1
|
Bayati S, Bagheri Harouni M, Mahdifar A. Magnomechanically induced transparency and tunable slow-fast light via a levitated micromagnet. OPTICS EXPRESS 2024; 32:14914-14928. [PMID: 38859155 DOI: 10.1364/oe.515093] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2023] [Accepted: 03/22/2024] [Indexed: 06/12/2024]
Abstract
In this paper, we theoretically investigate the magnomechanically induced transparency (MIT) phenomenon and slow-fast light propagation in a microwave cavity-magnomechanical system which includes a levitated ferromagnetic sphere. Magnetic dipole interaction determines the interaction between the photon, magnon, and center of mass motion of the cavity-magnomechanical system. As a result, we find that apart from coupling strength, which has an important role in MIT, the levitated ferromagnetic sphere's position provides us a parameter to manipulate the width of the transparency window. In addition, the control field's frequency has crucial influences on the MIT. Also this hybrid magnonic system allows us to demonstrate MIT in both the strong coupling and intermediate coupling regimes. More interestingly, we demonstrate tunable slow and fast light in this hybrid magnonic system. In other words, we show that the group delay can be adjusted by varying the control field's frequency, the sphere position, and the magnon-photon coupling strength. These parameters have an influence on the transformation from slow to fast light propagation and vice versa. Based on the recent experimental advancements, our results provide the possibility to engineer hybrid magnonic systems with levitated particles for the light propagation, and the quantum measurements and sensing of physical quantities.
Collapse
|
2
|
Bi MX, Fan H, Yan XH, Lai YC. Folding State within a Hysteresis Loop: Hidden Multistability in Nonlinear Physical Systems. PHYSICAL REVIEW LETTERS 2024; 132:137201. [PMID: 38613259 DOI: 10.1103/physrevlett.132.137201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2023] [Revised: 11/28/2023] [Accepted: 02/12/2024] [Indexed: 04/14/2024]
Abstract
Identifying hidden states in nonlinear physical systems that evade direct experimental detection is important as disturbances and noises can place the system in a hidden state with detrimental consequences. We study a cavity magnonic system whose main physics is photon and magnon Kerr effects. Sweeping a bifurcation parameter in numerical experiments (as would be done in actual experiments) leads to a hysteresis loop with two distinct stable steady states, but analytic calculation gives a third folded steady state "hidden" in the loop, which gives rise to the phenomenon of hidden multistability. We propose an experimentally feasible control method to drive the system into the folded hidden state. We demonstrate, through a ternary cavity magnonic system and a gene regulatory network, that such hidden multistability is in fact quite common. Our findings shed light on hidden dynamical states in nonlinear physical systems which are not directly observable but can present challenges and opportunities in applications.
Collapse
Affiliation(s)
- Meng-Xia Bi
- School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China
| | - Huawei Fan
- School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China
| | - Xiao-Hong Yan
- School of Material Science and Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Ying-Cheng Lai
- School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA
- Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
| |
Collapse
|
3
|
Li Y, Zhang Z, Liu C, Zheng D, Fang B, Zhang C, Chen A, Ma Y, Wang C, Liu H, Shen K, Manchon A, Xiao JQ, Qiu Z, Hu CM, Zhang X. Reconfigurable spin current transmission and magnon-magnon coupling in hybrid ferrimagnetic insulators. Nat Commun 2024; 15:2234. [PMID: 38472180 DOI: 10.1038/s41467-024-46330-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2023] [Accepted: 02/22/2024] [Indexed: 03/14/2024] Open
Abstract
Coherent spin waves possess immense potential in wave-based information computation, storage, and transmission with high fidelity and ultra-low energy consumption. However, despite their seminal importance for magnonic devices, there is a paucity of both structural prototypes and theoretical frameworks that regulate the spin current transmission and magnon hybridization mediated by coherent spin waves. Here, we demonstrate reconfigurable coherent spin current transmission, as well as magnon-magnon coupling, in a hybrid ferrimagnetic heterostructure comprising epitaxial Gd3Fe5O12 and Y3Fe5O12 insulators. By adjusting the compensated moment in Gd3Fe5O12, magnon-magnon coupling was achieved and engineered with pronounced anticrossings between two Kittel modes, accompanied by divergent dissipative coupling approaching the magnetic compensation temperature of Gd3Fe5O12 (TM,GdIG), which were modeled by coherent spin pumping. Remarkably, we further identified, both experimentally and theoretically, a drastic variation in the coherent spin wave-mediated spin current across TM,GdIG, which manifested as a strong dependence on the relative alignment of magnetic moments. Our findings provide significant fundamental insight into the reconfiguration of coherent spin waves and offer a new route towards constructing artificial magnonic architectures.
