1
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Stern HL, M Gilardoni C, Gu Q, Eizagirre Barker S, Powell OFJ, Deng X, Fraser SA, Follet L, Li C, Ramsay AJ, Tan HH, Aharonovich I, Atatüre M. A quantum coherent spin in hexagonal boron nitride at ambient conditions. NATURE MATERIALS 2024; 23:1379-1385. [PMID: 38769205 DOI: 10.1038/s41563-024-01887-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Accepted: 04/02/2024] [Indexed: 05/22/2024]
Abstract
Solid-state spin-photon interfaces that combine single-photon generation and long-lived spin coherence with scalable device integration-ideally under ambient conditions-hold great promise for the implementation of quantum networks and sensors. Despite rapid progress reported across several candidate systems, those possessing quantum coherent single spins at room temperature remain extremely rare. Here we report quantum coherent control under ambient conditions of a single-photon-emitting defect spin in a layered van der Waals material, namely, hexagonal boron nitride. We identify that the carbon-related defect has a spin-triplet electronic ground-state manifold. We demonstrate that the spin coherence is predominantly governed by coupling to only a few proximal nuclei and is prolonged by decoupling protocols. Our results serve to introduce a new platform to realize a room-temperature spin qubit coupled to a multiqubit quantum register or quantum sensor with nanoscale sample proximity.
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Affiliation(s)
- Hannah L Stern
- Cavendish Laboratory, University of Cambridge, Cambridge, UK.
- Photon Science Institute and Department of Physics and Department of Chemistry, The University of Manchester, Manchester, UK.
| | | | - Qiushi Gu
- Cavendish Laboratory, University of Cambridge, Cambridge, UK
| | | | - Oliver F J Powell
- Cavendish Laboratory, University of Cambridge, Cambridge, UK
- Hitachi Cambridge Laboratory, Hitachi Europe Ltd, Cambridge, UK
| | - Xiaoxi Deng
- Cavendish Laboratory, University of Cambridge, Cambridge, UK
| | | | - Louis Follet
- Cavendish Laboratory, University of Cambridge, Cambridge, UK
| | - Chi Li
- School of Mathematical and Physical Sciences, Faculty of Science, University of Technology Sydney, Ultimo, New South Wales, Australia
- ARC Centre of Excellence for Transformative Meta-Optical Systems, Faculty of Science, University of Technology Sydney, Ultimo, New South Wales, Australia
| | - Andrew J Ramsay
- Hitachi Cambridge Laboratory, Hitachi Europe Ltd, Cambridge, UK
| | - Hark Hoe Tan
- ARC Centre of Excellence for Transformative Meta-Optical Systems, Department of Electronic Materials Engineering, Research School of Physics, The Australian National University, Canberra, Australian Capital Territory, Australia
| | - Igor Aharonovich
- School of Mathematical and Physical Sciences, Faculty of Science, University of Technology Sydney, Ultimo, New South Wales, Australia
- ARC Centre of Excellence for Transformative Meta-Optical Systems, Faculty of Science, University of Technology Sydney, Ultimo, New South Wales, Australia
| | - Mete Atatüre
- Cavendish Laboratory, University of Cambridge, Cambridge, UK.
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2
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Islam MS, Chowdhury RK, Barthelemy M, Moczko L, Hebraud P, Berciaud S, Barsella A, Fras F. Large-Scale Statistical Analysis of Defect Emission in hBN: Revealing Spectral Families and Influence of Flake Morphology. ACS NANO 2024. [PMID: 39083640 DOI: 10.1021/acsnano.3c10403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/02/2024]
Abstract
Quantum emitters in two-dimensional layered hexagonal boron nitride are quickly emerging as a highly promising platform for next-generation quantum technologies. However, the precise identification and control of defects are key parameters to achieve the next step in their development. We conducted a comprehensive study by analyzing over 10,000 photoluminescence emission lines from liquid exfoliated hBN nanoflake samples, revealing 11 narrow sets of defect families within the 1.6 to 2.2 eV energy range. This challenges hypotheses of a random energy distribution. We also reported averaged defect parameters, including emission line widths, spatial density, phonon side bands, and Franck-Condon-related factors. These findings provide valuable insights into deciphering the microscopic origin of emitters in hBN hosts. We also explored the influence of the hBN host morphology on defect family formation, demonstrating its crucial impact. By tuning the flake size and arrangement, we achieve selective control of defect types while maintaining high spatial density. This offers a scalable approach to defect emission control, diverging from costly engineering methods. It emphasizes the significance of the morphological aspects of hBN hosts for gaining insights into defect origins and expanding their spectral control.
