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Wang K, Wu H, Zhang B, Yao X, Zhang J, Oxborrow M, Zhao Q. Tailoring Coherent Microwave Emission from a Solid-State Hybrid System for Room-Temperature Microwave Quantum Electronics. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2024; 11:e2401904. [PMID: 39007198 PMCID: PMC11425272 DOI: 10.1002/advs.202401904] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2024] [Revised: 06/18/2024] [Indexed: 07/16/2024]
Abstract
Quantum electronics operating in the microwave domain are burgeoning and becoming essential building blocks of quantum computers, sensors, and communication devices. However, the field of microwave quantum electronics has long been dominated by the need for cryogenic conditions to maintain delicate quantum characteristics. Here, a solid-state hybrid system, constituted by a photo-excited pentacene triplet spin ensemble coupled to a dielectric resonator, is reported for the first time capable of both coherent microwave quantum amplification and oscillation at X band via the masing process at room temperature. By incorporating external driving and active dissipation control into the hybrid system, efficient tuning of the maser emission characteristics at ≈9.4 GHz is achieved, which is key to optimizing the performance of the maser device. The work not only pushes the boundaries of the operating frequency and functionality of the existing pentacene masers but also demonstrates a universal route for controlling the masing process at room temperature, highlighting opportunities for optimizing emerging solid-state masers for quantum information processing and communication.
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Affiliation(s)
- Kaipu Wang
- Center for Quantum Technology Research and Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements (MOE), School of Physics, Beijing Institute of Technology, Beijing, 100081, China
| | - Hao Wu
- Center for Quantum Technology Research and Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements (MOE), School of Physics, Beijing Institute of Technology, Beijing, 100081, China
| | - Bo Zhang
- Center for Quantum Technology Research and Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements (MOE), School of Physics, Beijing Institute of Technology, Beijing, 100081, China
| | - Xuri Yao
- Center for Quantum Technology Research and Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements (MOE), School of Physics, Beijing Institute of Technology, Beijing, 100081, China
| | - Jiakai Zhang
- Xi'an Electronic Engineering Research Institute, Xi'an, 710100, China
| | - Mark Oxborrow
- Department of Materials, Imperial College London, South Kensington, London, SW7 2AZ, UK
| | - Qing Zhao
- Center for Quantum Technology Research and Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements (MOE), School of Physics, Beijing Institute of Technology, Beijing, 100081, China
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2
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Wang CG, Xu W, Li C, Shi L, Jiang J, Guo T, Yue WC, Li T, Zhang P, Lyu YY, Pan J, Deng X, Dong Y, Tu X, Dong S, Cao C, Zhang L, Jia X, Sun G, Kang L, Chen J, Wang YL, Wang H, Wu P. Integrated and DC-powered superconducting microcomb. Nat Commun 2024; 15:4009. [PMID: 38740761 DOI: 10.1038/s41467-024-48224-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2023] [Accepted: 04/24/2024] [Indexed: 05/16/2024] Open
Abstract
Frequency combs, specialized laser sources emitting multiple equidistant frequency lines, have revolutionized science and technology with unprecedented precision and versatility. Recently, integrated frequency combs are emerging as scalable solutions for on-chip photonics. Here, we demonstrate a fully integrated superconducting microcomb that is easy to manufacture, simple to operate, and consumes ultra-low power. Our turnkey apparatus comprises a basic nonlinear superconducting device, a Josephson junction, directly coupled to a superconducting microstrip resonator. We showcase coherent comb generation through self-started mode-locking. Therefore, comb emission is initiated solely by activating a DC bias source, with power consumption as low as tens of picowatts. The resulting comb spectrum resides in the microwave domain and spans multiple octaves. The linewidths of all comb lines can be narrowed down to 1 Hz through a unique coherent injection-locking technique. Our work represents a critical step towards fully integrated microwave photonics and offers the potential for integrated quantum processors.
