materials ,010306 general physics ,High dynamic range ,Physics ,Magnetic order ,business.industry ,Magnon ,Settore FIS/01 - Fisica Sperimentale ,Undulator ,DRIVEN ,Physik (inkl. Astronomie) ,021001 nanoscience & nanotechnology ,PULSES ,Surfaces ,LIGHT ,Coherent control ,Radiator (engine cooling) ,Optoelectronics ,TERAHERTZ EMISSION ,0210 nano-technology ,business - Abstract
Recent advancements of accelerator technology enable the generation of carrier-envelope-phase stable THz pulses with high fields at adjustable high repetition rates. The appropriate choice of THz radiator allows generation of narrow-band, spectrally dense, multicycle THz transients of tunable THz frequency which are ideally suited to selectively excite low-energy excitations such as magnons or phonons. They also allow one to study the frequency dependence of nonresonant THz-field interactions with various order parameters with high dynamic range. In this paper, we discuss the future prospects of this new type of THz light source for studying the coherent control of magnetic order based on recent results.
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- 2018
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11. Antiferromagnetic opto-spintronics
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Manfred Fiebig, Alexey Kimel, Tobias Kampfrath, and Petr Němec
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Magnetometer ,General Physics and Astronomy ,02 engineering and technology ,analytical techniques ,01 natural sciences ,Electromagnetic radiation ,law.invention ,Magnetization ,law ,Spectroscopy of Solids and Interfaces ,0103 physical sciences ,Antiferromagnetism ,characterization ,010306 general physics ,optical spectroscopy ,Physics ,spintronics ,Spintronics ,Spins ,Condensed matter physics ,500 Naturwissenschaften und Mathematik::530 Physik::530 Physik ,021001 nanoscience & nanotechnology ,Magnetic field ,Ferromagnetism ,electronic devices ,spintronic devices ,Condensed Matter::Strongly Correlated Electrons ,0210 nano-technology - Abstract
Control and detection of spin order in ferromagnetic materials is the main principle enabling magnetic information to be stored and read in current technologies. Antiferromagnetic materials, on the other hand, are far less utilized, despite having some appealing features. For instance, the absence of net magnetization and stray fields eliminates crosstalk between neighbouring devices, and the absence of a primary macroscopic magnetization makes spin manipulation in antiferromagnets inherently faster than in ferromagnets. However, control of spins in antiferromagnets requires exceedingly high magnetic fields, and antiferromagnetic order cannot be detected with conventional magnetometry. Here we provide an overview and illustrative examples of how electromagnetic radiation can be used for probing and modification of the magnetic order in antiferromagnets. We also discuss possible research directions that are anticipated to be among the main topics defining the future of this rapidly developing field. An overview of how electromagnetic radiation can be used for probing and modification of the magnetic order in antiferromagnets, and possible future research directions.
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- 2018
12. Terahertz electrical writing speed in an antiferromagnetic memory
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Peter Wadley, Jairo Sinova, K. Olejník, Zdeněk Kašpar, R. P. Campion, Vít Novák, Tom Seifert, Tomas Jungwirth, Petr Kužel, Manuel Baumgartner, Melanie Müller, Tobias Kampfrath, Petr Němec, Joerg Wunderlich, and Pietro Gambardella
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Terahertz radiation ,Physics::Optics ,02 engineering and technology ,Hardware_PERFORMANCEANDRELIABILITY ,01 natural sciences ,Computer Science::Hardware Architecture ,Hertz ,0103 physical sciences ,Hardware_INTEGRATEDCIRCUITS ,Antiferromagnetism ,Atomic lattice ,010306 general physics ,Research Articles ,Spin-½ ,Physics ,Multidisciplinary ,business.industry ,SciAdv r-articles ,021001 nanoscience & nanotechnology ,electrical writing ,Ferromagnetism ,Applied Sciences and Engineering ,writing speed ,Computer Science ,Optoelectronics ,Condensed Matter::Strongly Correlated Electrons ,antiferromagnetic memory ,0210 nano-technology ,business ,Realization (systems) ,Research Article - Abstract
The speed of writing of state-of-the-art ferromagnetic memories is physically limited by an intrinsic gigahertz threshold. Recently, realization of memory devices based on antiferromagnets, in which spin directions periodically alternate from one atomic lattice site to the next has moved research in an alternative direction. We experimentally demonstrate at room temperature that the speed of reversible electrical writing in a memory device can be scaled up to terahertz using an antiferromagnet. A current-induced spin-torque mechanism is responsible for the switching in our memory devices throughout the 12-order-of-magnitude range of writing speeds from hertz to terahertz. Our work opens the path toward the development of memory-logic technology reaching the elusive terahertz band., Science Advances, 4 (3), ISSN:2375-2548
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- 2018
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13. Terahertz Sum-Frequency Excitation of a Raman-Active Phonon
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Tobias Kampfrath, Sebastian F. Maehrlein, Alexander Paarmann, and Martin Wolf
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Terahertz radiation ,Phonon ,FOS: Physical sciences ,Physics::Optics ,General Physics and Astronomy ,02 engineering and technology ,01 natural sciences ,law.invention ,symbols.namesake ,law ,0103 physical sciences ,010306 general physics ,Physics ,Condensed Matter - Materials Science ,Optical lattice ,business.industry ,Magnon ,Materials Science (cond-mat.mtrl-sci) ,021001 nanoscience & nanotechnology ,Laser ,Coherent control ,symbols ,Optoelectronics ,Atomic physics ,0210 nano-technology ,Raman spectroscopy ,business ,Raman scattering - Abstract
In stimulated Raman scattering, two incident optical waves induce a force oscillating at the difference of the two light frequencies. This process has enabled important applications such as the excitation and coherent control of phonons and magnons by femtosecond laser pulses. Here, we experimentally and theoretically demonstrate the so far neglected up-conversion counterpart of this process: THz sum-frequency excitation of a Raman-active phonon mode, which is tantamount to two-photon absorption by an optical transition between two adjacent vibrational levels. Coherent control of an optical lattice vibration of diamond is achieved by an intense terahertz pulse whose spectrum is centered at half the phonon frequency of 40 THz. Remarkably, the carrier- envelope phase of the THz pulse is directly transferred into the phase of the lattice vibration. New prospects in general infrared spectroscopy, action spectroscopy, and lattice trajectory control in the electronic ground state emerge.
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- 2017
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14. Resonant and nonresonant control over matter and light by intense terahertz transients
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Koichiro Tanaka, Keith A. Nelson, and Tobias Kampfrath
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Physics ,business.industry ,Terahertz radiation ,Far-infrared laser ,Fundamental interaction ,Atomic and Molecular Physics, and Optics ,Electronic, Optical and Magnetic Materials ,Magnetic field ,Terahertz spectroscopy and technology ,Photomixing ,Optics ,Optoelectronics ,business ,Terahertz time-domain spectroscopy ,Spectroscopy - Abstract
This article provides an overview and illustrative examples of how the electric and magnetic fields of intense terahertz transients can be used to resonantly, and even nonresonantly, control matter and light. It discusses the fundamental interaction mechanisms of intense terahertz radiation with matter.
