1
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Hoenig D, Thielemann F, Karpa L, Walker T, Mohammadi A, Schaetz T. Trapping Ion Coulomb Crystals in an Optical Lattice. PHYSICAL REVIEW LETTERS 2024; 132:133003. [PMID: 38613289 DOI: 10.1103/physrevlett.132.133003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2023] [Revised: 11/14/2023] [Accepted: 02/12/2024] [Indexed: 04/14/2024]
Abstract
We report the optical trapping of multiple ions localized at individual lattice sites of a one-dimensional optical lattice. We observe a fivefold increased range of axial dc-electric field strength for which ions can be optically trapped with high probability and an increase of the axial eigenfrequency by 2 orders of magnitude compared to an optical dipole trap without interference but of similar intensity. Our findings motivate an alternative pathway to extend arrays of trapped ions in size and dimension, enabling quantum simulations with particles interacting at long range.
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Affiliation(s)
- Daniel Hoenig
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, 79104 Freiburg, Germany
| | - Fabian Thielemann
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, 79104 Freiburg, Germany
| | - Leon Karpa
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, 79104 Freiburg, Germany
- Leibniz Universität Hannover, Institut für Quantenoptik, 30167 Hannover, Germany
| | - Thomas Walker
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, 79104 Freiburg, Germany
| | - Amir Mohammadi
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, 79104 Freiburg, Germany
| | - Tobias Schaetz
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, 79104 Freiburg, Germany
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2
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Lehmann G, Spatschek KH. Formation and properties of spatially inhomogeneous plasma density gratings. Phys Rev E 2023; 108:055204. [PMID: 38115416 DOI: 10.1103/physreve.108.055204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2023] [Accepted: 10/04/2023] [Indexed: 12/21/2023]
Abstract
Volume plasma density gratings receive increasing interest since, compared to solid-state optical media, they posses significantly higher damage thresholds. The gratings are produced by counterpropagating laser pulses in underdense plasma. When analyzing their optical properties, usually they are assumed to be homogeneous in space. The latter assumption, however, breaks down, especially when the gratings are produced by short high-power laser pump pulses. Then, generically the plasma grating posses an inhomogeneous envelope which results from the superposition of the pump pulses envelopes. The present paper discusses the effect of grating inhomogeneity on reflection and transmission of probe pulses. A Gaussian plasma density grating becomes an apodized grating which offers significant improvement over homogeneous gratings due to side-lobe suppression while maintaining reflectivity and a narrow bandwidth. On the other hand, the reflected probe pulses receive a chirp which depends on the spatial scale. For a Gaussian grating a cubic spectral phase appears. Numerical particle-in-cell simulations are supported by theoretical analysis based on coupled mode equations as well as an effective medium approach.
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Affiliation(s)
- G Lehmann
- Institut für Theoretische Physik I, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - K H Spatschek
- Institut für Theoretische Physik I, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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3
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Kiefer P, Hakelberg F, Wittemer M, Bermúdez A, Porras D, Warring U, Schaetz T. Floquet-Engineered Vibrational Dynamics in a Two-Dimensional Array of Trapped Ions. PHYSICAL REVIEW LETTERS 2019; 123:213605. [PMID: 31809155 DOI: 10.1103/physrevlett.123.213605] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2019] [Indexed: 06/10/2023]
Abstract
We demonstrate Floquet engineering in a basic yet scalable 2D architecture of individually trapped and controlled ions. Local parametric modulations of detuned trapping potentials steer the strength of long-range interion couplings and the related Peierls phase of the motional state. In our proof of principle, we initialize large coherent states and tune modulation parameters to control trajectories, directions, and interferences of the phonon flow. Our findings open a new pathway for future Floquet-based trapped-ion quantum simulators targeting correlated topological phenomena and dynamical gauge fields.