Collapse
Affiliation(s)
- Yan Li
- Physical Science and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Saudi Arabia
| | - Zhitao Zhang
- Guangdong Provincial Key Laboratory of Semiconductor, Optoelectronic Materials and Intelligent Photonic Systems, School of Science, Harbin Institute of Technology (Shenzhen), 518055, Shenzhen, China
| | - Chen Liu
- Physical Science and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Saudi Arabia
| | - Dongxing Zheng
- Physical Science and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Saudi Arabia
| | - Bin Fang
- Physical Science and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Saudi Arabia
| | - Chenhui Zhang
- Physical Science and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Saudi Arabia
| | - Aitian Chen
- Physical Science and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Saudi Arabia
| | - Yinchang Ma
- Physical Science and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Saudi Arabia
| | - Chunmei Wang
- Guangdong Provincial Key Laboratory of Semiconductor, Optoelectronic Materials and Intelligent Photonic Systems, School of Science, Harbin Institute of Technology (Shenzhen), 518055, Shenzhen, China
| | - Haoliang Liu
- Guangdong Provincial Key Laboratory of Semiconductor, Optoelectronic Materials and Intelligent Photonic Systems, School of Science, Harbin Institute of Technology (Shenzhen), 518055, Shenzhen, China.
| | - Ka Shen
- The Center for Advanced Quantum Studies and Department of Physics, Beijing Normal University, 100875, Beijing, China.
| | | | - John Q Xiao
- Department of Physics and Astronomy, University of Delaware, Newark, Newark, DE, 19716, USA
| | - Ziqiang Qiu
- Department of Physics, University of California at Berkeley, Berkeley, CA, 94720, USA
| | - Can-Ming Hu
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB, R3T 2N2, Canada
| | - Xixiang Zhang
- Physical Science and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Saudi Arabia.
| |
Collapse
|
4
|
Ghasemian E. Dissipative dynamics of optomagnonic nonclassical features via anti-Stokes optical pulses: squeezing, blockade, anti-correlation, and entanglement. Sci Rep 2023; 13:12757. [PMID: 37550430 PMCID: PMC10406899 DOI: 10.1038/s41598-023-39822-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Accepted: 07/31/2023] [Indexed: 08/09/2023] Open
Abstract
We propose a feasible experimental model to investigate the generation and characterization of nonclassical states in a cavity optomagnonic system consisting of a ferromagnetic YIG sphere that simultaneously supports both the magnon mode and two whispering gallery modes of optical photons. The photons undergo the magnon-induced Brillouin light scattering, which is a well-established tool for the cavity-assisted manipulations of magnons as well as magnon spintronics. At first, we derive the desired interaction Hamiltonian under the influence of the anti-Stokes scattering process and then proceed to analyze the dynamical evolution of quantum statistics of photons and magnons as well as their intermodal entanglement. The results show that both photons and magnons generally acquire some nonclassical features, e.g., the strong antibunching and anti-correlation. Interestingly, the system may experience the perfect photon and magnon blockade phenomena, simultaneously. Besides, the nonclassical features may be protected against the unwanted environmental effects for a relatively long time, especially, in the weak driving field regime and when the system is initiated with a small number of particles. However, it should be noted that some fast quantum-classical transitions may occur in-between. Although the unwanted dissipative effects plague the nonclassical features, we show that this system can be adopted to prepare optomagnonic entangled states. The generation of entangled states depends on the initial state of the system and the interaction regime. The intermodal photon-magnon entanglement may be generated and pronounced, especially, if the system is initialized with low intensity even Schrödinger cat state in the strong coupling regime. The cavity-assisted manipulation of magnons is a unique and flexible mechanism that allows an interesting test bed for investigating the interdisciplinary contexts involving quantum optics and spintronics. Moreover, such a hybrid optomagnonic system may be used to design both on-demand single-photon and single-magnon sources and may find potential applications in quantum information processing.
Collapse
Affiliation(s)
- E Ghasemian
- Department of Electrical Engineering, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr, Iran.
| |
Collapse
|
5
|
Yao B, Gui YS, Rao JW, Zhang YH, Lu W, Hu CM. Coherent Microwave Emission of Gain-Driven Polaritons. PHYSICAL REVIEW LETTERS 2023; 130:146702. [PMID: 37084460 DOI: 10.1103/physrevlett.130.146702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Revised: 12/19/2022] [Accepted: 02/16/2023] [Indexed: 05/03/2023]
Abstract
By developing a gain-embedded cavity magnonics platform, we create a gain-driven polariton (GDP) that is activated by an amplified electromagnetic field. Distinct effects of gain-driven light-matter interaction, such as polariton auto-oscillations, polariton phase singularity, self-selection of a polariton bright mode, and gain-induced magnon-photon synchronization, are theoretically studied and experimentally manifested. Utilizing the gain-sustained photon coherence of the GDP, we demonstrate polariton-based coherent microwave amplification (∼40 dB) and achieve high-quality coherent microwave emission (Q>10^{9}).