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- 2013
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15. Ultrafast photocurrents at the surface of the three-dimensional topological insulator Bi 2 Se 3
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Gregor Mussler, Andrzej Hruban, Martin Wolf, Markus Münzenberg, Lukas Braun, Luca Perfetti, Tobias Kampfrath, Marcin Konczykowski, Thomas Schumann, Fritz-Haber-Institut der Max-Planck-Gesellschaft (FHI), Max Planck Society, PGI-9 and JARA-FIT, Forschungszentrum Ju¨lich, 52425 Ju¨lich, Germany, Institute of Electronic Materials Technology, 01-919 Warsaw, Poland, Laboratoire des Solides Irradiés (LSI), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Institut für Physik [Greifswald], Ernst-Moritz-Arndt-Universität Greifswald, and ANR-13-IS04-0001,IRIDOTI,Dopage par Irradiation des IsolantsTopologiques(2013)
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Electromagnetic field ,Terahertz radiation ,Science ,General Physics and Astronomy ,Physics::Optics ,02 engineering and technology ,terahertz spectroscopy ,01 natural sciences ,Article ,General Biochemistry, Genetics and Molecular Biology ,0103 physical sciences ,Light beam ,[PHYS.COND]Physics [physics]/Condensed Matter [cond-mat] ,010306 general physics ,Spin-½ ,Physics ,Multidisciplinary ,Condensed matter physics ,business.industry ,Scattering ,General Chemistry ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,021001 nanoscience & nanotechnology ,topological insulators ,Orders of magnitude (time) ,Topological insulator ,Optoelectronics ,0210 nano-technology ,business ,Ultrashort pulse - Abstract
Three-dimensional topological insulators are fascinating materials with insulating bulk yet metallic surfaces that host highly mobile charge carriers with locked spin and momentum. Remarkably, surface currents with tunable direction and magnitude can be launched with tailored light beams. To better understand the underlying mechanisms, the current dynamics need to be resolved on the timescale of elementary scattering events (∼10 fs). Here, we excite and measure photocurrents in the model topological insulator Bi2Se3 with a time resolution of 20 fs by sampling the concomitantly emitted broadband terahertz (THz) electromagnetic field from 0.3 to 40 THz. Strikingly, the surface current response is dominated by an ultrafast charge transfer along the Se–Bi bonds. In contrast, photon-helicity-dependent photocurrents are found to be orders of magnitude smaller than expected from generation scenarios based on asymmetric depopulation of the Dirac cone. Our findings are of direct relevance for broadband optoelectronic devices based on topological-insulator surface currents., Surface currents in topological insulators can be controlled by light, but the underlying mechanisms are not well understood. Here, Braun et al. report an ultrafast shift photocurrent at the surface of Ca-doped Bi2Se3, whereas injection currents are much smaller than expected from asymmetric depopulation of the Dirac cone.
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- 2016
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16. Nonlinear Terahertz-Spin Interaction in Thulium Orthoferrite
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Tobias Kampfrath, A. K. Zvezdin, S. Baierl, Matthias Hohenleutner, Alexey Kimel, Rupert Huber, and Rostislav Mikhaylovskiy
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0301 basic medicine ,Physics ,Orthoferrite ,Condensed matter physics ,Spins ,Terahertz radiation ,Magnon ,Physics::Optics ,chemistry.chemical_element ,02 engineering and technology ,021001 nanoscience & nanotechnology ,03 medical and health sciences ,chemistry.chemical_compound ,Optical rectification ,symbols.namesake ,030104 developmental biology ,Thulium ,chemistry ,Spectroscopy of Solids and Interfaces ,Faraday effect ,symbols ,Condensed Matter::Strongly Correlated Electrons ,0210 nano-technology ,Spin (physics) - Abstract
Few cycle THz transients pump electronic transitions coupled to the spin system in thulium orthoferrite to trigger coherent magnons. Exploiting this novel driving mechanism we realize the first nonlinear interaction between THz pulses and spins.
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- 2016
17. Nonlinear spin control by terahertz-driven anisotropy fields
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S. Baierl, A. K. Zvezdin, Matthias Hohenleutner, Rostislav Mikhaylovskiy, Tobias Kampfrath, Alexey Kimel, and Rupert Huber
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Physics ,Zeeman effect ,Spintronics ,Condensed matter physics ,Spins ,Terahertz radiation ,ddc:530 ,Physics::Optics ,02 engineering and technology ,021001 nanoscience & nanotechnology ,530 Physik ,01 natural sciences ,Atomic and Molecular Physics, and Optics ,Electronic, Optical and Magnetic Materials ,Magnetic anisotropy ,symbols.namesake ,Coupling (physics) ,Quantum mechanics ,Spectroscopy of Solids and Interfaces ,0103 physical sciences ,symbols ,010306 general physics ,0210 nano-technology ,Anisotropy ,Spin-½ - Abstract
Future information technologies, such as ultrafast data recording, quantum computation or spintronics, call for ever faster spin control by light1-16. Intense terahertz pulses can couple to spins on the intrinsic energy scale of magnetic excitations5,11. Here, we explore a novel electric dipole-mediated mechanism of nonlinear terahertz-spin coupling that is much stronger than linear Zeeman coupling to the terahertz magnetic field5,10. Using the prototypical antiferromagnet thulium orthoferrite (TmFeO3), we demonstrate that resonant terahertz pumping of electronic orbital transitions modifies the magnetic anisotropy for ordered Fe3+ spins and triggers large-amplitude coherent spin oscillations. This mechanism is inherently nonlinear, it can be tailored by spectral shaping of the terahertz waveforms and its efficiency outperforms the Zeeman torque by an order of magnitude. Because orbital states govern the magnetic anisotropy in all transition-metal oxides, the demonstrated control scheme is expected to be applicable to many magnetic materials.
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- 2016
18. Terahertz-Driven Nonlinear Spin Response of Antiferromagnetic Nickel Oxide
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Manfred Fiebig, Christoph Lange, T.-M. Do, Rupert Huber, Tobias Kampfrath, S. Baierl, Matthias Hohenleutner, J.H. Mentink, L. Braun, Georg Woltersdorf, and Alexander Sell
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Physics ,Condensed matter physics ,Terahertz radiation ,Theory of Condensed Matter ,Magnon ,ddc:530 ,Physics::Optics ,General Physics and Astronomy ,02 engineering and technology ,530 Physik ,021001 nanoscience & nanotechnology ,01 natural sciences ,Magnetic field ,Deflection (physics) ,MAGNETIZATION ,ULTRAFAST ,RESONANCE ,DYNAMICS ,LIGHT ,GENERATION ,WAVES ,ORDER ,FIELD ,0103 physical sciences ,Femtosecond ,Antiferromagnetism ,Condensed Matter::Strongly Correlated Electrons ,010306 general physics ,0210 nano-technology ,Ultrashort pulse ,GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries) ,Spin-½ - Abstract
Terahertz magnetic fields with amplitudes of up to 0.4 Tesla drive magnon resonances in nickel oxide while the induced dynamics is recorded by femtosecond magneto-optical probing. We observe distinct spin-mediated optical nonlinearities, including oscillations at the second harmonic of the 1 THz magnon mode. The latter originate from coherent dynamics of the longitudinal component of the antiferromagnetic order parameter, which are probed by magneto-optical effects of second order in the spin deflection. These observations allow us to dynamically disentangle electronic from lattice-related contributions to magnetic linear birefringence and dichroism---information so far only accessible by ultrafast THz spin control. The nonlinearities discussed here foreshadow physics that will become essential in future subcycle spin switching.