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Affiliation(s)
- Philip Kiefer
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
| | - Frederick Hakelberg
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
| | - Matthias Wittemer
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
| | - Alejandro Bermúdez
- Departamento de Física Teórica, Universidad Complutense, 28040 Madrid, Spain
| | - Diego Porras
- Instituto de Física Fundamental IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain
| | - Ulrich Warring
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
| | - Tobias Schaetz
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
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4
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Wittemer M, Hakelberg F, Kiefer P, Schröder JP, Fey C, Schützhold R, Warring U, Schaetz T. Phonon Pair Creation by Inflating Quantum Fluctuations in an Ion Trap. PHYSICAL REVIEW LETTERS 2019; 123:180502. [PMID: 31763879 DOI: 10.1103/physrevlett.123.180502] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2019] [Revised: 08/22/2019] [Indexed: 06/10/2023]
Abstract
Quantum theory predicts intriguing dynamics during drastic changes of external conditions. We switch the trapping field of two ions sufficiently fast to tear apart quantum fluctuations, i.e., create pairs of phonons and, thereby, squeeze the ions' motional state. This process can be interpreted as an experimental analog to cosmological particle creation and is accompanied by the formation of spatial entanglement. Hence, our platform allows one to study the causal connections of squeezing, pair creation, and entanglement and might permit one to cross-fertilize between concepts in cosmology and applications of quantum information processing.
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Affiliation(s)
- Matthias Wittemer
- Physikalisches Institut, Universität Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
| | - Frederick Hakelberg
- Physikalisches Institut, Universität Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
| | - Philip Kiefer
- Physikalisches Institut, Universität Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
| | - Jan-Philipp Schröder
- Physikalisches Institut, Universität Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
| | - Christian Fey
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Fachbereich Physik, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Ralf Schützhold
- Fakultät für Physik, Universität Duisburg-Essen, Lotharstrasse 1, 47057 Duisburg, Germany
- Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstrasse 400, 01328 Dresden, Germany
- Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany
| | - Ulrich Warring
- Physikalisches Institut, Universität Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
| | - Tobias Schaetz
- Physikalisches Institut, Universität Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
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5
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Hakelberg F, Kiefer P, Wittemer M, Warring U, Schaetz T. Interference in a Prototype of a Two-Dimensional Ion Trap Array Quantum Simulator. PHYSICAL REVIEW LETTERS 2019; 123:100504. [PMID: 31573283 DOI: 10.1103/physrevlett.123.100504] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2019] [Indexed: 06/10/2023]
Abstract
Trapped ions are a promising platform for envisioned quantum simulators, with outstanding results in one-dimensional ion crystals. However, theory requires not only interactions at long range, but also higher dimensionality. We operate a basic triangular array of three individually trapped ions based on scalable microfabrication technology. We demonstrate coherent coupling, tunable in real time and enabling interference in 2D, an essential building block for a reconfigurable quantum simulator. Mitigating motional heating will permit accessing the quantum regime and 2D experimental quantum simulations.
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Affiliation(s)
- Frederick Hakelberg
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
| | - Philip Kiefer
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
| | - Matthias Wittemer
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
| | - Ulrich Warring
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
| | - Tobias Schaetz
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
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6
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Lehmann G, Spatschek KH. Plasma volume holograms for focusing and mode conversion of ultraintense laser pulses. Phys Rev E 2019; 100:033205. [PMID: 31640054 DOI: 10.1103/physreve.100.033205] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2019] [Indexed: 11/07/2022]
Abstract
Beating of a broad laser reference beam with a quite general focused object beam inside a plasma volume generates a dynamic plasma hologram. Both beams may be of moderate intensity. The volume hologram can be read out by an ultraintense main beam (of similar structure as the reference beam) producing an object beam replica. For the latter, intensity in the focus may become extremely large. As an application, the possibility of a read-out focused Gaussian laser pulse with intensity of several 10^{19}W/cm^{2} in focus is shown by three-dimensional numerical simulations. Besides the focusing possibility, the hologram may also act as a mode converter for high-intensity laser pulses. Generating a plasma hologram with a focused Laguerre-Gaussian object beam results in a staggered plasma density grating, allowing the production of high-intensity vortex beam replica.
