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Xu B, Chen Z, Hänsch TW, Picqué N. Near-ultraviolet photon-counting dual-comb spectroscopy. Nature 2024; 627:289-294. [PMID: 38448594 PMCID: PMC10937374 DOI: 10.1038/s41586-024-07094-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2023] [Accepted: 01/19/2024] [Indexed: 03/08/2024]
Abstract
Ultraviolet spectroscopy provides unique insights into the structure of matter with applications ranging from fundamental tests to photochemistry in the Earth's atmosphere and astronomical observations from space telescopes1-8. At longer wavelengths, dual-comb spectroscopy, using two interfering laser frequency combs, has become a powerful technique capable of simultaneously providing a broad spectral range and very high resolution9. Here we demonstrate a photon-counting approach that can extend the unique advantages of this method into ultraviolet regions where nonlinear frequency conversion tends to be very inefficient. Our spectrometer, based on two frequency combs with slightly different repetition frequencies, provides a wide-span, high-resolution frequency calibration within the accuracy of an atomic clock, and overall consistency of the spectra. We demonstrate a signal-to-noise ratio at the quantum limit and an optimal use of the measurement time, provided by the multiplexed recording of all spectral data on a single photon-counter10. Our initial experiments are performed in the near-ultraviolet and in the visible spectral ranges with alkali-atom vapour, with a power per comb line as low as a femtowatt. This crucial step towards precision broadband spectroscopy at short wavelengths paves the way for extreme-ultraviolet dual-comb spectroscopy, and, more generally, opens up a new realm of applications for photon-level diagnostics, as encountered, for example, when driving single atoms or molecules.
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Affiliation(s)
- Bingxin Xu
- Max-Planck Institute of Quantum Optics, Garching, Germany
| | - Zaijun Chen
- Max-Planck Institute of Quantum Optics, Garching, Germany
- Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, USA
| | - Theodor W Hänsch
- Max-Planck Institute of Quantum Optics, Garching, Germany
- Faculty of Physics, Ludwig-Maximilian University of Munich, Munich, Germany
| | - Nathalie Picqué
- Max-Planck Institute of Quantum Optics, Garching, Germany.
- Max-Born Institute for Nonlinear Optics and Short-Pulse Spectroscopy, Berlin, Germany.
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2
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Cui Z, Sun M, Liu D, Zhu J. High-peak-power picosecond deep-UV laser sources. OPTICS EXPRESS 2022; 30:43354-43370. [PMID: 36523035 DOI: 10.1364/oe.474513] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2022] [Accepted: 10/14/2022] [Indexed: 06/17/2023]
Abstract
Ultrafast deep-UV laser sources have extensive applications across a wide number of fields, whether biomedicine, photolithography, industrial processing, or state-of-the-art scientific research. However, it has been challenging to obtain deep-UV laser sources with high conversion efficiency and output peak power. Here, we simultaneously demonstrated high-peak-power picosecond deep-UV laser sources at two typical wavebands of 263.2 and 210.5 nm via the efficient fourth- and fifth-harmonic generation. The highest peak power of 263.2 and 210.5 nm laser radiations were up to 2.13 GW (6.72 ps) and 1.38 GW (5.08 ps). The overall conversion efficiencies from the fundamental wave to the fourth and fifth harmonic were up to 42.9% and 28.8%, respectively. The demonstrated results represent the highest conversion efficiencies and output peak powers of picosecond deep-UV laser sources at present to our knowledge. Additionally, we also systematically characterized the deep-UV optical properties of typical birefringent and nonlinear borate crystals, including α-BaB2O4, β-BaB2O4, LiB3O5, and CsLiB6O10 crystals. The experiments and obtained numerous new optical data in this work will contribute to the generation of ultrahigh-peak-power deep-UV and vacuum-UV laser sources and crucial applications in both science and industry, such as high-energy-density physics, material science, and laser machining.