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- 2016
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19. THz quantum optics with dark excitons in Cu 2 O: from stimulated emission to nonlinear population control
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S. Leinß, Dietmar Fröhlich, B. A. Schmid, Robert A. Kaindl, Martin Wolf, Rupert Huber, K. v. Volkmann, Tobias Kampfrath, and Alfred Leitenstorfer
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Quantum optics ,Larmor precession ,Physics ,Rabi cycle ,Phonon ,Terahertz radiation ,Quasiparticle ,Physics::Optics ,Stimulated emission ,Atomic physics ,Condensed Matter Physics ,Terahertz spectroscopy and technology - Abstract
Fundamental quantum optical processes in photogenerated excitons in Cu2O are demonstrated using few-cycle terahertz pulses and field-sensitive electro-optic sampling: (i) In a dilute ensemble of 3p excitons, stimulated terahertz emission from internal transitions to the energetically lower 2s state is observed at a photon energy of 6.6 meV, with a cross section of 10-14 cm2. (ii) An optically dark, dense, and cold 1s-paraexciton gas is prepared by two-photon generation of electron-hole pairs and subsequent phonon cooling. Intense multi-terahertz fields of order MV/cm coherently promote 70% of the quasiparticles from the 1s to the 2p state via a partial internal Rabi oscillation. Electro-optic detection monitors the Larmor precession of the Bloch vector directly in the time domain, with femtosecond resolution. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
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- 2008
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20. Coherent ultrafast spin-dynamics probed in three dimensional topological insulators
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J. Kampmeier, Lukas Braun, Gregor Mussler, Christian Heiliger, Fabio Boschini, Claudia Dallera, Tobias Kampfrath, Ettore Carpene, Markus Münzenberg, Jagadeesh S. Moodera, Michael Czerner, Detlev Grützmacher, Ferhat Katmis, Christian Franz, Maria Mansurova, Massachusetts Institute of Technology. Department of Physics, Massachusetts Institute of Technology. Plasma Science and Fusion Center, Katmis, Ferhat, and Moodera, Jagadeesh
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Physics ,Condensed Matter - Materials Science ,Multidisciplinary ,Condensed matter physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Condensed-matter physics ,Electronics ,photonics and device physics ,Optical materials and structures ,Exchange interaction ,ultrafast spin topological insulators ,Materials Science (cond-mat.mtrl-sci) ,FOS: Physical sciences ,dynamics ,spin ,Article ,Momentum ,Magnetization ,Ultrafast ,Ferromagnetism ,Topological insulator ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Femtosecond ,Orbit (dynamics) ,Ultrafast, spin, dynamics ,Condensed Matter::Strongly Correlated Electrons ,Spin-½ - Abstract
Topological insulators are candidates to open up a novel route in spin based electronics. Different to traditional ferromagnetic materials, where the carrier spin-polarization and magnetization are based on the exchange interaction, the spin properties in topological insulators are based on the coupling of spin- and orbit interaction connected to its momentum. Specific ways to control the spin-polarization with light have been demonstrated: the energy momentum landscape of the Dirac cone provides spin-momentum locking of the charge current and its spin. We investigate a spin-related signal present only during the laser excitation studying real and imaginary part of the complex Kerr angle by disentangling spin and lattice contributions. This coherent signal is only present at the time of the pump-pulses’ light field and can be described in terms of a Raman coherence time. The Raman transition involves states at the bottom edge of the conduction band. We demonstrate a coherent femtosecond control of spin-polarization for electronic states at around the Dirac cone., National Science Foundation (U.S.) (DMR-1207469), United States. Office of Naval Research (N00014-13-1-0301), National Science Foundation (U.S.). Materials Research Science and Engineering Centers (Program) (Award DMR-0819762), National Science Foundation (U.S.). Science and Technology Center for Integrated Quantum Materials (Grant DMR-1231319)
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- 2015
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21. Ultrafast dynamics of fluctuations in high-temperature superconductors far from equilibrium
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C. J. van der Beek, C. Piovera, Tobias Kampfrath, Giulio Biroli, Martin Wolf, Luca Perfetti, Bruno Sciolla, Laboratoire des Solides Irradiés (LSI), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Department of Physics and CMSE, Massachusetts Institute of Technology (MIT), Johannes Gutenberg - Universität Mainz (JGU), Fachbereich Physik [Berlin], Freie Universität Berlin, Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Johannes Gutenberg - Universität Mainz = Johannes Gutenberg University (JGU), Fachbereich Physik [Freie Univeristät Berlin] | Department of Physics [Freie Univeristät Berlin], and De Laborderie, Emmanuelle
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Superconductivity ,Physics ,[PHYS]Physics [physics] ,High-temperature superconductivity ,Condensed matter physics ,Transition temperature ,Condensed Matter - Superconductivity ,General Physics and Astronomy ,Non-equilibrium thermodynamics ,FOS: Physical sciences ,02 engineering and technology ,Conductivity ,021001 nanoscience & nanotechnology ,01 natural sciences ,[PHYS] Physics [physics] ,law.invention ,Superconductivity (cond-mat.supr-con) ,law ,Condensed Matter::Superconductivity ,0103 physical sciences ,Femtosecond ,010306 general physics ,0210 nano-technology ,Scaling ,Ultrashort pulse - Abstract
Despite extensive work on high-temperature superconductors, the critical behavior of an incipient condensate has so far been studied exclusively under equilibrium conditions. Here, we excite Bi2Sr2CaCu2O8+d with a femtosecond laser pulse and monitor the subsequent nonequilibrium dynamics of the mid-infrared conductivity. Our data allow us to discriminate temperature regimes where superconductivity is either coherent, fluctuating or vanishingly small. Above the transition temperature Tc, we make the striking observation that the relaxation to equilibrium exhibits power-law dynamics and scaling behavior, both for optimally and underdoped superconductors. Our findings can in part be modeled using time-dependent Ginzburg-Landau theory and provide strong indication of universality in systems far from equilibrium., Comment: 5 pages, 4 figures
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- 2015
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22. Accessing the fundamentals of magnetotransport in metals with terahertz probes
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Victor Spetter, Andy Thomas, Frederick Casper, H. Grimm, Mathias Kläui, Zuanming Jin, Alexander Tkach, Tobias Kampfrath, Mischa Bonn, and Dmitry Turchinovich
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Physics ,ENERGY-BANDS ,SPECTROSCOPY ,Condensed matter physics ,Scattering ,Terahertz radiation ,SPIN DYNAMICS ,General Physics and Astronomy ,Giant magnetoresistance ,RELAXATION ,Electron ,Physik (inkl. Astronomie) ,GIANT MAGNETORESISTANCE ,Thermal conduction ,DEMAGNETIZATION ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,TRANSPORT ,Condensed Matter::Materials Science ,LAYERED MAGNETIC-STRUCTURES ,Ferromagnetism ,FERROMAGNETIC NICKEL ,Condensed Matter::Strongly Correlated Electrons ,Spin (physics) ,Electron scattering ,TEMPERATURE - Abstract
Spin-dependent conduction in metals underlies all modern magnetic memory technologies, such as giant magnetoresistance (GMR). The charge current in ferromagnetic transition metals is carried by two non-mixing populations of sp-band Fermi-level electrons: one of majority-spin and one of minority-spin. These electrons experience spin-dependent momentum scattering with localized electrons, which originate from the spin-split d-band. The direct observation of magnetotransport under such fundamental conditions, however, requires magnetotransport measurements on the same timescale as the electron momentum scattering, which takes place in the sub-100 fs regime. Using terahertz electromagnetic probes, we directly observe the magnetotransport in a metallic system under the fundamental conditions, and determine the spin-dependent densities and momentum scattering times of conduction electrons. We show that traditional measurements significantly underestimate the spin asymmetry in electron scattering, a key parameter responsible for effects such as GMR. Furthermore, we demonstrate the possibility of magnetic modulation of terahertz waves, along with heat- and contact-free GMR readout using ultrafast terahertz signals. Terahertz radiation is used to directly probe magnetotransport in metallic multilayers on the timescale of electron momentum scattering—the fundamental conditions of Nevill Mott’s model of spin-dependent conduction in metals.