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Affiliation(s)
- Md Samiul Islam
- Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS, UMR 7504, F-67000 Strasbourg, France
| | - Rup Kumar Chowdhury
- Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS, UMR 7504, F-67000 Strasbourg, France
| | - Marie Barthelemy
- Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS, UMR 7504, F-67000 Strasbourg, France
| | - Loic Moczko
- Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS, UMR 7504, F-67000 Strasbourg, France
| | - Pascal Hebraud
- Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS, UMR 7504, F-67000 Strasbourg, France
| | - Stephane Berciaud
- Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS, UMR 7504, F-67000 Strasbourg, France
| | - Alberto Barsella
- Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS, UMR 7504, F-67000 Strasbourg, France
| | - Francois Fras
- Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS, UMR 7504, F-67000 Strasbourg, France
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3
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Kretzschmar T, Ritter S, Kumar A, Vogl T, Eilenberger F, Schmidt F. Quantitative Investigation of Quantum Emitter Yield in Drop-Casted Hexagonal Boron Nitride Nanoflakes. ACS APPLIED OPTICAL MATERIALS 2024; 2:1427-1435. [PMID: 39086657 PMCID: PMC11287792 DOI: 10.1021/acsaom.4c00200] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/29/2024] [Revised: 06/15/2024] [Accepted: 06/25/2024] [Indexed: 08/02/2024]
Abstract
Single photon emitters (SPEs) are a key component for their use as pure photon source in quantum technologies. In this study, we investigate the generation of SPEs from drop-casted hexagonal boron nitride (hBN) nanoflakes, examining the influence of the immersion solution and the source of hBN. We show that, depending on the utilized supplier and solution, the number and quality of the emitters change. We perform a comprehensive optical characterization of the deposited nanoflakes to assess the quality of the generated SPEs. Importantly, we provide quantitative data on SPE yields, highlighting significant variations among solvents and different sources of hBN. We find that hBN from Merck drop-casted in acetone provided the best quality emitters with a g (2) < 0.1 and photoluminescence intensities above 300 kCounts/s. Their number of SPEs among all photon emitters was also the highest, with about 14%, rendering a total yield of about 1.25% of all drop-casted flakes. These numbers hold particular significance when evaluating drop-casting as a practical method for the generation of SPEs and their deposition and incorporation within existing nanophotonic systems. By choosing appropriate solvents and source materials' quality and yield of SPEs can be significantly increased, showcasing further optimization potential for the development of future quantum applications.
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Affiliation(s)
- Tom Kretzschmar
- Institute
of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-University, D-07745 Jena, Germany
| | - Sebastian Ritter
- Institute
of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-University, D-07745 Jena, Germany
| | - Anand Kumar
- Institute
of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-University, D-07745 Jena, Germany
- Department
of Computer Engineering, School of Computation, Information and Technology, Technical University Munich, D-80333 Munich, Germany
- Munich
Center for Quantum Science and Technology (MCQST), D-80799 Munich, Germany
| | - Tobias Vogl
- Institute
of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-University, D-07745 Jena, Germany
- Department
of Computer Engineering, School of Computation, Information and Technology, Technical University Munich, D-80333 Munich, Germany
- Munich
Center for Quantum Science and Technology (MCQST), D-80799 Munich, Germany
| | - Falk Eilenberger
- Institute
of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-University, D-07745 Jena, Germany
- Fraunhofer
Institute for Applied Optics and Precision Engineering IOF, D-07745 Jena, Germany
- Max
Planck School of Photonics, D-07745 Jena, Germany
| | - Falko Schmidt
- Institute
of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-University, D-07745 Jena, Germany
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4
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Singla S, Joshi P, López-Morales GI, Sarkar S, Sarkar S, Flick J, Chakraborty B. Probing Correlation of Optical Emission and Defect Sites in Hexagonal Boron Nitride by High-Resolution STEM-EELS. NANO LETTERS 2024. [PMID: 38888554 DOI: 10.1021/acs.nanolett.4c01477] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/20/2024]
Abstract
Optically bright emitters in hexagonal boron nitride (hBN) often acting as a source of a single-photon are mostly attributed to point-defect centers, featuring localized intra-bandgap electronic states. Although vacancies, anti-sites, and impurities have been proposed as candidates, the exact physical and chemical nature of most hBN single-photon emitters (SPEs) within the visible region are still up for debate. Combining site-specific high-angle annular dark-field imaging (HAADF) with electron energy loss spectroscopy (EELS), we resolve and identify a few carbon substitutions among neighboring hBN hexagons, all within the same sample region, from which typical defect emission is observed. Our experimental results are further supported by first-principles calculations, through which the stability and possible optical transitions of the proposed carbon-defect complex are assessed. The presented correlation between optical emission and defects provides valuable information toward the controlled creation of emitters in hBN, highlighting carbon complexes as another probable cause of its visible SPEs.