Collapse
Affiliation(s)
- Bimu Yao
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, R3T 2N2, Canada
- State Key Laboratory of Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
| | - Y S Gui
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, R3T 2N2, Canada
| | - J W Rao
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, R3T 2N2, Canada
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
| | - Y H Zhang
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, R3T 2N2, Canada
| | - Wei Lu
- State Key Laboratory of Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
| | - C-M Hu
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, R3T 2N2, Canada
| |
Collapse
|
6
|
Rao JW, Yao B, Wang CY, Zhang C, Yu T, Lu W. Unveiling a Pump-Induced Magnon Mode via Its Strong Interaction with Walker Modes. PHYSICAL REVIEW LETTERS 2023; 130:046705. [PMID: 36763434 DOI: 10.1103/physrevlett.130.046705] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2022] [Revised: 11/16/2022] [Accepted: 01/05/2023] [Indexed: 06/18/2023]
Abstract
We observe a power-dependent anticrossing of Walker spin-wave modes under microwave pumping when a ferrimagnet is placed in a microwave waveguide that does not support any discrete photon mode. We interpret this unexpected anticrossing as the generation of a pump-induced magnon mode that couples strongly to the Walker modes of the ferrimagnet. This anticrossing inherits an excellent tunability from the pump, which allows us to control the anticrossing via the pump power, frequency, and waveform. Further, we realize a remarkable functionality of this anticrossing, namely, a microwave frequency comb, in terms of the nonlinear interaction that mixes the pump and probe frequencies. Such a frequency comb originates from the magnetic dynamics and thereby does not suffer from the charge noise. The unveiled hybrid magnonics driven away from its equilibrium enriches the utilization of anticrossing for coherent information processing.
Collapse
Affiliation(s)
- J W Rao
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
| | - Bimu Yao
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
- State Key Laboratory of Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China
| | - C Y Wang
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
| | - C Zhang
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
| | - Tao Yu
- School of Physics, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Wei Lu
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
- State Key Laboratory of Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China
| |
Collapse
|
7
|
Kong C, Bao XM, Liu JB, Xiong H. Magnon-mediated nonreciprocal microwave transmission based on quantum interference. OPTICS EXPRESS 2021; 29:25477-25487. [PMID: 34614878 DOI: 10.1364/oe.430619] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2021] [Accepted: 07/19/2021] [Indexed: 06/13/2023]
Abstract
Nonreciprocity has always been a subject of interest and plays a key role in a variety of applications like signal processing and noise isolation. In this work, we propose a simple and feasible scheme to implement nonreciprocal microwave transmission in a high-quality-factor superconducting cavity with ferrimagnetic materials. We derive necessary requirements to create nonreciprocity in our system where a magnon mode and two microwave modes are coupled to each other, highlighting the adjustability of a static magnetic field controlled nonreciprocal transmission based on quantum interference between different transmission paths, which breaks time-reversal symmetry of the three-mode cavity magnonics system. The high light isolation adjusted within a range of different magnetic fields can be obtained by modulating the photon-magnon coupling strength. Due to the simplicity of the device and the system tunability, our results may facilitate potential applications for light magnetic sensing and coherent information processing.
Collapse
|
8
|
Rao JW, Xu PC, Gui YS, Wang YP, Yang Y, Yao B, Dietrich J, Bridges GE, Fan XL, Xue DS, Hu CM. Interferometric control of magnon-induced nearly perfect absorption in cavity magnonics. Nat Commun 2021; 12:1933. [PMID: 33772003 PMCID: PMC7997962 DOI: 10.1038/s41467-021-22171-7] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2020] [Accepted: 02/25/2021] [Indexed: 11/23/2022] Open
Abstract
The perfect absorption of electromagnetic waves has promoted many applications, including photovoltaics, radar cloaking, and molecular detection. Unlike conventional methods of critical coupling that require asymmetric boundaries or coherent perfect absorption that require multiple coherent incident beams, here we demonstrate single-beam perfect absorption in an on-chip cavity magnonic device without breaking its boundary symmetry. By exploiting magnon-mediated interference between two internal channels, both reflection and transmission of our device can be suppressed to zero, resulting in magnon-induced nearly perfect absorption (MIPA). Such interference can be tuned by the strength and direction of an external magnetic field, thus showing versatile controllability. Furthermore, the same multi-channel interference responsible for MIPA also produces level attraction (LA)-like hybridization between a cavity magnon polariton mode and a cavity photon mode, demonstrating that LA-like hybridization can be surprisingly realized in a coherently coupled system.
Collapse
Affiliation(s)
- J W Rao
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada, R3T 2N2
| | - P C Xu
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada, R3T 2N2
| | - Y S Gui
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada, R3T 2N2
| | - Y P Wang
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada, R3T 2N2
| | - Y Yang
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada, R3T 2N2
| | - Bimu Yao
- State Key Laboratory of Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai, 200083, China.