- Published
- 2015
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23. Comprehensive view on ultrafast dynamics of ferromagnetic films
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Rainer G. Ulbrich, Tobias Kampfrath, W. Felsch, P. Guderian, M. Lüttich, Markus Münzenberg, Marija Djordjevic, Jagadeesh S. Moodera, and P. Moschkau
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Physics ,Magnetization dynamics ,Condensed matter physics ,Spin polarization ,Spin engineering ,02 engineering and technology ,Electron ,021001 nanoscience & nanotechnology ,Condensed Matter Physics ,01 natural sciences ,Ferromagnetism ,Spin wave ,0103 physical sciences ,Spin Hall effect ,Spinplasmonics ,010306 general physics ,0210 nano-technology - Abstract
The relaxation mechanisms in magnetic thin films studied in all-optical pump probe experiments involve electrons, spin and lattice as well as the different couplings in between those. With this technique, the evolution of the electron and spin dynamics can be studied directly in real time from 100 fs to ns timescale. We give a comprehensive view of the current understanding of the processes involved. The details of the spin relaxation-mechanisms on the ultrafast and Landau-Lifshitz-Gilbert time scales are still unknown. Time-resolved reflectivity measurements on ferromagnetic transition metal films give an insight into the specific electronic and lattice relaxation processes. The time-resolved Kerr rotation measurements address the demagnetization and relaxation of the spin system. The demagnetization of the spin system observed in general is strongly coupled to the relaxation mechanism of the electrons, thus follows almost instantaneously the dynamics of the electron system. On the longer time scale, coherent magnetization dynamics is described by the Landau-Lifshitz-Gilbert equation and results in a precession with periods of 50 to 200 ps typical for ferromagnets. The full understanding of the mechanisms will be only accessible by a complete analysis of the interaction between electrons, lattice and spin system. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
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- 2006
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24. Probing ultra-fast processes with high dynamic range at 4th-generation light sources: Arrival time and intensity binning at unprecedented repetition rates
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Sebastian F. Maehrlein, Bertram Green, Tobias Kampfrath, Sergey Kovalev, N. Stojanovic, Michael Gensch, Alan Fisher, and Torsten Golz
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Photon ,Terahertz radiation ,02 engineering and technology ,01 natural sciences ,7. Clean energy ,Experimental Methodologies ,law.invention ,ultra-fast ,ARTICLES ,Optics ,law ,0103 physical sciences ,lcsh:QD901-999 ,ddc:530 ,Sensitivity (control systems) ,010306 general physics ,Instrumentation ,Spectroscopy ,High dynamic range ,Physics ,high field THz ,Radiation ,business.industry ,Dynamic range ,021001 nanoscience & nanotechnology ,Condensed Matter Physics ,Laser ,lcsh:Crystallography ,0210 nano-technology ,business ,Ultrashort pulse ,Excitation - Abstract
Understanding dynamics on ultrafast timescales enables unique and new insights into important processes in the materials and life sciences. In this respect, the fundamental pump-probe approach based on ultra-short photon pulses aims at the creation of stroboscopic movies. Performing such experiments at one of the many recently established accelerator-based 4th-generation light sources such as free-electron lasers (FELs) or superradiant THz sources allows an enormous widening of the accessible parameter space for the excitation and/or probing light pulses. Compared to table-top devices, critical issues of this type of experiment are fluctuations of the timing between the accelerator and external laser systems and intensity instabilities of the accelerator-based photon sources. Existing solutions have so far been only demonstrated at low repetition rates and/or achieved a limited dynamic range in comparison to table-top experiments, while the 4th generation of accelerator-based light sources is based on superconducting radio-frequency (SRF) technology which enables operation at MHz or even GHz repetition rates. In this article, we present the successful demonstration of ultra-fast accelerator-laser pump-probe experiments performed at an unprecedentedly high repetition rate in the few-hundred-kHz regime and with a currently achievable optimal time resolution of 13 femtoseconds (fs) (rms). Our scheme, based on the pulse-resolved detection of multiple beam parameters relevant for the experiment, allows us to achieve an excellent sensitivity in real-world ultra-fast experiments, as demonstrated for the example of THz-field-driven coherent spin precession.
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- 2017
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25. THz Spin Dynamics: Phonon-Induced Spin Order
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Rupert Huber, Alexander Sell, Kyung Wan Kim, Alfred Leitenstorfer, Tobias Kampfrath, Alexej Pashkin, and Michael Porer
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Physics ,Zeeman effect ,Spin polarization ,Condensed matter physics ,Phonon ,Magnon ,Physics::Optics ,Zero field splitting ,symbols.namesake ,Spin wave ,symbols ,Condensed Matter::Strongly Correlated Electrons ,Quantum spin liquid ,Spin-½ - Abstract
Two concepts of ultrafast spin control at THz frequencies are presented: Exploiting a coherent phonon mode we transiently induce and destroy spin order in pnictides at a frequency as high as 5.5 THz. Strong THz magnetic fields control magnons in antiferromagnetic NiO coherently by direct Zeeman coupling.
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- 2014
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26. Ultrafast Spin Precession and Transport Controlled and Probed with Terahertz Radiation
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Marco Battiato, Alexander Sell, Markus Münzenberg, Tobias Kampfrath, Rupert Huber, Frank Freimuth, Martin Wolf, Peter M. Oppeneer, and Alfred Leitenstorfer
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Physics ,Zeeman effect ,Spintronics ,Condensed matter physics ,010308 nuclear & particles physics ,Terahertz radiation ,Physics::Optics ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,01 natural sciences ,Terahertz spectroscopy and technology ,3. Good health ,symbols.namesake ,Nuclear magnetic resonance ,Spin wave ,0103 physical sciences ,Spin Hall effect ,symbols ,Precession ,Condensed Matter::Strongly Correlated Electrons ,010306 general physics ,Spin (physics) ,Ultrashort pulse ,Computer Science::Databases - Abstract
We present examples of how terahertz (THz) electromagnetic transients can be used to control spin precession in antiferromagnets (through the THz Zeeman torque) and to probe spin transport in magnetic heterostructures (through the THz inverse spin Hall effect), on femtosecond time scales.