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Affiliation(s)
- G Lehmann
- Institut für Theoretische Physik, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - K H Spatschek
- Institut für Theoretische Physik, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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7
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Carnio EG, Breuer HP, Buchleitner A. Wave-Particle Duality in Complex Quantum Systems. J Phys Chem Lett 2019; 10:2121-2129. [PMID: 30965007 DOI: 10.1021/acs.jpclett.9b00676] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Stunning progress in the experimental resolution and control of natural or man-made complex systems at the level of their quantum mechanical constituents raises the question, across diverse subdisciplines of physics, chemistry, and biology, whether the fundamental quantum nature may condition the dynamical and functional system properties on mesoscopic if not macroscopic scales. However, which are the distinctive signatures of quantum properties in complex systems, notably when modulated by environmental stochasticity and dynamical instabilities? It appears that, to settle this question across the above communities, a shared understanding is needed of the central feature of quantum mechanics: wave-particle duality. In this Perspective, we elaborate how randomness induced by this very quantum property can be discerned from the stochasticity ubiquitous in complex systems already on the classical level. We argue that in the study of increasingly complex systems, such distinction requires the analysis of single incidents of quantum dynamical processes.
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Affiliation(s)
- Edoardo G Carnio
- Physikalisches Institut , Albert-Ludwigs-Universität Freiburg , Hermann-Herder-Str. 3 , 79104 Freiburg im Breisgau , Federal Republic of Germany
| | - Heinz-Peter Breuer
- Physikalisches Institut , Albert-Ludwigs-Universität Freiburg , Hermann-Herder-Str. 3 , 79104 Freiburg im Breisgau , Federal Republic of Germany
- Freiburg Institute for Advanced Studies (FRIAS) , Albert-Ludwigs-Universität Freiburg , Albertstr. 19 , 79104 Freiburg im Breisgau , Federal Republic of Germany
| | - Andreas Buchleitner
- Physikalisches Institut , Albert-Ludwigs-Universität Freiburg , Hermann-Herder-Str. 3 , 79104 Freiburg im Breisgau , Federal Republic of Germany
- Freiburg Institute for Advanced Studies (FRIAS) , Albert-Ludwigs-Universität Freiburg , Albertstr. 19 , 79104 Freiburg im Breisgau , Federal Republic of Germany
- Erwin Schrödinger International Institute for Mathematics and Physics , University of Vienna , Boltzmanngasse 9 , 1090 Vienna , Austria
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8
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Lehmann G, Spatschek KH. Plasma-based polarizer and waveplate at large laser intensity. Phys Rev E 2018; 97:063201. [PMID: 30011484 DOI: 10.1103/physreve.97.063201] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2018] [Indexed: 06/08/2023]
Abstract
A plasma photonic crystal consists of a plasma density grating which is created in underdense plasma by counterpropagating laser beams. When a high-power laser pulse impinges the crystal, it might be reflected or transmitted. So far only one type of pulse polarization, namely the so-called s wave (or TE mode) was investigated (when the electric field vector is perpendicular to the plane of incidence). Here, when investigating also so-called p waves (or TM modes, where the magnetic field vector is perpendicular to the plane of incidence), it is detected that the transmission and reflection properties of the plasma photonic crystal depend on polarization. A simple analytic model of the crystal allows one to make precise predictions. The first conclusion is that in some operational regime the crystal can act as a plasma polarizer for high-intensity laser pulses. Also, differences in phase velocities for grazing incidence between s and p polarization are found. Thus, secondly, the crystal can be utilized as a waveplate, e.g., transforming linearly polarized laser light into circular polarization. All these processes extend to laser intensities beyond the damage intensities of so far used solid state devices.