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Affiliation(s)
- Chen-Guang Wang
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- National Key Laboratory of Spintronics, Nanjing University, Suzhou, China
| | - Wuyue Xu
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- National Key Laboratory of Spintronics, Nanjing University, Suzhou, China
| | - Chong Li
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- National Key Laboratory of Spintronics, Nanjing University, Suzhou, China
| | - Lili Shi
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
| | - Junliang Jiang
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
| | - Tingting Guo
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
| | - Wen-Cheng Yue
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- National Key Laboratory of Spintronics, Nanjing University, Suzhou, China
| | - Tianyu Li
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- National Key Laboratory of Spintronics, Nanjing University, Suzhou, China
| | - Ping Zhang
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
| | - Yang-Yang Lyu
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
| | | | - Xiuhao Deng
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, China
- Hefei National Laboratory, Hefei, China
| | - Ying Dong
- College of Metrology Measurement and Instrument, China Jiliang University, Hangzhou, China
| | - Xuecou Tu
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Hefei National Laboratory, Hefei, China
| | - Sining Dong
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- National Key Laboratory of Spintronics, Nanjing University, Suzhou, China
| | - Chunhai Cao
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
| | - Labao Zhang
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Hefei National Laboratory, Hefei, China
| | - Xiaoqing Jia
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Hefei National Laboratory, Hefei, China
| | - Guozhu Sun
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Hefei National Laboratory, Hefei, China
| | - Lin Kang
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Hefei National Laboratory, Hefei, China
| | - Jian Chen
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
| | - Yong-Lei Wang
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China.
- Purple Mountain Laboratories, Nanjing, China.
- National Key Laboratory of Spintronics, Nanjing University, Suzhou, China.
| | - Huabing Wang
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China.
- Purple Mountain Laboratories, Nanjing, China.
| | - Peiheng Wu
- Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing, China.
- Purple Mountain Laboratories, Nanjing, China.
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3
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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: 4] [Impact Index Per Article: 2.0] [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}).
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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
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4
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Wen Y, Ares N, Schupp F, Pei T, Briggs G, Laird E. A coherent nanomechanical oscillator driven by single-electron tunnelling. NATURE PHYSICS 2020; 16:75-82. [PMID: 31915459 PMCID: PMC6949122 DOI: 10.1038/s41567-019-0683-5] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
A single-electron transistor embedded in a nanomechanical resonator represents an extreme limit of electron-phonon coupling. While it allows fast and sensitive electromechanical measurements, it also introduces backaction forces from electron tunnelling that randomly perturb the mechanical state. Despite the stochastic nature of this backaction, it has been predicted to create self-sustaining coherent mechanical oscillations under strong coupling conditions. Here, we verify this prediction using real-time measurements of a vibrating carbon nanotube transistor. This electromechanical oscillator has some similarities with a laser. The single-electron transistor pumped by an electrical bias acts as a gain medium and the resonator acts as a phonon cavity. Although the operating principle is unconventional because it does not involve stimulated emission, we confirm that the output is coherent. We demonstrate other analogues of laser behaviour, including injection locking, classical squeezing through anharmonicity, and frequency narrowing through feedback.
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Affiliation(s)
- Yutian Wen
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
| | - N. Ares
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
| | - F.J. Schupp
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
| | - T. Pei
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
| | - G.A.D. Briggs
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
| | - E.A. Laird
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, United Kingdom
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5
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Simon SH, Cooper NR. Theory of the Josephson Junction Laser. PHYSICAL REVIEW LETTERS 2018; 121:027004. [PMID: 30085722 DOI: 10.1103/physrevlett.121.027004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2017] [Revised: 03/29/2018] [Indexed: 06/08/2023]
Abstract
We develop an analytic theory for the recently demonstrated Josephson junction laser [M. C. Cassidy et al., Science 355, 939 (2017)SCIEAS0036-807510.1126/science.aah6640]. By working in the time-domain representation (rather than the frequency domain), a single nonlinear equation is obtained for the dynamics of the device, which is fully solvable in some regimes of operation. The nonlinear drive is seen to lead to mode-locked output, with a period set by the round-trip time of the resonant cavity.