- Published
- 2014
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27. Intense terahertz pulses: probing and controlling fundamental motions of electrons, spins and ions
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Tobias Kampfrath
- Subjects
Physics ,Spins ,Terahertz radiation ,Physics::Optics ,Electron ,Atomic physics ,Spin (physics) ,Terahertz time-domain spectroscopy ,Electromagnetic radiation ,Terahertz spectroscopy and technology ,Ion - Abstract
Terahertz radiation permits resonant and sensitive probing of electron transport, spin precession and ion vibration in solids. Recently developed sources of strong-field terahertz pulses even allow one to gain control over these fundamental modes.
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- 2014
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28. Subcycle control of terahertz waveform polarization using all-optically induced transient metamaterials
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Martin Wolf, Thirumalai Venkatesan, Jan Nötzold, N. Kamaraju, Linke Jian, Surajit Saha, Tobias Kampfrath, Andrea Rubano, R. Kramer Campen, Kamaraju, N., Rubano, Andrea, Jian, Linke, Saha, Surajit, Venkatesan, T., Nã¶tzold, Jan, Kramer Campen, R., Wolf, Martin, and Kampfrath, Tobias
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Physics ,Terahertz gap ,business.industry ,Terahertz radiation ,Electronic, Optical and Magnetic Material ,Metamaterial ,Physics::Optics ,FOS: Physical sciences ,Terahertz metamaterial ,Polarizer ,Polarization (waves) ,Atomic and Molecular Physics, and Optics ,Electronic, Optical and Magnetic Materials ,Terahertz spectroscopy and technology ,law.invention ,Photomixing ,Optics ,law ,Terahertz polarization control ,Optoelectronics ,business ,Ultrashort pulse ,Physics - Optics ,Optics (physics.optics) ,Terahertz optic - Abstract
Coherent radiation with frequencies ranging from 0.3 to 30 THz has recently become accessible by femtosecond laser technology. Terahertz (THz) waves have already found many applications in spectroscopy and imaging, and they can be manipulated using static optical elements such as lenses, polarizers, and filters. However, ultrafast modulation of THz radiation is required as well, for instance in short-range wireless communication or for preparing shaped THz transients for coherent control of numerous material excitations. Here, we demonstrate an all-optically created transient metamaterial that permits to manipulate the polarization of THz waveforms with sub-cycle precision. The polarization-modulated pulses are potentially interesting for controlling elementary motions such as vibrations of crystal lattices, rotations of molecules, and the precession of spins., Comment: 14 pages, 7 Figures
- Published
- 2014
29. Ultrafast terahertz spin dynamics: from phonon-induced spin order to coherent magnon control
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Alexej Pashkin, Martin Wolf, Alfred Leitenstorfer, Alexander Sell, Tobias Kampfrath, Christian Bernhard, Rupert Huber, Kyung Wan Kim, Jure Demsar, and Michael Porer
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Physics ,Zeeman effect ,Condensed matter physics ,Terahertz radiation ,Phonon ,Magnetism ,Magnon ,Physics::Optics ,symbols.namesake ,Spin wave ,Femtosecond ,symbols ,Condensed Matter::Strongly Correlated Electrons ,Ultrashort pulse - Abstract
Ultrashort pulses in the terahertz (THz) spectral range allow us to study and control spin dynamics on time scales faster than a single oscillation cycle of light. In a first set of experiments, we harness an optically triggered coherent lattice vibration to induce a transient spin-density wave in BaFe2As2, the parent compound of pnictide superconductors. The time-dependent multi-THz response of the non-equilibrium phases shows that the ordering quasi-adiabatically follows a coherent lattice oscillation at a frequency as high as 5.5 THz. The results suggest important implications for unconventional superconductivity. In a second step, we utilize the magnetic field component of intense THz transients to directly switch on and off coherent spin waves in the antiferromagnetic nickel oxide NiO. A femtosecond optical probe traces the magnetic dynamics in the time domain and verifies that the THz field addresses spins selectively via Zeeman interaction. This concept provides a universal ultrafast handle on magnetic excitations in the electronic ground state.
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- 2013
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30. Ultrafast tilting of the dispersion of a photonic crystal and adiabatic spectral compression of light pulses
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Laurens Kuipers, Thomas F. Krauss, Daryl M. Beggs, Tobias Kampfrath, European Commission, EPSRC, University of St Andrews. School of Physics and Astronomy, and University of St Andrews. Microphotonics and Photonic Crystals Group
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Shadow mask ,Materials science ,Silicon ,Superlattice ,Spectral compression ,General Physics and Astronomy ,FOS: Physical sciences ,chemistry.chemical_element ,Physics::Optics ,Slow light ,Flattening ,Optics ,Adiabatic process ,QC ,Photonic crystal ,Physics ,business.industry ,QC Physics ,chemistry ,Femtosecond ,Optoelectronics ,business ,Ultrashort pulse ,Refractive index ,Bandwidth-limited pulse ,Optics (physics.optics) ,Physics - Optics - Abstract
We demonstrate, by theory and experiment, the ultrafast tilting of the dispersion curve of a photonic-crystal waveguide following the absorption of a femtosecond pump pulse. By shaping the pump-beam cross section with a nanometric shadow mask, different waveguide eigenmodes acquire different spatial overlap with the perturbing pump, leading to a local flattening of the dispersion by up to 11%. We find that such partial mode perturbation can be used to adiabatically compress the spectrum of a light pulse traveling through the waveguide. Publisher PDF
- Published
- 2012
31. Thermalization of photoexcited carriers in bismuth investigated by time-resolved terahertz spectroscopy and ab initio calculations
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Nathalie Vast, Tobias Kampfrath, Christian Frischkorn, Luca Perfetti, Paola Gava, Jérôme Faure, Christian R. Ast, Martin Wolf, Iurii Timrov, Laboratoire des Solides Irradiés (LSI), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Fachbereich Physik [Freie Univeristät Berlin] | Department of Physics [Freie Univeristät Berlin], Freie Universität Berlin, Fritz-Haber-Institut der Max-Planck-Gesellschaft (FHI), Max Planck Society, Max-Planck-Institut für Festkörperforschung, Max-Planck-Gesellschaft, Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), and Fachbereich Physik [Berlin]
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Physics ,chemistry.chemical_element ,02 engineering and technology ,021001 nanoscience & nanotechnology ,Condensed Matter Physics ,01 natural sciences ,Electronic, Optical and Magnetic Materials ,Bismuth ,Terahertz spectroscopy and technology ,Thermalisation ,Nuclear magnetic resonance ,chemistry ,Ab initio quantum chemistry methods ,0103 physical sciences ,Atomic physics ,010306 general physics ,0210 nano-technology - Abstract
International audience; The charge carrier dynamics of photoexcited bismuth generates a Drude response that evolves over time. Our data show that the plasma frequency of bismuth displays an initial increase and a subsequent decay. We have performed ab initio calculations on bulk bismuth within the density functional theory and show that this peculiar behavior is due to local extrema in the valence and conduction bands. It follows that most of the carriers first accumulate in these extrema and reach the Fermi level only 0.6 ps after the photoexcitation. © 2012 American Physical Society.
