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Zeng H, He ZQ, Fan YR, Luo Y, Lyu C, Wu JP, Li YB, Liu S, Wang D, Zhang DC, Zeng JJ, Deng GW, Wang Y, Song HZ, Wang Z, You LX, Guo K, Sun CZ, Luo Y, Guo GC, Zhou Q. Quantum Light Generation Based on GaN Microring toward Fully On-Chip Source. Phys Rev Lett 2024; 132:133603. [PMID: 38613308 DOI: 10.1103/physrevlett.132.133603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2023] [Revised: 12/12/2023] [Accepted: 01/29/2024] [Indexed: 04/14/2024]
Abstract
An integrated quantum light source is increasingly desirable in large-scale quantum information processing. Despite recent remarkable advances, a new material platform is constantly being explored for the fully on-chip integration of quantum light generation, active and passive manipulation, and detection. Here, for the first time, we demonstrate a gallium nitride (GaN) microring based quantum light generation in the telecom C-band, which has potential toward the monolithic integration of quantum light source. In our demonstration, the GaN microring has a free spectral range of 330 GHz and a near-zero anomalous dispersion region of over 100 nm. The generation of energy-time entangled photon pair is demonstrated with a typical raw two-photon interference visibility of 95.5±6.5%, which is further configured to generate a heralded single photon with a typical heralded second-order autocorrelation g_{H}^{(2)}(0) of 0.045±0.001. Our results pave the way for developing a chip-scale quantum photonic circuit.
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Affiliation(s)
- Hong Zeng
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
- Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Zhao-Qin He
- Department of Electronic Engineering, Tsinghua University, Beijing 100084, China
| | - Yun-Ru Fan
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
- Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Yue Luo
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Chen Lyu
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Jin-Peng Wu
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
- Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Yun-Bo Li
- Department of Fundamental Network Technology, China Mobile Research Institute, Beijing 100053, China
| | - Sheng Liu
- Department of Fundamental Network Technology, China Mobile Research Institute, Beijing 100053, China
| | - Dong Wang
- Department of Fundamental Network Technology, China Mobile Research Institute, Beijing 100053, China
| | - De-Chao Zhang
- Department of Fundamental Network Technology, China Mobile Research Institute, Beijing 100053, China
| | - Juan-Juan Zeng
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
- Center for Quantum Internet, Tianfu Jiangxi Laboratory, Chengdu 641419, China
| | - Guang-Wei Deng
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
- Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - You Wang
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
- Southwest Institute of Technical Physics, Chengdu 610041, China
| | - Hai-Zhi Song
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
- Southwest Institute of Technical Physics, Chengdu 610041, China
| | - Zhen Wang
- National Key Laboratory of Materials for Integrated Circuits, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China
| | - Li-Xing You
- National Key Laboratory of Materials for Integrated Circuits, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China
| | - Kai Guo
- Institute of Systems Engineering, AMS, Beijing 100141, China
| | - Chang-Zheng Sun
- Department of Electronic Engineering, Tsinghua University, Beijing 100084, China
| | - Yi Luo
- Department of Electronic Engineering, Tsinghua University, Beijing 100084, China
| | - Guang-Can Guo
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
- Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China, Chengdu 611731, China
- Center for Quantum Internet, Tianfu Jiangxi Laboratory, Chengdu 641419, China
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
| | - Qiang Zhou
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
- Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China, Chengdu 611731, China
- Center for Quantum Internet, Tianfu Jiangxi Laboratory, Chengdu 641419, China
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
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Li BL, Guo ML, Chen JF, Fang JW, Fan BY, Zhou Q, Wang Y, Song HZ, Niu XB, Arutyunov KY, Guo GC, Deng GW. Very high-frequency, gate-tunable CrPS 4 nanomechanical resonator with single mode. Opt Lett 2023; 48:2571-2574. [PMID: 37186711 DOI: 10.1364/ol.489345] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
Two-dimensional (2D) antiferromagnetic semiconductor chromium thiophosphate (CrPS4) has gradually become a major candidate material for low-dimensional nanoelectromechanical devices due to its remarkable structural, photoelectric characteristics and potentially magnetic properties. Here, we report the experimental study of a new few-layer CrPS4 nanomechanical resonator demonstrating excellent vibration characteristics through the laser interferometry system, including the uniqueness of resonant mode, the ability to work at the very high frequency, and gate tuning. In addition, we demonstrate that the magnetic phase transition of CrPS4 strips can be effectively detected by temperature-regulated resonant frequencies, which proves the coupling between magnetic phase and mechanical vibration. We believe that our findings will promote the further research and applications of the resonator for 2D magnetic materials in the field of optical/mechanical signal sensing and precision measurement.