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, 201210, China.
| | - J Dietrich
- Department of Electrical Engineering, University of Manitoba, Winnipeg, Canada, R3T 2N2
| | - G E Bridges
- Department of Electrical Engineering, University of Manitoba, Winnipeg, Canada, R3T 2N2
| | - X L Fan
- The Key Lab for Magnetism and Magnetic Materials of Ministry of Education, Lanzhou University, Lanzhou, 730000, China
| | - D S Xue
- The Key Lab for Magnetism and Magnetic Materials of Ministry of Education, Lanzhou University, Lanzhou, 730000, China
| | - C-M Hu
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada, R3T 2N2.
| |
Collapse
|
9
|
Li Y, Zhao C, Amin VP, Zhang Z, Vogel M, Xiong Y, Sklenar J, Divan R, Pearson J, Stiles MD, Zhang W, Hoffmann A, Novosad V. Phase-resolved electrical detection of hybrid magnonic devices. APPLIED PHYSICS LETTERS 2021; 118:10.1063/5.0042784. [PMID: 36452035 PMCID: PMC9706546 DOI: 10.1063/5.0042784] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2021] [Accepted: 05/03/2021] [Indexed: 06/17/2023]
Abstract
We demonstrate the electrical detection of magnon-magnon hybrid dynamics in yttrium iron garnet/permalloy (YIG/Py) thin film bilayer devices. Direct microwave current injection through the conductive Py layer excites the hybrid dynamics consisting of the uniform mode of Py and the first standing spin wave (n = 1) mode of YIG, which are coupled via interfacial exchange. Both the two hybrid modes, with Py or YIG dominated excitations, can be detected via the spin rectification signals from the conductive Py layer, providing phase resolution of the coupled dynamics. The phase characterization is also applied to a nonlocally excited Py device, revealing the additional phase shift due to the perpendicular Oersted field. Our results provide a device platform for exploring hybrid magnonic dynamics and probing their phases, which are crucial for implementing coherent information processing with magnon excitations.
Collapse
Affiliation(s)
- Yi Li
- Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, USA†
| | - Chenbo Zhao
- Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, USA†
| | - Vivek P. Amin
- Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, USA
- Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Zhizhi Zhang
- Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, USA†
| | - Michael Vogel
- Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, USA†
- Institute of Physics and Center for Interdisciplinary Nanostructure Science and Technology (CINSaT), University of Kassel, Heinrich-Plett-Strasse 40, Kassel 34132, Germany
| | - Yuzan Xiong
- Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, USA†
- Department of Physics, Oakland University, Rochester, MI 48309, USA
| | - Joseph Sklenar
- Department of Physics and Astronomy, Wayne State University, Detroit, Michigan 48202, USA
| | - Ralu Divan
- Center for Nanoscale Materials, Argonne National Laboratory, Argonne, IL 60439, USA
| | - John Pearson
- Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, USA†
| | - Mark D. Stiles
- Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Wei Zhang
- Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, USA†
- Department of Physics, Oakland University, Rochester, MI 48309, USA
| | - Axel Hoffmann
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign Urbana, IL 61801, USA
| | - Valentine Novosad
- Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, USA†
| |
Collapse
|
10
|
Yang ZB, Liu JS, Jin H, Zhu QH, Zhu AD, Liu HY, Ming Y, Yang RC. Entanglement enhanced by Kerr nonlinearity in a cavity-optomagnonics system. OPTICS EXPRESS 2020; 28:31862-31871. [PMID: 33115150 DOI: 10.1364/oe.404522] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2020] [Accepted: 09/29/2020] [Indexed: 06/11/2023]
Abstract
We present a method to enhance steady-state bipartite and tripartite entanglement in a cavity-optomagnonics system by utilizing the Kerr nonlinearity originating from the magnetocrystalline anisotropy. The system comprises two microwave cavities and a magnon and represents the collective motion of several spins in a macroscopic ferrimagnet. We prove that Kerr nonlinearity is reliable for the enhancement of entanglement and produces a small frequency shift in the optimal detuning. Our system is more robust against the environment-induced decoherence than traditional optomechanical systems. Finally, we briefly analyze the validity of the system and demonstrate its feasibility for detecting the generated entanglement.
Collapse
|
11
|
Xiong Y, Li Y, Hammami M, Bidthanapally R, Sklenar J, Zhang X, Qu H, Srinivasan G, Pearson J, Hoffmann A, Novosad V, Zhang W. Probing magnon-magnon coupling in exchange coupled Y[Formula: see text]Fe[Formula: see text]O[Formula: see text]/Permalloy bilayers with magneto-optical effects. Sci Rep 2020; 10:12548. [PMID: 32724049 PMCID: PMC7387351 DOI: 10.1038/s41598-020-69364-6] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2020] [Accepted: 07/10/2020] [Indexed: 11/09/2022] Open
Abstract
We demonstrate the magnetically-induced transparency (MIT) effect in Y[Formula: see text]Fe[Formula: see text]O[Formula: see text](YIG)/Permalloy (Py) coupled bilayers. The measurement is achieved via a heterodyne detection of the coupled magnetization dynamics using a single wavelength that probes the magneto-optical Kerr and Faraday effects of Py and YIG, respectively. Clear features of the MIT effect are evident from the deeply modulated ferromagnetic resonance of Py due to the perpendicular-standing-spin-wave of YIG. We develop a phenomenological model that nicely reproduces the experimental results including the induced amplitude and phase evolution caused by the magnon-magnon coupling. Our work offers a new route towards studying phase-resolved spin dynamics and hybrid magnonic systems.