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3
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Solaro C, Debavelaere C, Cladé P, Guellati-Khelifa S. Atom Interferometer Driven by a Picosecond Frequency Comb. PHYSICAL REVIEW LETTERS 2022; 129:173204. [PMID: 36332244 DOI: 10.1103/physrevlett.129.173204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2022] [Accepted: 09/26/2022] [Indexed: 06/16/2023]
Abstract
We demonstrate a light-pulse atom interferometer based on the diffraction of free-falling atoms by a picosecond frequency-comb laser. More specifically, we coherently split and recombine wave packets of cold ^{87}Rb atoms by driving stimulated Raman transitions between the |5s ^{2}S_{1/2},F=1⟩ and |5s ^{2}S_{1/2},F=2⟩ hyperfine states, using two trains of picosecond pulses in a counterpropagating geometry. We study the impact of the pulses' length as well as the interrogation time onto the contrast of the atom interferometer. Our experimental data are well reproduced by a numerical simulation based on an effective coupling that depends on the overlap between the pulses and the atomic cloud. These results pave the way for extending light-pulse interferometry to transitions in other spectral regions and therefore to other species, for new possibilities in metrology, sensing of gravito-inertial effects, and tests of fundamental physics.
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Affiliation(s)
- Cyrille Solaro
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, 75005 Paris, France
| | - Clément Debavelaere
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, 75005 Paris, France
| | - Pierre Cladé
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, 75005 Paris, France
| | - Saïda Guellati-Khelifa
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, 75005 Paris, France
- Conservatoire National des Arts et Métiers, 75003 Paris, France
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4
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Ermolov A, Heide C, Dienstbier P, Köttig F, Tani F, Hommelhoff P, Russell PSJ. Carrier-envelope-phase-stable soliton-based pulse compression to 4.4 fs and ultraviolet generation at the 800 kHz repetition rate. OPTICS LETTERS 2019; 44:5005-5008. [PMID: 31613249 DOI: 10.1364/ol.44.005005] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2019] [Accepted: 09/09/2019] [Indexed: 06/10/2023]
Abstract
In this Letter, we report the generation of a femtosecond supercontinuum extending from the ultraviolet to the near-infrared spectrum and detection of its carrier-envelope-phase (CEP) variation by f-to-2f interferometry. The spectrum is generated in a gas-filled hollow-core photonic crystal fiber, where soliton dynamics allows the CEP-stable self-compression of the optical parametric chirped-pulse amplifier pump pulses at 800 nm to a duration of 1.7 optical cycles, followed by dispersive wave emission. The source provides up to 1 μJ of pulse energy at the 800 kHz repetition rate, resulting in 0.8 W of average power, and it can be extremely useful, for example in strong-field physics, pump-probe measurements, and ultraviolet frequency comb metrology.
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5
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Dreissen LS, Roth C, Gründeman EL, Krauth JJ, Favier M, Eikema KSE. High-Precision Ramsey-Comb Spectroscopy Based on High-Harmonic Generation. PHYSICAL REVIEW LETTERS 2019; 123:143001. [PMID: 31702181 DOI: 10.1103/physrevlett.123.143001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2019] [Indexed: 06/10/2023]
Abstract
High-harmonic generation (HHG) is widely used for up-conversion of amplified (near) infrared ultrafast laser pulses to short wavelengths. We demonstrate that Ramsey-comb spectroscopy, based on two such pulses derived from a frequency-comb laser, enables us to observe phase effects in this process with a few mrad precision. As a result, we could perform the most accurate spectroscopic measurement based on light from HHG, illustrated with a determination of the 5p^{6}→5p^{5}8s^{2}[3/2]_{1} transition at 110 nm in ^{132}Xe. We improve its relative accuracy 10^{4} times to a value of 2.3×10^{-10}. This is 3.6 times better than shown before involving HHG, and promising to enable 1S-2S spectroscopy of He^{+} for fundamental tests.