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Chen H, Zhao ZF, Li WJ, Cheng ZD, Suo JJ, Li BL, Guo ML, Fan BY, Zhou Q, Wang Y, Song HZ, Niu XB, Li XY, Arutyunov KY, Guo GC, Deng GW. Gate-tunable bolometer based on strongly coupled graphene mechanical resonators. Opt Lett 2023; 48:81-84. [PMID: 36563374 DOI: 10.1364/ol.476010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2022] [Accepted: 11/21/2022] [Indexed: 06/17/2023]
Abstract
Bolometers based on graphene have demonstrated outstanding performance with high sensitivity and short response time. In situ adjustment of bolometers is very important in various applications, but it is still difficult to implement in many systems. Here we propose a gate-tunable bolometer based on two strongly coupled graphene nanomechanical resonators. Both resonators are exposed to the same light field, and we can measure the properties of one bolometer by directly tracking the resonance frequency shifts, and indirectly measure the other bolometer through mechanical coupling. We find that the sensitivity and the response bandwidth of both bolometers can be independently adjusted by tuning the corresponding gate voltages. Moreover, the properties of the indirectly measured bolometer show a dependence on the coupling between the two resonators, with other parameters being fixed. Our method has the potential to optimize the design of large-scale bolometer arrays, and open new horizons in infrared/terahertz astronomy and communication systems.
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Suo JJ, Li WJ, Cheng ZD, Zhao ZF, Chen H, Li BL, Zhou Q, Wang Y, Song HZ, Niu XB, Deng GW. Tuning the nonlinearity of graphene mechanical resonators by Joule heating. J Phys Condens Matter 2022; 34:374004. [PMID: 35779515 DOI: 10.1088/1361-648x/ac7dd7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2022] [Accepted: 07/01/2022] [Indexed: 06/15/2023]
Abstract
As an inherent property of the device itself, nonlinearity in micro-/nano- electromechanical resonators is difficult to eliminate, and it has shown a wide range of applications in basic research, sensing and other fields. While many application scenarios require tunability of the nonlinearity, inherent nonlinearity of a mechanical resonator is difficult to be changed. Here, we report the experimental observation of a Joule heating induced tuning effect on the nonlinearity of graphene mechanical resonators. We fabricated multiple graphene mechanical resonators and detected their resonant properties by an optical interference method. The mechanical vibration of the resonators will enter from the linear to the nonlinear intervals if we enhance the external driving power to a certain value. We found that at a fixed drive power, the nonlinearity of a mechanical resonator can be tuned by applying a dc bias current on the resonator itself. The tuning mechanism could be explained by the nonlinear amplitude-frequency dependence theory. Our results may provide a research platform for the study of mechanical nonlinearity by using atomic-thin layer materials.
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Affiliation(s)
- Jiao-Jiao Suo
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, People's Republic of China
- School of Materials and Energy, University of Electronic Science and Technology of China, Chengdu, People's Republic of China
| | - Wei-Jie Li
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, People's Republic of China
- School of Materials and Energy, University of Electronic Science and Technology of China, Chengdu, People's Republic of China
| | - Ze-Di Cheng
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, People's Republic of China
| | - Zi-Fan Zhao
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, People's Republic of China
- School of Materials and Energy, University of Electronic Science and Technology of China, Chengdu, People's Republic of China
| | - Hui Chen
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, People's Republic of China
- School of Materials and Energy, University of Electronic Science and Technology of China, Chengdu, People's Republic of China
| | - Bo-Lin Li
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, People's Republic of China
- School of Materials and Energy, University of Electronic Science and Technology of China, Chengdu, People's Republic of China
| | - Qiang Zhou
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, People's Republic of China
- Southwest Institute of Technical Physics, Chengdu, People's Republic of China
| | - You Wang
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, People's Republic of China
- Southwest Institute of Technical Physics, Chengdu, People's Republic of China
| | - Hai-Zhi Song
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, People's Republic of China
- Southwest Institute of Technical Physics, Chengdu, People's Republic of China
| | - Xiao-Bin Niu
- School of Materials and Energy, University of Electronic Science and Technology of China, Chengdu, People's Republic of China
| | - Guang-Wei Deng
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, People's Republic of China
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5
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Li WJ, Cheng ZD, Kang LZ, Zhang RM, Fan BY, Zhou Q, Wang Y, Song HZ, Arutyunov KY, Niu XB, Deng GW. Phonon lasing with an atomic thin membrane resonator at room temperature. Opt Express 2021; 29:16241-16248. [PMID: 34154191 DOI: 10.1364/oe.423904] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2021] [Accepted: 04/26/2021] [Indexed: 06/13/2023]
Abstract
Graphene has been considered as one of the best materials to implement mechanical resonators due to their excellent properties such as low mass, high quality factors and tunable resonant frequencies. Here we report the observation of phonon lasing induced by the photonthermal pressure in a few-layer graphene resonator at room temperature, where the graphene resonator and the silicon substrate form an optical cavity. A marked threshold in the oscillation amplitude and a narrowing linewidth of the vibration mode are observed, which confirms a phonon lasing process in the graphene resonator. Our findings will stimulate the studies on phononic phenomena, help to establish new functional devices based on graphene mechanical resonators, and might find potential applications in classical and quantum sensing fields, as well as in information processing.