Collapse
Affiliation(s)
- Yuzan Xiong
- Department of Physics, Oakland University, Rochester, MI 48309 USA
- Department of Electronic and Computer Engineering, Oakland University, Rochester, MI 48309 USA
| | - Yi Li
- Materials Science Division, Argonne National Laboratory, Argonne, IL 60439 USA
| | - Mouhamad Hammami
- Department of Physics, Oakland University, Rochester, MI 48309 USA
| | | | - Joseph Sklenar
- Department of Physics and Astronomy, Wayne State University, Detroit, MI 48201 USA
| | - Xufeng Zhang
- Center for Nanoscale Materials, Argonne National Laboratory, Argonne, IL 60439 USA
| | - Hongwei Qu
- Department of Electronic and Computer Engineering, Oakland University, Rochester, MI 48309 USA
| | | | - John Pearson
- Materials Science Division, Argonne National Laboratory, Argonne, IL 60439 USA
| | - Axel Hoffmann
- Materials Science Division, Argonne National Laboratory, Argonne, IL 60439 USA
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA
| | - Valentine Novosad
- Materials Science Division, Argonne National Laboratory, Argonne, IL 60439 USA
| | - Wei Zhang
- Department of Physics, Oakland University, Rochester, MI 48309 USA
- Materials Science Division, Argonne National Laboratory, Argonne, IL 60439 USA
| |
Collapse
|
12
|
Shim J, Kim SJ, Kim SK, Lee KJ. Enhanced Magnon-Photon Coupling at the Angular Momentum Compensation Point of Ferrimagnets. PHYSICAL REVIEW LETTERS 2020; 125:027205. [PMID: 32701310 DOI: 10.1103/physrevlett.125.027205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2020] [Accepted: 06/18/2020] [Indexed: 06/11/2023]
Abstract
We theoretically show that the coupling between magnons in an antiferromagnetically coupled ferrimagnet and microwave photons in a cavity is largely enhanced at the angular momentum compensation point (T_{A}) when T_{A} is distinct from the magnetization compensation point. The origin of the enhanced magnon-photon coupling at T_{A} is identified as the antiferromagnetic spin dynamics combined with a finite magnetization. Moreover, we show that strong magnon-photon coupling can be achieved at high excitation frequency in a ferrimagnet, which is challenging to achieve for a ferromagnet due to low magnon frequency and for an antiferromagnet due to weak magnon-photon coupling. Our results will invigorate research on magnon-photon coupling by proposing ferrimagnets as a versatile platform that offers advantages of both ferromagnets and antiferromagnets.
Collapse
Affiliation(s)
- Jaechul Shim
- Department of Materials Science and Engineering, Korea University, Seoul 02841, Korea
- Semiconductor R&D Center, Samsung Electronics Co. Ltd., Hwaseong, Gyeonggi 18448, Korea
| | - Seok-Jong Kim
- KU-KIST Graduate School of Converging Science and Technology, Korea University, Seoul 02841, Korea
| | - Se Kwon Kim
- Department of Physics, KAIST, Daejeon 34141, Korea
- Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA
| | - Kyung-Jin Lee
- Department of Materials Science and Engineering, Korea University, Seoul 02841, Korea
- KU-KIST Graduate School of Converging Science and Technology, Korea University, Seoul 02841, Korea
| |
Collapse
|
13
|
Yu W, Wang J, Yuan HY, Xiao J. Prediction of Attractive Level Crossing via a Dissipative Mode. PHYSICAL REVIEW LETTERS 2019; 123:227201. [PMID: 31868418 DOI: 10.1103/physrevlett.123.227201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2019] [Revised: 09/13/2019] [Indexed: 06/10/2023]
Abstract
The new field of spin cavitronics focuses on the interaction between the magnon excitation of a magnetic element and the electromagnetic wave in a microwave cavity. In the strong interaction regime, such an interaction usually gives rise to the level anticrossing for the magnonic and the electromagnetic mode. Recently, the attractive level crossing has been observed, and it is explained by a non-Hermitian model Hamiltonian. However, the mechanism of such attractive coupling is still unclear. We reveal the secret by using a simple model with two harmonic oscillators coupled to a third oscillator with large dissipation. We further identify this dissipative third party as the invisible cavity mode with large leakage in cavity-magnon experiments. This understanding enables one to design dissipative coupling in all sorts of coupled systems.