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Affiliation(s)
- Steven H Simon
- Rudolf Peierls Centre, Oxford University, OX1 3NP, United Kingdom
| | - Nigel R Cooper
- T.C.M. Group, Cavendish Laboratory, J.J. Thomson Avenue, Cambridge, CB3 0HE, United Kingdom
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6
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Roxworthy BJ, Aksyuk VA. Electrically tunable plasmomechanical oscillators for localized modulation, transduction, and amplification. OPTICA 2018; 5:10.1364/optica.5.000071. [PMID: 39479354 PMCID: PMC11523045 DOI: 10.1364/optica.5.000071] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2017] [Accepted: 12/07/2017] [Indexed: 11/02/2024]
Abstract
Plasmomechanical systems are an emerging class of device that hold great promise for manipulating light-matter interactions with high speed and sub-diffraction spatial resolution. However, realizing their potential requires developing active plasmomechanical systems that can localize their functionality to the level of an individual sub-wavelength plasmonic resonator. Here, we present an active, electrically tunable plasmomechanical system that uses a localized-gap plasmonic resonator to mediate optical, thermal, and mechanical interactions within a subwavelength footprint. Our device enables facile electromechanical modulation of localized plasmons, selective sub-diffraction transduction of nanomechanical motion, and functions as a plasmomechanical oscillator that can be injection locked to and thus amplify weak external stimuli. These functionalities benefit applications in nanomechanical sensing, spatial light modulators, and reconfigurable metasurfaces.
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Affiliation(s)
- Brian J. Roxworthy
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
| | - Vladimir A. Aksyuk
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
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7
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Cottet A, Dartiailh MC, Desjardins MM, Cubaynes T, Contamin LC, Delbecq M, Viennot JJ, Bruhat LE, Douçot B, Kontos T. Cavity QED with hybrid nanocircuits: from atomic-like physics to condensed matter phenomena. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:433002. [PMID: 28925381 DOI: 10.1088/1361-648x/aa7b4d] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Circuit QED techniques have been instrumental in manipulating and probing with exquisite sensitivity the quantum state of superconducting quantum bits coupled to microwave cavities. Recently, it has become possible to fabricate new devices in which the superconducting quantum bits are replaced by hybrid mesoscopic circuits combining nanoconductors and metallic reservoirs. This mesoscopic QED provides a new experimental playground to study the light-matter interaction in electronic circuits. Here, we present the experimental state of the art of mesoscopic QED and its theoretical description. A first class of experiments focuses on the artificial atom limit, where some quasiparticles are trapped in nanocircuit bound states. In this limit, the circuit QED techniques can be used to manipulate and probe electronic degrees of freedom such as confined charges, spins, or Andreev pairs. A second class of experiments uses cavity photons to reveal the dynamics of electron tunneling between a nanoconductor and fermionic reservoirs. For instance, the Kondo effect, the charge relaxation caused by grounded metallic contacts, and the photo-emission caused by voltage-biased reservoirs have been studied. The tunnel coupling between nanoconductors and fermionic reservoirs also enable one to obtain split Cooper pairs, or Majorana bound states. Cavity photons represent a qualitatively new tool to study these exotic condensed matter states.
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Affiliation(s)
- Audrey Cottet
- Laboratoire Pierre Aigrain, Ecole Normale Supérieure, CNRS UMR 8551, Laboratoire associé aux universités Pierre et Marie Curie et Denis Diderot, 24, rue Lhomond, 75231 Paris Cedex 05, France
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8
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Liu YY, Stehlik J, Eichler C, Mi X, Hartke TR, Gullans MJ, Taylor JM, Petta JR. Threshold Dynamics of a Semiconductor Single Atom Maser. PHYSICAL REVIEW LETTERS 2017; 119:097702. [PMID: 28949587 DOI: 10.1103/physrevlett.119.097702] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2017] [Indexed: 06/07/2023]
Abstract
We demonstrate a single atom maser consisting of a semiconductor double quantum dot (DQD) that is embedded in a high-quality-factor microwave cavity. A finite bias drives the DQD out of equilibrium, resulting in sequential single electron tunneling and masing. We develop a dynamic tuning protocol that allows us to controllably increase the time-averaged repumping rate of the DQD at a fixed level detuning, and quantitatively study the transition through the masing threshold. We further examine the crossover from incoherent to coherent emission by measuring the photon statistics across the masing transition. The observed threshold behavior is in agreement with an existing single atom maser theory when small corrections from lead emission are taken into account.