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- 2012
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32. Maximizing the amplitude of coherent phonons with shaped laser pulses
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Toru Shimada, Tobias Kampfrath, Martin Wolf, and Christian Frischkorn
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Physics ,Oscillation ,Phonon ,Phase (waves) ,General Physics and Astronomy ,Laser ,law.invention ,Optical rectification ,Amplitude ,law ,Quantum electrodynamics ,Quantum mechanics ,Pulse wave ,Excitation - Abstract
We perform model calculations of coherent lattice vibrations in solids driven by ultrashort laser pulses. In order to maximize the amplitude of the coherent phonon in the time domain, an evolutionary algorithm optimizes the driving laser field. We find that only a Fourier-limited single pulse yields the maximum phonon amplitude, irrespective of the actual physical excitation mechanism (impulsive or displacive). This result is in clear contrast to the widespread intuition that excitation by a pulse train in phase with the oscillation leads to the largest amplitude of an oscillator. We rationalize this result by an intuitive model and discuss implications for other nonlinear processes such as optical rectification.
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- 2012
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33. Sub-cycle THz nonlinear optics mediated by electric and magnetic field coupling
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Christian Schmidt, Martin Wolf, F. Junginger, Alexander Sell, Alexej Pashkin, Alfred Leitenstorfer, Rupert Huber, Olaf Schubert, Boris Mayer, Tobias Kampfrath, Daniele Brida, and S. Mahrlein
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Physics ,business.industry ,Terahertz radiation ,Indium antimonide ,Physics::Optics ,Nonlinear optics ,Optical field ,Terahertz spectroscopy and technology ,Magnetic field ,Condensed Matter::Materials Science ,chemistry.chemical_compound ,Magnetization ,chemistry ,Electric field ,Optoelectronics ,business - Abstract
Intense THz electric and magnetic fields are exploited to drive extreme nonlinearities in semiconductors, magnetically ordered solids, and molecular systems. Electro-optic sampling allows us to perform field-sensitive two-dimensional spectroscopy, including four- and six-wave mixing in indium antimonide, as well as THz bias — optical probe experiments beyond static dielectric breakdown fields. Finally, we introduce a novel scheme for coherent spin control in antiferromagnetic nickel oxide mediated by the THz magnetic field component.
- Published
- 2011
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34. Light-matter interaction in photonic crystal nanocavities
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Matteo Burresi, S. Noda, B.S. Song, Laurens Kuipers, Jord C. Prangsma, Tobias Kampfrath, and D. van Oosten
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Physics ,Mode volume ,business.industry ,Near-field optics ,Measure (physics) ,Physics::Optics ,Metamaterial ,Yablonovite ,Optics ,Polarizability ,Optoelectronics ,business ,Nanoring ,Photonic crystal - Abstract
Summary form only given. Due to their small mode volume, photonic crystal nanocavities are an ideal tool to study enhanced light-matter interactions. As the cavity resonance and Q-factor will change under the influence of objects brought into its evanescent field, the cavity can be used to measure the polarizability of those objects. We show for the first time that a photonic crystal nanocavities, can even be used to measure the magnetic polarizability of a metal nanoring. This is the first measurement of magnetic light-matter interaction at optical frequencies.
- Published
- 2011
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35. Experimental observation of evanescent modes at the interface to slow-light photonic crystal waveguides
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Yuri S. Kivshar, C. Martijn de Sterke, Andrey A. Sukhorukov, Laurens Kuipers, Tobias Kampfrath, Sangwoo Ha, Marko Spasenović, Thomas F. Krauss, Thomas P. White, and University of St Andrews. School of Physics and Astronomy
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Physics ,Field intensity ,business.industry ,Physics::Optics ,Slow light ,Atomic and Molecular Physics, and Optics ,Laser optics ,Marie curie ,Optics ,QC Physics ,Photonic crystal waveguides ,Research council ,Evanescent mode ,business ,QC ,Photonic crystal - Abstract
We experimentally study the fields close to an interface between two photonic crystal waveguides that have different dispersion properties. After the transition from a waveguide in which the group velocity of light is v(g) similar to c/10 to a waveguide in which it is v(g) similar to c/100, we observe a gradual increase in the field intensity and the lateral spreading of the mode. We attribute this evolution to the existence of a weakly evanescent mode that exponentially decays away from the interface. We compare this to the situation where the transition between the waveguides only leads to a minor change in group velocity and show that, in that case, the evolution is absent. Furthermore, we apply novel numerical mode extraction techniques to confirm experimental results. (C) 2011 Optical Society of America Publisher PDF
- Published
- 2011
36. Multi-THz fields exceeding 100 MV/cm: an ultrabroadband source for sub-cycle nonlinear optics
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Daniele Brida, Tobias Kampfrath, Rupert Huber, F. Junginger, S. Mahrlein, Alfred Leitenstorfer, Bernhard Mayer, Martin Wolf, Giulio Cerullo, Christian Schmidt, Marco Marangoni, Olaf Schubert, and Alexander Sell
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Physics ,business.industry ,Terahertz radiation ,Physics::Optics ,Nonlinear optics ,Polarization (waves) ,Laser ,law.invention ,Optics ,Coherent control ,law ,Electric field ,Femtosecond ,Optoelectronics ,business ,Excitation - Abstract
We present a table-top source of extremely intense multi-THz transients covering the spectral region between 0.1 and 140 THz. Electric field amplitudes of up to 108 MV/cm and pulse durations as short as a single cycle are demonstrated with our hybrid Er:fiber-Ti:sapphire laser system. All THz waveforms are electro-optically detected. This source opens the door to a regime of non-perturbative THz nonlinearities in condensed matter. First examples range from coherent control of excitons, via a breakdown of the power expansion of the nonlinear polarization in bulk semiconductors to twodimensional multi-wave mixing and direct femtosecond spin control by magnetic field excitation.
- Published
- 2011
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37. Coherent terahertz control of antiferromagnetic spin waves
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Alexander Sell, Rupert Huber, Martin Wolf, S. Mahrlein, Alexej Pashkin, Thomas Dekorsy, Manfred Fiebig, Gregor Klatt, Alfred Leitenstorfer, and Tobias Kampfrath
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Physics ,Zeeman effect ,Spectroscopy ,Ultrafast photonics ,Terahertz optics ,Condensed matter physics ,Spin polarization ,Terahertz radiation ,Physics::Optics ,530 Physik ,Atomic and Molecular Physics, and Optics ,Electronic, Optical and Magnetic Materials ,Terahertz spectroscopy and technology ,symbols.namesake ,Spin wave ,Electric field ,symbols ,ddc:530 ,Ultrashort pulse ,Spin-½ - Abstract
Ultrafast charge and spin excitations in the elusive terahertz regime1,2 of the electromagnetic spectrum play a pivotal role in condensed matter3,4,5,6,7,8,9,10,11,12,13. The electric field of free-space terahertz pulses has provided a direct gateway to manipulating the motion of charges on the femtosecond timescale6,7,8,9. Here, we complement this process by showing that the magnetic component of intense terahertz transients enables ultrafast control of the spin degree of freedom. Single-cycle terahertz pulses switch on and off coherent spin waves in antiferromagnetic NiO at frequencies as high as 1 THz. An optical probe pulse with a duration of 8 fs follows the terahertz-induced magnetic dynamics directly in the time domain and verifies that the terahertz field addresses spins selectively by means of the Zeeman interaction. This concept provides a universal ultrafast means to control previously inaccessible magnetic excitations in the electronic ground state. Researchers report the direct observation of ultrafast magnetic dynamics using the magnetic component of highly intense terahertz wave pulses with a time resolution of 8 fs. This concept provides a universal ultrafast method of visualizing magnetic excitations in the electronic ground state.