Collapse
Affiliation(s)
- Weichao Yu
- Department of Physics and State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China
- Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
| | - Jiongjie Wang
- Department of Physics and State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China
| | - H Y Yuan
- Department of Physics, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China
| | - Jiang Xiao
- Department of Physics and State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China
- Institute for Nanoelectronics Devices and Quantum Computing, Fudan University, Shanghai 200433, China
| |
Collapse
|
14
|
Liu H, Sun D, Zhang C, Groesbeck M, Mclaughlin R, Vardeny ZV. Observation of exceptional points in magnonic parity-time symmetry devices. SCIENCE ADVANCES 2019; 5:eaax9144. [PMID: 31803837 PMCID: PMC6874485 DOI: 10.1126/sciadv.aax9144] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/03/2019] [Accepted: 09/18/2019] [Indexed: 06/10/2023]
Abstract
Non-Hermitian Hamiltonians may still have real eigenvalues, provided that a combined parity-time (ƤƮ) symmetry exists. The prospect of ƤƮ symmetry has been explored in several physical systems such as photonics, acoustics, and electronics. The eigenvalues in these systems undergo a transition from real to complex at exceptional points (EPs), where the ƤƮ symmetry is broken. Here, we demonstrate the existence of EP in magnonic devices composed of two coupled magnets with different magnon losses. The eigenfrequencies and damping rates change from crossing to anti-crossing at the EP when the coupling strength increases. The magnonic dispersion includes a strong "acoustic-like" mode and a weak "optic-like" mode. Moreover, upon microwave radiation, the ƤƮ magnonic devices act as magnon resonant cavity with unique response compared to conventional magnonic systems.
Collapse
Affiliation(s)
- Haoliang Liu
- Department of Physics and Astronomy, University of Utah, Salt Lake City, UT 84112, USA
| | - Dali Sun
- Department of Physics and Astronomy, University of Utah, Salt Lake City, UT 84112, USA
- Department of Physics, North Carolina State University, Raleigh, NC 27695, USA
| | - Chuang Zhang
- Department of Physics and Astronomy, University of Utah, Salt Lake City, UT 84112, USA
| | - Matthew Groesbeck
- Department of Physics and Astronomy, University of Utah, Salt Lake City, UT 84112, USA
| | - Ryan Mclaughlin
- Department of Physics and Astronomy, University of Utah, Salt Lake City, UT 84112, USA
| | - Z. Valy Vardeny
- Department of Physics and Astronomy, University of Utah, Salt Lake City, UT 84112, USA
| |
Collapse
|
15
|
Wang YP, Rao JW, Yang Y, Xu PC, Gui YS, Yao BM, You JQ, Hu CM. Nonreciprocity and Unidirectional Invisibility in Cavity Magnonics. PHYSICAL REVIEW LETTERS 2019; 123:127202. [PMID: 31633946 DOI: 10.1103/physrevlett.123.127202] [Citation(s) in RCA: 42] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2019] [Indexed: 05/16/2023]
Abstract
We reveal the cooperative effect of coherent and dissipative magnon-photon couplings in an open cavity magnonic system, which leads to nonreciprocity with a considerably large isolation ratio and flexible controllability. Furthermore, we discover unidirectional invisibility for microwave propagation, which appears at the zero-damping condition for hybrid magnon-photon modes. A simple model is developed to capture the generic physics of the interference between coherent and dissipative couplings, which accurately reproduces the observations over a broad range of parameters. This general scheme could inspire methods to achieve nonreciprocity in other systems.
Collapse
Affiliation(s)
- Yi-Pu Wang
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada R3T 2N2
| | - J W Rao
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada R3T 2N2
| | - Y Yang
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada R3T 2N2
| | - Peng-Chao Xu
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada R3T 2N2
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
| | - Y S Gui
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada R3T 2N2
| | - B M Yao
- State Key Laboratory of Infrared Physics, Chinese Academy of Sciences, Shanghai 200083, People's Republic of China
| | - J Q You
- Interdisciplinary Center of Quantum Information and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics and State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, China
| | - C-M Hu
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada R3T 2N2
| |
Collapse
|
16
|
Li Y, Polakovic T, Wang YL, Xu J, Lendinez S, Zhang Z, Ding J, Khaire T, Saglam H, Divan R, Pearson J, Kwok WK, Xiao Z, Novosad V, Hoffmann A, Zhang W. Strong Coupling between Magnons and Microwave Photons in On-Chip Ferromagnet-Superconductor Thin-Film Devices. PHYSICAL REVIEW LETTERS 2019; 123:107701. [PMID: 31573284 DOI: 10.1103/physrevlett.123.107701] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2019] [Indexed: 06/10/2023]
Abstract
We demonstrate strong magnon-photon coupling of a thin-film Permalloy device fabricated on a coplanar superconducting resonator. A coupling strength of 0.152 GHz and a cooperativity of 68 are found for a 30-nm-thick Permalloy stripe. The coupling strength is tunable by rotating the biasing magnetic field or changing the volume of Permalloy. We also observe an enhancement of magnon-photon coupling in the nonlinear regime of the superconducting resonator, which is attributed to the nucleation of dynamic flux vortices. Our results demonstrate a critical step towards future integrated hybrid systems for quantum magnonics and on-chip coherent information transfer.