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Affiliation(s)
- Y-Y Liu
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - J Stehlik
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - C Eichler
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - X Mi
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - T R Hartke
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - M J Gullans
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, NIST and University of Maryland, College Park, Maryland 20742, USA
| | - J M Taylor
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, NIST and University of Maryland, College Park, Maryland 20742, USA
| | - J R Petta
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
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9
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Seitner MJ, Abdi M, Ridolfo A, Hartmann MJ, Weig EM. Parametric Oscillation, Frequency Mixing, and Injection Locking of Strongly Coupled Nanomechanical Resonator Modes. PHYSICAL REVIEW LETTERS 2017; 118:254301. [PMID: 28696761 DOI: 10.1103/physrevlett.118.254301] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2016] [Indexed: 06/07/2023]
Abstract
We study locking phenomena of two strongly coupled, high quality factor nanomechanical resonator modes to a common parametric drive at a single drive frequency in different parametric driving regimes. By controlled dielectric gradient forces we tune the resonance frequencies of the flexural in-plane and out-of-plane oscillation of the high stress silicon nitride string through their mutual avoided crossing. For the case of the strong common parametric drive signal-idler generation via nondegenerate parametric two-mode oscillation is observed. Broadband frequency tuning of the very narrow linewidth signal and idler resonances is demonstrated. When the resonance frequencies of the signal and idler get closer to each other, partial injection locking, injection pulling, and complete injection locking to half of the drive frequency occurs depending on the pump strength. Furthermore, satellite resonances, symmetrically offset from the signal and idler by their beat note, are observed, which can be attributed to degenerate four-wave mixing in the highly nonlinear mechanical oscillations.
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Affiliation(s)
| | - Mehdi Abdi
- Department of Physics, Technische Universität München, 85748 Garching, Germany
- Institute for Theoretical Physics, Ulm University, 89081 Ulm, Germany
| | - Alessandro Ridolfo
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra (MIFT), Universita di Messina, 98166 Messina, Italy
| | - Michael J Hartmann
- Institute of Photonics and Quantum Sciences, Heriot-Watt University, EH14 4AS Edinburgh, United Kingdom
| | - Eva M Weig
- Department of Physics, University of Konstanz, 78457 Konstanz, Germany
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10
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Cassidy MC, Bruno A, Rubbert S, Irfan M, Kammhuber J, Schouten RN, Akhmerov AR, Kouwenhoven LP. Demonstration of an ac Josephson junction laser. Science 2017; 355:939-942. [DOI: 10.1126/science.aah6640] [Citation(s) in RCA: 60] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2016] [Accepted: 02/03/2017] [Indexed: 11/03/2022]
Affiliation(s)
- M. C. Cassidy
- QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, Netherlands
| | - A. Bruno
- QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, Netherlands
| | - S. Rubbert
- Kavli Institute for Nanoscience, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, Netherlands
| | - M. Irfan
- Kavli Institute for Nanoscience, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, Netherlands
| | - J. Kammhuber
- QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, Netherlands
| | - R. N. Schouten
- QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, Netherlands
- Kavli Institute for Nanoscience, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, Netherlands
| | - A. R. Akhmerov
- Kavli Institute for Nanoscience, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, Netherlands
| | - L. P. Kouwenhoven
- QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, Netherlands
- Kavli Institute for Nanoscience, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, Netherlands
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