- Published
- 2011
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38. Magnetoelectric point scattering theory for metamaterial scatterers
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Tobias Kampfrath, Ivana Sersic, Christelle Tuambilangana, and A. Femius Koenderink
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Physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Condensed matter physics ,Scattering ,FOS: Physical sciences ,Metamaterial ,Physics::Optics ,Condensed Matter Physics ,Physical optics ,Electronic, Optical and Magnetic Materials ,Split-ring resonator ,Dipole ,Reciprocity (electromagnetism) ,Quantum electrodynamics ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Scattering theory ,Anisotropy ,Optics (physics.optics) ,Physics - Optics - Abstract
We present a new, fully analytical point scattering model which can be applied to arbitrary anisotropic magneto-electric dipole scatterers, including split ring resonators (SRRs), chiral and anisotropic plasmonic scatterers. We have taken proper account of reciprocity and radiation damping for electric and magnetic scatterers with any general polarizability tensor. Specifically, we show how reciprocity and energy balance puts constraints on the electrodynamic responses arbitrary scatterers can have to light. Our theory sheds new light on the magnitude of cross sections for scattering and extinction, and for instance on the emergence of structural chirality in the optical response of geometrically non-chiral scatterers like SRRs. We apply the model to SRRs and discuss how to extract individual components of the polarizability matrix and extinction cross sections. Finally, we show that our model describes well the extinction of stereo-dimers of split rings, while providing new insights in the underlying coupling mechanisms., 12 pages, 3 figures
- Published
- 2011
39. Intense terahertz fields: electric and magnetic nonlinearities on the sub-cycle scale
- Author
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Rupert Huber, Bernhard Mayer, Tobias Kampfrath, Marco Marangoni, Daniele Brida, Giulio Cerullo, F. Junginger, Martin Wolf, Alfred Leitenstorfer, Alexander Sell, and Olaf Schubert
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Physics ,Scale (ratio) ,business.industry ,Terahertz radiation ,Cavity quantum electrodynamics ,Laser ,Magnetic field ,law.invention ,Optics ,Far infrared ,law ,Electric field ,Optoelectronics ,business ,Bose–Einstein condensate - Abstract
High-intensity single- and few-cycle transients covering the mid and far infrared are generated and electro-optically monitored by a passively CEP-locked laser. These pulses drive strong nonlinearities via electric and magnetic field coupling.
- Published
- 2011
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40. Terahertz quantum optics with solid-state systems
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Giorgio Biasiol, Cristiano Ciuti, S. De Liberato, Aji A. Anappara, Lucia Sorba, Alexander Sell, Rupert Huber, K. v. Volkmann, G. Gunter, Tobias Kampfrath, Martin Wolf, S. Leinß, A. Tredicucci, Alfred Leitenstorfer, Leitenstorfer, A., Huber, R., Sell, A., Anappara, A. A., Gunter, G., Leins, S., Volkmann, K. V., Kampfrath, T., Wolf, M., De Liberato, S., Ciuti, C., Biasiol, G., Sorba, L., and Tredicucci, Alessandro
- Subjects
Physics ,Quantum optics ,Amplitude ,Optics ,business.industry ,Terahertz radiation ,Electric field ,Optoelectronics ,Sensitivity (control systems) ,Photonics ,business ,Quantum ,Ultrashort pulse - Abstract
Recent studies on ultrafast dynamics of solids and nanostructures using few-cycle electromagnetic transients in the far and mid infrared spectral regions are presented. We are able to excite with phase-locked wave forms reaching peak amplitudes beyond 1 V/Aring which are comparable to inner-atomic fields. At the same time, a quantum-limited sensitivity is approached in electro-optic detection. Such capabilities are promising a completely new access to the quantum properties of both condensed matter and light.
- Published
- 2010
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- View/download PDF
41. Ultrafast adiabatic manipulation of slow light in a photonic crystal
- Author
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Daryl M. Beggs, Andrea Melloni, Tobias Kampfrath, Thomas F. Krauss, Thomas P. White, Laurens Kuipers, EPSRC, and University of St Andrews. School of Physics and Astronomy
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Physics ,Resonator ,business.industry ,Transitions ,Physics::Optics ,Slow light ,Electromagnetic radiation ,Atomic and Molecular Physics, and Optics ,QC Physics ,Optics ,Femtosecond ,Atomic physics ,Adiabatic process ,business ,Refractive index ,Ultrashort pulse ,QC ,Photonic crystal - Abstract
We demonstrate by experiment and theory that a light pulse propagating through a Si-based photonic-crystal waveguide is adiabatically blueshifted when the refractive index of the Si is reduced on a femtosecond time scale. Thanks to the use of slow-light modes, we are able to shift a 1.3-ps pulse at telecom frequencies by 0.3 THz with an efficiency as high as 80% in a waveguide as short as 19 mu m. An analytic theory reproduces the experimental data excellently, which shows that adiabatic dynamics are possible even on the femtosecond time scale as long as the external stimulus conserves the spatial symmetry of the system. Publisher PDF
- Published
- 2010
- Full Text
- View/download PDF
42. Extreme THz nonlinearities in bulk and nanostructured semiconductors
- Author
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Alexander Sell, Rupert Huber, Konrad von Volkmann, Alfred Leitenstorfer, Tobias Kampfrath, A. Tredicucci, Aji A. Anappara, Stephan W. Koch, Machillo Kira, Lucia Sorba, J. T. Steiner, Martin Wolf, Giorgio Biasiol, Song J. J. Tsen K. T. Betz M. Elezzabi A. Y., Sell, A., Anappara, A. A., Kampfrath, T., Volkmann, K. V., Wolf, M., Steiner, J. T., Kira, M., Koch, S. W., Biasiol, G., Sorba, L., Tredicucci, Alessandro, Leitenstorfer, A., and Huber, R.
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Physics ,Quantum optics ,Condensed matter physics ,Condensed Matter::Other ,business.industry ,Terahertz radiation ,Physics::Optics ,Polarization (waves) ,Semiconductor ,Coherent control ,Electric field ,Femtosecond ,Polariton ,Optoelectronics ,business - Abstract
Phase-locked electromagnetic transients in the terahertz (THz) spectral domain have become a unique contact-free probe of the femtosecond dynamics of low-energy excitations in semiconductors. Access to their nonlinear response, however, has been limited by a shortage of sufficiently intense THz emitters. Here we introduce a novel high-field source for THz transients featuring peak amplitudes of up to 108 MV/cm. This facility allows us to explore the non-perturbative response of semiconductors to intense fields tailored with sub-cycle precision. In a first experiment intense transients drive Rabi-oscillations between excitonic states in Cu2O, implying exciting perspectives for future THz quantum optics. At electric fields beyond 10 MV/cm, we observe the breakdown of the power expansion of the nonlinear polarization in bulk semiconductors. Furthermore, we employ the intense magnetic field components of our transients to coherently control spin waves in antiferromagnetically ordered solids. Finally, intersubband cavity polaritons in semiconductor microcavities are exploited to push light-matter coupling to an unprecedented ultrastrong and sub-cycle regime.