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Affiliation(s)
- L S Dreissen
- LaserLaB, Department of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - C Roth
- LaserLaB, Department of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - E L Gründeman
- LaserLaB, Department of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - J J Krauth
- LaserLaB, Department of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - M Favier
- LaserLaB, Department of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - K S E Eikema
- LaserLaB, Department of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
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6
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Shi L, Andrade JRC, Tajalli A, Geng J, Yi J, Heidenblut T, Segerink FB, Babushkin I, Kholodtsova M, Merdji H, Bastiaens B, Morgner U, Kovacev M. Generating Ultrabroadband Deep-UV Radiation and Sub-10 nm Gap by Hybrid-Morphology Gold Antennas. NANO LETTERS 2019; 19:4779-4786. [PMID: 31244236 DOI: 10.1021/acs.nanolett.9b02100] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We experimentally investigate the interaction between hybrid-morphology gold optical antennas and a few-cycle Ti:sapphire laser up to ablative intensities, demonstrating rich nonlinear plasmonic effects and promising applications in coherent frequency upconversion and nanofabrication technology. The two-dimensional array of hybrid antennas consists of elliptical apertures combined with bowties in its minor axis. The plasmonic resonance frequency of the bowties is red-shifted with respect to the laser central frequency and thus mainly enhances the third harmonic spectrum at long wavelengths. The gold film between two neighboring elliptical apertures forms an hourglass-shaped structure, which acts as a "plasmonic lens" and thus strongly reinforces surface currents into a small area. This enhanced surface current produces a rotating magnetic field that deeply penetrates into the substrate. At resonant frequency, the magnetic field is further intensified by the bowties. The resonant frequency of the hourglass is blueshifted with respect to the laser central frequency. Consequently, it spectacularly extends the third harmonic spectrum toward short wavelengths. The resultant third harmonic signal ranges from 230 to 300 nm, much broader than the emission from a sapphire crystal. In addition, the concentration of surface current within the neck of the hourglass antenna results in a structural modification through laser ablation, producing sub-10 nm sharp metallic gaps. Moreover, after laser illumination the optical field hotspots are imprinted around the antennas, allowing us to confirm the subwavelength enhancement of the electric near-field intensity.
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Affiliation(s)
- Liping Shi
- Institute of Quantum Optics , Leibniz University Hannover , Welfengarten 1 , 30167 , Hannover , Germany
- Cluster of Excellence PhoenixD (Photonics, Optics, and Engineering-Innovation Across Disciplines) , 30167 , Hannover , Germany
| | - José R C Andrade
- Institute of Quantum Optics , Leibniz University Hannover , Welfengarten 1 , 30167 , Hannover , Germany
- Cluster of Excellence PhoenixD (Photonics, Optics, and Engineering-Innovation Across Disciplines) , 30167 , Hannover , Germany
| | - Ayhan Tajalli
- Institute of Quantum Optics , Leibniz University Hannover , Welfengarten 1 , 30167 , Hannover , Germany
- Cluster of Excellence PhoenixD (Photonics, Optics, and Engineering-Innovation Across Disciplines) , 30167 , Hannover , Germany
| | - Jiao Geng
- Institute of Quantum Optics , Leibniz University Hannover , Welfengarten 1 , 30167 , Hannover , Germany
| | - Juemin Yi
- Institute of Physics and Center of Interface Science , Carl von Ossietzky University Oldenburg , 26129 , Oldenburg , Germany
| | - Torsten Heidenblut
- Cluster of Excellence PhoenixD (Photonics, Optics, and Engineering-Innovation Across Disciplines) , 30167 , Hannover , Germany
- Institute of Materials Science , Leibniz University Hannover , An der University 2 , 30823 , Garbsen, Hannover Germany
| | - Frans B Segerink