Collapse
Affiliation(s)
- Yi Li
- Department of Physics, Oakland University, Rochester, Michigan 48309, USA
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Tomas Polakovic
- Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
- Department of Physics, Drexel University, Philadelphia, Pennsylvania 19104, USA
| | - Yong-Lei Wang
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, 210093, Nanjing, China
| | - Jing Xu
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
- Department of Physics, Northern Illinois University, Dekalb, Illinois 60115, USA
| | - Sergi Lendinez
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Zhizhi Zhang
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
- School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Junjia Ding
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Trupti Khaire
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Hilal Saglam
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
- Department of Physics, Illinois Institute of Technology, Chicago Illinois 60616, USA
| | - Ralu Divan
- Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - John Pearson
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Wai-Kwong Kwok
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Zhili Xiao
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
- Department of Physics, Northern Illinois University, Dekalb, Illinois 60115, USA
| | - Valentine Novosad
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Axel Hoffmann
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Wei Zhang
- Department of Physics, Oakland University, Rochester, Michigan 48309, USA
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| |
Collapse
|
17
|
Kong C, Wang B, Liu ZX, Xiong H, Wu Y. Magnetically controllable slow light based on magnetostrictive forces. OPTICS EXPRESS 2019; 27:5544-5556. [PMID: 30876185 DOI: 10.1364/oe.27.005544] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2018] [Accepted: 02/02/2019] [Indexed: 06/09/2023]
Abstract
The magnetostrictive effect provides an opportunity for exploring fundamental phenomena related to the phonon-magnon interaction. Here we show a tunable slow light in a cavity magnetomechanical system consisting of photon, magnon and phonon modes with a nonlinear phonon-magnon interaction, which originates from magnetostrictive forces. For a strong photon-magnon coupling strength, we can observe a transparency (absorption) window for the probe by placing a strong control field on the red (blue) detuned sideband of the hybridized modes, which are comprised of photons and magnons. In this work, we mainly show the characteristic changes in dispersion in the range of the transparency window. The value of group delay can be continuously adjusted by using different frequencies of magnon, which are determined by the external bias magnetic field and therefore can be conveniently tuned in a broad range. Both the intensity and the frequency of the control field have an influence on the transformation from subluminal to superluminal propagation and vice versa. Furthermore, one may achieve long-lived slow light (group delay of millisecond order) by enlarging the pump power. These results may find applications in information interconversion based on coherent coupling among photons, phonons and magnons.
Collapse
|
18
|
Clark TJ, Vadakkumbatt V, Souris F, Ramp H, Davis JP. Cryogenic microwave filter cavity with a tunability greater than 5 GHz. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2018; 89:114704. [PMID: 30501360 DOI: 10.1063/1.5051042] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2018] [Accepted: 11/02/2018] [Indexed: 06/09/2023]
Abstract
A wide variety of applications of microwave cavities, such as measurement and control of superconducting qubits, magnonic resonators, and phase noise filters, would be well served by having a highly tunable microwave resonance. Often this tunability is desired in situ at low temperatures, where one can take advantage of superconducting cavities. To date, such cryogenic tuning while maintaining a high quality factor has been limited to ∼500 MHz. Here we demonstrate a three-dimensional superconducting microwave cavity that shares one wall with a pressurized volume of helium. Upon pressurization of the helium chamber, the microwave cavity is deformed, which results in in situ tuning of its resonant frequency by more than 5 GHz, greater than 60% of the original 8 GHz resonant frequency. The quality factor of the cavity remains approximately constant at ≈7 × 103 over the entire range of tuning. As a demonstration of its usefulness, we implement a tunable cryogenic phase noise filter, which reduces the phase noise of our source by approximately 10 dB above 400 kHz.
Collapse
Affiliation(s)
- T J Clark
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E9, Canada
| | - V Vadakkumbatt
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E9, Canada
| | - F Souris
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E9, Canada
| | - H Ramp
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E9, Canada
| | - J P Davis
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E9, Canada
| |
Collapse
|
19
|
Harder M, Yang Y, Yao BM, Yu CH, Rao JW, Gui YS, Stamps RL, Hu CM. Level Attraction Due to Dissipative Magnon-Photon Coupling. PHYSICAL REVIEW LETTERS 2018; 121:137203. [PMID: 30312103 DOI: 10.1103/physrevlett.121.137203] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2018] [Revised: 09/03/2018] [Indexed: 06/08/2023]
Abstract
We report dissipative magnon-photon coupling caused by the cavity Lenz effect, where the magnons in a magnet induce a rf current in the cavity, leading to a cavity backaction that impedes the magnetization dynamics. This effect is revealed in our experiment as level attraction with a coalescence of hybridized magnon-photon modes, which is distinctly different from level repulsion with mode anticrossing caused by coherent magnon-photon coupling. We develop a method to control the interpolation of coherent and dissipative magnon-photon coupling, and observe a matching condition where the two effects cancel. Our work sheds light on the so-far hidden side of magnon-photon coupling, opening a new avenue for controlling and utilizing light-matter interactions.