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Affiliation(s)
- G Lehmann
- Institut für Theoretische Physik I, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - K H Spatschek
- Institut für Theoretische Physik I, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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9
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Hakelberg F, Kiefer P, Wittemer M, Schaetz T, Warring U. Hybrid setup for stable magnetic fields enabling robust quantum control. Sci Rep 2018. [PMID: 29535399 PMCID: PMC5849637 DOI: 10.1038/s41598-018-22671-5] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Abstract
Well controlled and highly stable magnetic fields are desired for a wide range of applications in physical research, including quantum metrology, sensing, information processing, and simulation. Here we introduce a low-cost hybrid assembly of rare-earth magnets and magnetic field coils to generate a field strength of \documentclass[12pt]{minimal}
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\begin{document}$$\simeq $$\end{document}≃10.9 mT with a calculated spatial variation of less than 10−6 within a diameter of spherical volume of 150 μm. We characterise its tuneability and stability performance using a single Mg+ atom confined in a radio-frequency surface-electrode trap under ultra-high vacuum conditions. The strength of the field can be tuned with a relative precision of ≤2 × 10−5 and we find a passive temporal stability of our setup of better than 1.0 × 10−4 over the course of one hour. Slow drifts on time scales of a few minutes are actively stabilised by adjusting electric currents in the magnetic field coils. In this way, we observe coherence times of electronic superposition states of greater than six seconds using a first-order field insensitive (clock) transition. In a first application, we demonstrate sensing of magnetic fields with amplitudes of ≥0.2 μT oscillating at \documentclass[12pt]{minimal}
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\begin{document}$$\simeq $$\end{document}≃2π × 60 MHz. Our approach can be implemented in compact and robust applications with strict power and load requirements.
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Affiliation(s)
- Frederick Hakelberg
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Straße 3, 79104, Freiburg, Germany.
| | - Philip Kiefer
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Straße 3, 79104, Freiburg, Germany
| | - Matthias Wittemer
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Straße 3, 79104, Freiburg, Germany
| | - Tobias Schaetz
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Straße 3, 79104, Freiburg, Germany
| | - Ulrich Warring
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Straße 3, 79104, Freiburg, Germany
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10
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Hong S, Lee M, Kwon YD, Cho DID, Kim T. Experimental Methods for Trapping Ions Using Microfabricated Surface Ion Traps. J Vis Exp 2017:56060. [PMID: 28872137 PMCID: PMC5614346 DOI: 10.3791/56060] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Abstract
Ions trapped in a quadrupole Paul trap have been considered one of the strong physical candidates to implement quantum information processing. This is due to their long coherence time and their capability to manipulate and detect individual quantum bits (qubits). In more recent years, microfabricated surface ion traps have received more attention for large-scale integrated qubit platforms. This paper presents a microfabrication methodology for ion traps using micro-electro-mechanical system (MEMS) technology, including the fabrication method for a 14 µm-thick dielectric layer and metal overhang structures atop the dielectric layer. In addition, an experimental procedure for trapping ytterbium (Yb) ions of isotope 174 (174Yb+) using 369.5 nm, 399 nm, and 935 nm diode lasers is described. These methodologies and procedures involve many scientific and engineering disciplines, and this paper first presents the detailed experimental procedures. The methods discussed in this paper can easily be extended to the trapping of Yb ions of isotope 171 (171Yb+) and to the manipulation of qubits.
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Affiliation(s)
- Seokjun Hong
- ISRC/ASRI, Department of Electrical and Computer Engineering, Seoul National University
| | - Minjae Lee
- ISRC/ASRI, Department of Electrical and Computer Engineering, Seoul National University
| | | | - Dong-Il Dan Cho
- ISRC/ASRI, Department of Electrical and Computer Engineering, Seoul National University
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Clos G, Porras D, Warring U, Schaetz T. Time-Resolved Observation of Thermalization in an Isolated Quantum System. PHYSICAL REVIEW LETTERS 2016; 117:170401. [PMID: 27824460 DOI: 10.1103/physrevlett.117.170401] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2016] [Indexed: 06/06/2023]
Abstract
We use trapped atomic ions forming a hybrid Coulomb crystal and exploit its phonons to study an isolated quantum system composed of a single spin coupled to an engineered bosonic environment. We increase the complexity of the system by adding ions and controlling coherent couplings and, thereby, we observe the emergence of thermalization: Time averages of spin observables approach microcanonical averages while related fluctuations decay. Our platform features precise control of system size, coupling strength, and isolation from the external world to explore the dynamics of equilibration and thermalization.
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Affiliation(s)
- Govinda Clos
- Physikalisches Institut, Albert-Ludwigs-Universität, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
| | - Diego Porras
- Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, United Kingdom
| | - Ulrich Warring
- Physikalisches Institut, Albert-Ludwigs-Universität, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
| | - Tobias Schaetz
- Physikalisches Institut, Albert-Ludwigs-Universität, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
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