- Optical Sciences, MESA+ Institute for Nanotechnology , University of Twente , P.O. Box 217, 7500AE Enschede , The Netherlands
| | - Ihar Babushkin
- Institute of Quantum Optics , Leibniz University Hannover , Welfengarten 1 , 30167 , Hannover , Germany
- Cluster of Excellence PhoenixD (Photonics, Optics, and Engineering-Innovation Across Disciplines) , 30167 , Hannover , Germany
| | - Maria Kholodtsova
- LIDYL, CEA, CNRS , Universite Paris-Saclay , CEA Saclay 91191 , Gif-sur-Yvette , France
| | - Hamed Merdji
- LIDYL, CEA, CNRS , Universite Paris-Saclay , CEA Saclay 91191 , Gif-sur-Yvette , France
| | - Bert Bastiaens
- Laser Physics and Nonlinear Optics, MESA+ Institute for Nanotechnology , University of Twente , 7500AE Enschede , The Netherlands
| | - Uwe Morgner
- Institute of Quantum Optics , Leibniz University Hannover , Welfengarten 1 , 30167 , Hannover , Germany
- Cluster of Excellence PhoenixD (Photonics, Optics, and Engineering-Innovation Across Disciplines) , 30167 , Hannover , Germany
| | - Milutin Kovacev
- Institute of Quantum Optics , Leibniz University Hannover , Welfengarten 1 , 30167 , Hannover , Germany
- Cluster of Excellence PhoenixD (Photonics, Optics, and Engineering-Innovation Across Disciplines) , 30167 , Hannover , Germany
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7
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Seres J, Seres E, Serrat C, Young EC, Speck JS, Schumm T. All-solid-state VUV frequency comb at 160 nm using high-harmonic generation in nonlinear femtosecond enhancement cavity. OPTICS EXPRESS 2019; 27:6618-6628. [PMID: 30876243 DOI: 10.1364/oe.27.006618] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2019] [Accepted: 02/13/2019] [Indexed: 06/09/2023]
Abstract
We realized a solid-state-based vacuum ultraviolet frequency comb by harmonics generation in an external enhancement cavity. Optical conversions were so far reported by only using gaseous media. We present a theory that allows the most suited solid generation medium to be selected for specific target harmonics by adapting the material's bandgap. We experimentally use a thin AlN film grown on a sapphire substrate to realize a compact frequency comb high-harmonic source in the Deep Ultraviolet (DUV) / Vacuum Ultraviolet (VUV) spectral range. By extending our earlier VUV source [Opt. Express26, 21900 (2018)] with the enhancement cavity, a sub-Watt level Ti:sapphire femtosecond frequency comb is enhanced to 24 W stored average power, its 3rd, 5th, and 7th harmonics are generated, and the targeted 5th harmonic's power at 160 nm increased by two orders of magnitude. The emerging nonlinear effects in the solid medium, together with suitable intra-cavity dispersion management, support optimal enhancement and stable locking. To demonstrate the realized frequency comb's spectroscopic ability, we report on the beat measurement between the 3rd harmonic beam and a 266 nm CW laser reaching about 1 MHz accuracy.
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8
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Altmann RK, Dreissen LS, Salumbides EJ, Ubachs W, Eikema KSE. Deep-Ultraviolet Frequency Metrology of H_{2} for Tests of Molecular Quantum Theory. PHYSICAL REVIEW LETTERS 2018; 120:043204. [PMID: 29437464 DOI: 10.1103/physrevlett.120.043204] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2017] [Indexed: 06/08/2023]
Abstract
Molecular hydrogen and its isotopic and ionic species are benchmark systems for testing quantum chemical theory. Advances in molecular energy structure calculations enable the experimental verification of quantum electrodynamics and potentially a determination of the proton charge radius from H_{2} spectroscopy. We measure the ground state energy in ortho-H_{2} relative to the first electronically excited state by Ramsey-comb laser spectroscopy on the EF^{1}Σ_{g}^{+}-X^{1}Σ_{g}^{+}(0,0) Q1 transition. The resulting transition frequency of 2 971 234 992 965(73) kHz is 2 orders of magnitude more accurate than previous measurements. This paves the way for a considerably improved determination of the dissociation energy (D_{0}) for fundamental tests with molecular hydrogen.