Collapse
Affiliation(s)
- M Harder
- Department of Physics and Astronomy, University of Manitoba, Winnipeg R3T 2N2, Canada
| | - Y Yang
- Department of Physics and Astronomy, University of Manitoba, Winnipeg R3T 2N2, Canada
- State Key Laboratory of Infrared Physics, Chinese Academy of Sciences, Shanghai 200083, China
| | - B M Yao
- State Key Laboratory of Infrared Physics, Chinese Academy of Sciences, Shanghai 200083, China
| | - C H Yu
- Department of Physics and Astronomy, University of Manitoba, Winnipeg R3T 2N2, Canada
- Jiangsu Key Laboratory of ASIC Design, Nantong University, Nantong 226019, China
| | - J W Rao
- Department of Physics and Astronomy, University of Manitoba, Winnipeg R3T 2N2, Canada
| | - Y S Gui
- Department of Physics and Astronomy, University of Manitoba, Winnipeg R3T 2N2, Canada
| | - R L Stamps
- Department of Physics and Astronomy, University of Manitoba, Winnipeg R3T 2N2, Canada
| | - C-M Hu
- Department of Physics and Astronomy, University of Manitoba, Winnipeg R3T 2N2, Canada
| |
Collapse
|
20
|
Johansen Ø, Brataas A. Nonlocal Coupling between Antiferromagnets and Ferromagnets in Cavities. PHYSICAL REVIEW LETTERS 2018; 121:087204. [PMID: 30192613 DOI: 10.1103/physrevlett.121.087204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2018] [Indexed: 06/08/2023]
Abstract
Microwaves couple to magnetic moments in both ferromagnets and antiferromagnets. Although the magnons in ferromagnets and antiferromagnets radically differ, they can become entangled via strong coupling to the same microwave mode in a cavity. The equilibrium configuration of the magnetic moments crucially governs the coupling between the different magnons, because the antiferromagnetic and ferromagnetic magnons have opposite spins when their dispersion relations cross. We derive analytical expressions for the coupling strengths and find that the coupling between antiferromagnets and ferromagnets is comparable to the coupling between two ferromagnets. Our findings reveal a robust link between cavity spintronics with ferromagnets and antiferromagnets.
Collapse
Affiliation(s)
- Øyvind Johansen
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - Arne Brataas
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| |
Collapse
|
21
|
Zhang D, Luo XQ, Wang YP, Li TF, You JQ. Observation of the exceptional point in cavity magnon-polaritons. Nat Commun 2017; 8:1368. [PMID: 29116092 PMCID: PMC5676766 DOI: 10.1038/s41467-017-01634-w] [Citation(s) in RCA: 53] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2017] [Accepted: 10/05/2017] [Indexed: 11/09/2022] Open
Abstract
Magnon-polaritons are hybrid light-matter quasiparticles originating from the strong coupling between magnons and photons. They have emerged as a potential candidate for implementing quantum transducers and memories. Owing to the dampings of both photons and magnons, the polaritons have limited lifetimes. However, stationary magnon-polariton states can be reached by a dynamical balance between pumping and losses, so the intrinsically nonequilibrium system may be described by a non-Hermitian Hamiltonian. Here we design a tunable cavity quantum electrodynamics system with a small ferromagnetic sphere in a microwave cavity and engineer the dissipations of photons and magnons to create cavity magnon-polaritons which have non-Hermitian spectral degeneracies. By tuning the magnon-photon coupling strength, we observe the polaritonic coherent perfect absorption and demonstrate the phase transition at the exceptional point. Our experiment offers a novel macroscopic quantum platform to explore the non-Hermitian physics of the cavity magnon-polaritons.
Collapse
Affiliation(s)
- Dengke Zhang
- Quantum Physics and Quantum Information Division, Beijing Computational Science Research Center, Beijing, 100193, China.,Department of Engineering, University of Cambridge, Cambridge, CB3 0FA, UK
| | - Xiao-Qing Luo
- Quantum Physics and Quantum Information Division, Beijing Computational Science Research Center, Beijing, 100193, China
| | - Yi-Pu Wang
- Quantum Physics and Quantum Information Division, Beijing Computational Science Research Center, Beijing, 100193, China
| | - Tie-Fu Li
- Institute of Microelectronics, Tsinghua National Laboratory of Information Science and Technology, Tsinghua University, Beijing, 100084, China.
| | - J Q You
- Quantum Physics and Quantum Information Division, Beijing Computational Science Research Center, Beijing, 100193, China.
| |
Collapse
|