- Published
- 2010
- Full Text
- View/download PDF
43. Magnetic Light-Matter Interactions in a Photonic Crystal Nanocavity
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D. van Oosten, Laurens Kuipers, B. S. Song, Tobias Kampfrath, Jord C. Prangsma, Susumu Noda, Matteo Burresi, Nanophotonics, and Sub Physics of Condensed Matters begr
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Physics ,Condensed matter physics ,business.industry ,Superlattice ,General Physics and Astronomy ,Resonance ,Physics::Optics ,Inductive coupling ,Magnetic field ,Wavelength ,Polarizability ,Optical frequencies ,Optoelectronics ,business ,Photonic crystal - Abstract
We study the magnetic coupling between a metal-coated near-field probe and a photonic crystal nanocavity. The resonance of the nanocavity shifts to shorter wavelengths when the ringlike apex of the probe is above an antinode of the magnetic field of the cavity. We show that this can be attributed to a magnetic light-matter interaction and is in fact a manifestation of Lenz's law at optical frequencies. We use these measurements to determine the magnetic polarizability of the apex of the probe and find good agreement with theory. We discuss how this method could be applied to study the electric and magnetic polarizibilities of nano-objects.
- Published
- 2010
44. Terahertz fields beyond 100 MV/cm -new radiation for basic research
- Author
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Alexander Sell, Martin Wolf, Alfred Leitenstorfer, Tobias Kampfrath, Günther Krauss, and Rupert Huber
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Physics ,business.industry ,Terahertz radiation ,Far-infrared laser ,Physics::Optics ,Radiation ,Laser ,Inductive coupling ,Terahertz spectroscopy and technology ,law.invention ,Magnetic field ,Optics ,law ,Electric field ,Optoelectronics ,business - Abstract
Widely tunable phase-locked THz transients with electric and magnetic fields exceeding 100 MV/cm are generated by a novel table-top laser. These pulses are able to drive non-per-turbative optical nonlinearities by electric and magnetic coupling.
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- 2010
- Full Text
- View/download PDF
45. Complete response characterization of ultrafast linear photonic devices
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Daryl M. Beggs, Tobias Kampfrath, Laurens Kuipers, and Thomas F. Krauss
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Physics ,business.industry ,Bandwidth (signal processing) ,Nanophotonics ,Physics::Optics ,Optical switch ,Atomic and Molecular Physics, and Optics ,Optics ,Broadband ,Photonics ,business ,Ultrashort pulse ,Refractive index ,Complete response - Abstract
We present a method to fully characterize linear photonic devices that change their properties on ultrashort time scales. When we feed the device with a broadband input pulse and detect the resulting output field for a sufficient number of arrival times of the input, the device response to any other input with smaller bandwidth can be extracted numerically, without the need for additional measurements. Our approach is based on the formalism of linear time-varying systems, and we experimentally demonstrate its feasibility for the example of an ultrafast nanophotonic switch.
- Published
- 2009
46. Probing the magnetic field of light at optical frequencies
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A. Leinse, Matteo Burresi, Laurens Kuipers, D. van Oosten, R. Heideman, Tobias Kampfrath, and H. Schoenmaker
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Physics ,Multidisciplinary ,Optics ,Field (physics) ,business.industry ,Aperture ,Electric field ,Resolution (electron density) ,Metamaterial ,Near-field scanning optical microscope ,business ,Electromagnetic radiation ,Magnetic field - Abstract
Measuring Magnetic Light Compared to its electric component, the coupling between the magnetic field component of light and matter is usually extremely weak. With no effective way to measure it, we are effectively blind to light's magnetic component. Burresi et al. (p. 550 , published online 1 October; see the Perspective by Giessen and Vogelgesang ) coupled a metamaterial split-ring resonator to the tip of a scanning probe to measure the magnetic field vector of light at optical frequencies. The ability to measure the magnetic component of light should prove useful for the nanoscale characterization of optical waveguides and other optical devices.
- Published
- 2009
47. Nonlinear Terahertz Excitations of Optically Dark Para Excitons in Cu^2O
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S. W. Koch, Mackillo Kira, J. T. Steiner, Rupert Huber, Alfred Leitenstorfer, Tobias Kampfrath, Silvan Leinss, Martin Wolf, and K. v. Volkmann
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Condensed Matter::Quantum Gases ,Physics ,Photon ,Condensed matter physics ,Condensed Matter::Other ,Terahertz radiation ,Exciton ,Physics::Optics ,Nonlinear optics ,Optical polarization ,Terahertz spectroscopy and technology ,law.invention ,law ,Microscopic theory ,Bose–Einstein condensate - Abstract
A microscopic theory is applied to describe nonlinear terahertz excitations of optically-dark excitons in Cu 2 O. The theory is quantitatively compared to recent experiments. Signatures of Rabi flopping and ponderomotive contributions are discussed and disentangled.
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- 2009
- Full Text
- View/download PDF
48. Ultrafast Re-routing of Slow Light in a Nanophotonic Directional Coupler
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Daryl M. Beggs, Thomas F. Krauss, Tobias Kampfrath, Thomas P. White, and Laurens Kuipers
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Physics ,business.industry ,Port (circuit theory) ,Output coupler ,Laser ,Slow light ,Optical switch ,law.invention ,Optics ,Transmission (telecommunications) ,law ,Optoelectronics ,Power dividers and directional couplers ,business ,Ultrashort pulse - Abstract
We demonstrate that we can switch the transmission of a directional coupler from one output port to another within a time as short as 3ps with laser pulse energies of less than 10pJ.
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- 2009
- Full Text
- View/download PDF
49. Terahertz Nonlinear Response and Coherent Population Control of Dark Excitons in Cu2O
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Dietmar Fröhlich, Rupert Huber, Martin Wolf, K. v. Volkmann, S. Leinß, Alfred Leitenstorfer, and Tobias Kampfrath
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Larmor precession ,Physics ,Bloch sphere ,Rabi cycle ,Terahertz radiation ,business.industry ,Phonon ,Exciton ,Electrical engineering ,Physics::Optics ,Terahertz spectroscopy and technology ,Quasiparticle ,Atomic physics ,business - Abstract
An optically dark, dense, and cold 1s para exciton gas is prepared by two-photon generation of electron-hole pairs and subsequent phonon cooling. Intense multi-terahertz fields of order MV/cm coherently promote 70% of the quasiparticles from the 1s to the 2p state via a partial internal Rabi oscillation. Electro-optic sampling monitors the Larmor precession of the Bloch vector in real time.
- Published
- 2009
- Full Text
- View/download PDF
50. Terahertz coherent control of optically dark paraexcitons in Cu2O
- Author
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J. T. Steiner, Martin Wolf, Silvan Leinß, Stephan W. Koch, Rupert Huber, Tobias Kampfrath, Alfred Leitenstorfer, Konrad von Volkmann, and Mackillo Kira
- Subjects
Physics ,Nonlinear system ,Field (physics) ,Terahertz radiation ,Coherent control ,Quantum mechanics ,Degrees of freedom (physics and chemistry) ,General Physics and Astronomy ,Nonlinear optics ,Time domain ,Atomic physics ,Population inversion - Abstract
Intense multiterahertz fields of order megavolts per centimeter are used to coherently promote optically dark and dense paraexcitons in Cu2O from the 1s into the 2p state. The nonlinear field response of the intraexcitonic degrees of freedom is directly monitored in the time domain via ultrabroadband electro-optic sampling. The experimental results are analyzed with a microscopic many-body theory, identifying up to two internal Rabi cycles. The effects of population inversion and ponderomotive contributions are disentangled.
- Published
- 2008
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