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Affiliation(s)
- R K Altmann
- LaserLaB, Department of Physics and Astronomy, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - L S Dreissen
- LaserLaB, Department of Physics and Astronomy, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - E J Salumbides
- LaserLaB, Department of Physics and Astronomy, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - W Ubachs
- LaserLaB, Department of Physics and Astronomy, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - K S E Eikema
- LaserLaB, Department of Physics and Astronomy, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
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9
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Meek SA, Hipke A, Guelachvili G, Hänsch TW, Picqué N. Doppler-free Fourier transform spectroscopy. OPTICS LETTERS 2018; 43:162-165. [PMID: 29328222 DOI: 10.1364/ol.43.000162] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2017] [Accepted: 11/25/2017] [Indexed: 06/07/2023]
Abstract
Sub-Doppler broadband multi-heterodyne spectroscopy is proposed and experimentally demonstrated. Using two laser frequency combs of slightly different repetition frequencies, we have recorded Doppler-free two-photon dual-comb spectra of atomic rubidium resonances of a width of 6 MHz, while simultaneously interrogating a spectral span of 10 THz. The atomic transitions are uniquely identified via the intensity modulation of the observed fluorescence radiation. To the best of our knowledge, these results represent the first demonstration of Doppler-free Fourier transform spectroscopy and extend the range of applications of broadband spectroscopy towards precision nonlinear spectroscopy.
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10
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Zheng X, Sun YR, Chen JJ, Jiang W, Pachucki K, Hu SM. Measurement of the Frequency of the 2 ^{3}S-2 ^{3}P Transition of ^{4}He. PHYSICAL REVIEW LETTERS 2017; 119:263002. [PMID: 29328711 DOI: 10.1103/physrevlett.119.263002] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2017] [Indexed: 06/07/2023]
Abstract
The 2 ^{3}S-2 ^{3}P transition of ^{4}He was measured by comb-linked laser spectroscopy using a transverse-cooled atomic beam. The centroid frequency was determined to be 276 736 495 600.0(1.4) kHz, with a fractional uncertainty of 5.1×10^{-12}. This value is not only more accurate but also differs by as much as -49.5 kHz (20σ) from the previous result given by [Cancio Pastor et al., Phys. Rev. Lett. 92, 023001 (2004)PRLTAO0031-900710.1103/PhysRevLett.92.023001; Cancio Pastor et al.Phys. Rev. Lett.97, 139903(E) (2006)10.1103/PhysRevLett.97.139903; Cancio Pastor et al.Phys. Rev. Lett.108, 143001 (2012)10.1103/PhysRevLett.108.143001]. In combination with ongoing theoretical calculations, this work may allow the most accurate determination of the nuclear charge radius of helium.
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Affiliation(s)
- X Zheng
- Hefei National Laboratory for Physical Sciences and Microscale, iChem Center, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Y R Sun
- Hefei National Laboratory for Physical Sciences and Microscale, iChem Center, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - J-J Chen
- Hefei National Laboratory for Physical Sciences and Microscale, iChem Center, University of Science and Technology of China, Hefei 230026, China
| | - W Jiang
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - K Pachucki
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - S-M Hu
- Hefei National Laboratory for Physical Sciences and Microscale, iChem Center, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
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11
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Affiliation(s)
- Wim Vassen
- LaserLaB, Department of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
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12
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Beyer A, Maisenbacher L, Matveev A, Pohl R, Khabarova K, Grinin A, Lamour T, Yost DC, Hänsch TW, Kolachevsky N, Udem T. The Rydberg constant and proton size from atomic hydrogen. Science 2017; 358:79-85. [DOI: 10.1126/science.aah6677] [Citation(s) in RCA: 225] [Impact Index Per Article: 32.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2016] [Accepted: 08/28/2017] [Indexed: 11/03/2022]
Affiliation(s)
- Axel Beyer
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
| | | | - Arthur Matveev
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
| | - Randolf Pohl
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
| | - Ksenia Khabarova
- P.N. Lebedev Physical Institute, 119991 Moscow, Russia
- Russian Quantum Center, 143025 Skolkovo, Russia
| | - Alexey Grinin
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
| | - Tobias Lamour
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
| | - Dylan C. Yost
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
| | - Theodor W. Hänsch
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Ludwig-Maximilians-Universität, 80539 München, Germany
| | - Nikolai Kolachevsky
- P.N. Lebedev Physical Institute, 119991 Moscow, Russia
- Russian Quantum Center, 143025 Skolkovo, Russia
| | - Thomas Udem
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Ludwig-Maximilians-Universität, 80539 München, Germany
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