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Affiliation(s)
- Sakal Singla
- Department of Physics, Indian Institute of Technology Jammu, Jammu 181221, India
| | - Pragya Joshi
- Department of Physics, Indian Institute of Technology Jammu, Jammu 181221, India
| | | | - Suman Sarkar
- Central Instrumental Facility, Indian Institute of Technology Jammu, Jammu 181221, India
| | - Suman Sarkar
- Department of Materials Engineering, Indian Institute of Technology Jammu, Jammu 181221, India
| | - Johannes Flick
- Department of Physics, The Graduate Center, City University of New York, New York, New York 10016, United States
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
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5
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Shen L, Xiao D, Cao T. Proximity-Induced Exchange Interaction: A New Pathway for Quantum Sensing Using Spin Centers in Hexagonal Boron Nitride. J Phys Chem Lett 2024; 15:4359-4366. [PMID: 38619851 DOI: 10.1021/acs.jpclett.4c00722] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/16/2024]
Abstract
Defects in hexagonal boron nitride (hBN), a two-dimensional van der Waals material, have attracted a great deal of interest because of its potential in various quantum applications. Due to hBN's two-dimensional nature, the spin center in hBN can be engineered in the proximity of the target material, providing advantages over its three-dimensional counterparts, such as the nitrogen-vacancy center in diamond. Here we propose a novel quantum sensing protocol driven by exchange interaction between the spin center in hBN and the underlying magnetic substrate induced by the magnetic proximity effect. By first-principles calculation, we demonstrate that the induced exchange interaction dominates over the dipole-dipole interaction by orders of magnitude when in the proximity. The interaction remains antiferromagnetic across all stacking configurations between the spin center in hBN and the target van der Waals magnets. Additionally, we explored the scaling behavior of the exchange field as a function of the spatial separation between the spin center and the targets.
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Affiliation(s)
- Lingnan Shen
- Department of Physics, University of Washington, Seattle, Washington 98195-1560, United States
| | - Di Xiao
- Department of Physics, University of Washington, Seattle, Washington 98195-1560, United States
- Department of Materials Science & Engineering, University of Washington, Seattle, Washington 98195-2120, United States
- Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Ting Cao
- Department of Materials Science & Engineering, University of Washington, Seattle, Washington 98195-2120, United States
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6
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Fischer M, Sajid A, Iles-Smith J, Hötger A, Miakota DI, Svendsen MK, Kastl C, Canulescu S, Xiao S, Wubs M, Thygesen KS, Holleitner AW, Stenger N. Combining experiments on luminescent centres in hexagonal boron nitride with the polaron model and ab initio methods towards the identification of their microscopic origin. NANOSCALE 2023; 15:14215-14226. [PMID: 37594441 PMCID: PMC10472209 DOI: 10.1039/d3nr01511d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2023] [Accepted: 07/21/2023] [Indexed: 08/19/2023]
Abstract
The two-dimensional material hexagonal boron nitride (hBN) hosts luminescent centres with emission energies of ∼2 eV which exhibit pronounced phonon sidebands. We investigate the microscopic origin of these luminescent centres by combining ab initio calculations with non-perturbative open quantum system theory to study the emission and absorption properties of 26 defect transitions. Comparing the calculated line shapes with experiments we narrow down the microscopic origin to three carbon-based defects: C2CB, C2CN, and VNCB. The theoretical method developed enables us to calculate so-called photoluminescence excitation (PLE) maps, which show excellent agreement with our experiments. The latter resolves higher-order phonon transitions, thereby confirming both the vibronic structure of the optical transition and the phonon-assisted excitation mechanism with a phonon energy ∼170 meV. We believe that the presented experiments and polaron-based method accurately describe luminescent centres in hBN and will help to identify their microscopic origin.
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Affiliation(s)
- Moritz Fischer
- Department of Electrical and Photonics Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark.
- Centre for Nanostructured Graphene, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
- NanoPhoton - Center for Nanophotonics, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
| | - Ali Sajid
- Centre for Nanostructured Graphene, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
- Department of Physics, Technical University of Denmark, 2800 Kgs. Lynby, Denmark
- School of Physics and Astronomy, Monash University, Victoria 3800, Australia
| | - Jake Iles-Smith
- Department of Electrical and Electronic Engineering, The University of Manchester, Sackville Street Building, Manchester M1 3BB, UK
| | - Alexander Hötger
- Walter Schottky Institute and Physics Department, Technical University of Munich, 85748 Garching, Germany
| | - Denys I Miakota
- Department of Electrical and Photonics Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark.
| | - Mark K Svendsen
- Department of Physics, Technical University of Denmark, 2800 Kgs. Lynby, Denmark
| | - Christoph Kastl
- Walter Schottky Institute and Physics Department, Technical University of Munich, 85748 Garching, Germany
| | - Stela Canulescu
- Department of Electrical and Photonics Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark.
| | - Sanshui Xiao
- Department of Electrical and Photonics Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark.
- Centre for Nanostructured Graphene, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
- NanoPhoton - Center for Nanophotonics, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
| | - Martijn Wubs
- Department of Electrical and Photonics Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark.
- Centre for Nanostructured Graphene, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
- NanoPhoton - Center for Nanophotonics, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
| | - Kristian S Thygesen
- Centre for Nanostructured Graphene, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
- Department of Physics, Technical University of Denmark, 2800 Kgs. Lynby, Denmark
| | - Alexander W Holleitner
- Walter Schottky Institute and Physics Department, Technical University of Munich, 85748 Garching, Germany
| | - Nicolas Stenger
- Department of Electrical and Photonics Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark.
- Centre for Nanostructured Graphene, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
- NanoPhoton - Center for Nanophotonics, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
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7
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Cholsuk C, Suwanna S, Vogl T. Comprehensive Scheme for Identifying Defects in Solid-State Quantum Systems. J Phys Chem Lett 2023; 14:6564-6571. [PMID: 37458585 DOI: 10.1021/acs.jpclett.3c01475] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/28/2023]
Abstract
A solid-state quantum emitter is a crucial component for optical quantum technologies, ideally with a compatible wavelength for efficient coupling to other components in a quantum network. It is essential to understand fluorescent defects that lead to specific emitters. In this Letter, we employ density functional theory (DFT) to demonstrate the calculations of the complete optical fingerprints of quantum emitters in hexagonal boron nitride. Our results suggest that instead of comparing a single optical property, like the zero-phonon line energy, multiple properties should be used when comparing simulations to the experiment. Moreover, we apply this approach to predict the suitability of using the emitters in specific quantum applications. We therefore apply DFT calculations to identify quantum emitters with a lower risk of misassignments and a way to design optical quantum systems. Hence, we provide a recipe for classification and generation of universal quantum emitters in future hybrid quantum networks.
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Affiliation(s)
- Chanaprom Cholsuk
- Abbe Center of Photonics, Institute of Applied Physics, Friedrich Schiller University Jena, 07745 Jena, Germany
| | - Sujin Suwanna
- Optical and Quantum Physics Laboratory, Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
| | - Tobias Vogl
- Abbe Center of Photonics, Institute of Applied Physics, Friedrich Schiller University Jena, 07745 Jena, Germany
- Fraunhofer-Institute for Applied Optics and Precision Engineering IOF, 07745 Jena, Germany
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8
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Guo NJ, Li S, Liu W, Yang YZ, Zeng XD, Yu S, Meng Y, Li ZP, Wang ZA, Xie LK, Ge RC, Wang JF, Li Q, Xu JS, Wang YT, Tang JS, Gali A, Li CF, Guo GC. Coherent control of an ultrabright single spin in hexagonal boron nitride at room temperature. Nat Commun 2023; 14:2893. [PMID: 37210408 DOI: 10.1038/s41467-023-38672-6] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2022] [Accepted: 05/10/2023] [Indexed: 05/22/2023] Open
Abstract
Hexagonal boron nitride (hBN) is a remarkable two-dimensional (2D) material that hosts solid-state spins and has great potential to be used in quantum information applications, including quantum networks. However, in this application, both the optical and spin properties are crucial for single spins but have not yet been discovered simultaneously for hBN spins. Here, we realize an efficient method for arraying and isolating the single defects of hBN and use this method to discover a new spin defect with a high probability of 85%. This single defect exhibits outstanding optical properties and an optically controllable spin, as indicated by the observed significant Rabi oscillation and Hahn echo experiments at room temperature. First principles calculations indicate that complexes of carbon and oxygen dopants may be the origin of the single spin defects. This provides a possibility for further addressing spins that can be optically controlled.
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Affiliation(s)
- Nai-Jie Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
| | - Song Li
- Wigner Research Centre for Physics, Post Office Box 49, H-1525Budapest, Hungary
| | - Wei Liu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
| | - Yuan-Ze Yang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
| | - Xiao-Dong Zeng
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
| | - Shang Yu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
| | - Yu Meng
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
| | - Zhi-Peng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
| | - Zhao-An Wang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
| | - Lin-Ke Xie
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
| | - Rong-Chun Ge
- College of Physics, Sichuan University, Chengdu, 610064, China
| | - Jun-Feng Wang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
- College of Physics, Sichuan University, Chengdu, 610064, China
| | - Qiang Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
| | - Jin-Shi Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
| | - Yi-Tao Wang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, 230026, China.
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China.
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China.
| | - Jian-Shun Tang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, 230026, China.
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China.
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China.
| | - Adam Gali
- Wigner Research Centre for Physics, Post Office Box 49, H-1525Budapest, Hungary.
- Department of Atomic Physics, Institute of Physics, Budapest University of Technology and Economics, Muegyetem rakpart 3, H-1111Budapest, Hungary.
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, 230026, China.
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China.
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China.
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
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