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6
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Wei B, Cai WH, Ding C, Deng GW, Shimizu R, Zhou Q, Jin RB. Mid-infrared spectrally-uncorrelated biphotons generation from doped PPLN: a theoretical investigation. Opt Express 2021; 29:256-271. [PMID: 33362119 DOI: 10.1364/oe.412603] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2020] [Accepted: 12/11/2020] [Indexed: 06/12/2023]
Abstract
We theoretically investigate the preparation of mid-infrared (MIR) spectrally-uncorrelated biphotons from a spontaneous parametric down-conversion process using doped LN crystals, including MgO doped LN, ZnO doped LN, and In2O3 doped ZnLN with doping ratio from 0 to 7 mol%. The tilt angle of the phase-matching function and the corresponding poling period are calculated under type-II, type-I, and type-0 phase-matching conditions. We also calculate the thermal properties of the doped LN crystals and their performance in Hong-Ou-Mandel interference. It is found that the doping ratio has a substantial impact on the group-velocity-matching (GVM) wavelengths. Especially, the GVM2 wavelength of co-doped InZnLN crystal has a tunable range of 678.7 nm, which is much broader than the tunable range of less than 100 nm achieved by the conventional method of adjusting the temperature. It can be concluded that the doping ratio can be utilized as a degree of freedom to manipulate the biphoton state. The spectrally uncorrelated biphotons can be used to prepare pure single-photon source and entangled photon source, which may have promising applications for quantum-enhanced sensing, imaging, and communications at the MIR range.
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8
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Luo G, Zhang ZZ, Deng GW, Li HO, Cao G, Xiao M, Guo GC, Tian L, Guo GP. Author Correction: Strong indirect coupling between graphene-based mechanical resonators via a phonon cavity. Nat Commun 2019; 10:1343. [PMID: 30886149 PMCID: PMC6423086 DOI: 10.1038/s41467-019-09240-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/03/2022] Open
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9
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Luo G, Zhang ZZ, Deng GW, Li HO, Cao G, Xiao M, Guo GC, Tian L, Guo GP. Strong indirect coupling between graphene-based mechanical resonators via a phonon cavity. Nat Commun 2018; 9:383. [PMID: 29374169 PMCID: PMC5786116 DOI: 10.1038/s41467-018-02854-4] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2017] [Accepted: 01/04/2018] [Indexed: 11/25/2022] Open
Abstract
Mechanical resonators are promising systems for storing and manipulating information. To transfer information between mechanical modes, either direct coupling or an interface between these modes is needed. In previous works, strong coupling between different modes in a single mechanical resonator and direct interaction between neighboring mechanical resonators have been demonstrated. However, coupling between distant mechanical resonators, which is a crucial request for long-distance classical and quantum information processing using mechanical devices, remains an experimental challenge. Here, we report the experimental observation of strong indirect coupling between separated mechanical resonators in a graphene-based electromechanical system. The coupling is mediated by a far-off-resonant phonon cavity through virtual excitations via a Raman-like process. By controlling the resonant frequency of the phonon cavity, the indirect coupling can be tuned in a wide range. Our results may lead to the development of gate-controlled all-mechanical devices and open up the possibility of long-distance quantum mechanical experiments. Non-neighbouring mechanical resonators can interact via indirect coupling. Here, the authors leverage a resonant phonon cavity in a graphene-based electromechanical system to demonstrate strong indirect coupling between separated mechanical resonators.
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Affiliation(s)
- Gang Luo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, Anhui, China.,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, Anhui, China
| | - Zhuo-Zhi Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, Anhui, China.,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, Anhui, China
| | - Guang-Wei Deng
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, Anhui, China. .,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, Anhui, China.
| | - Hai-Ou Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, Anhui, China.,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, Anhui, China
| | - Gang Cao
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, Anhui, China.,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, Anhui, China
| | - Ming Xiao
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, Anhui, China.,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, Anhui, China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, Anhui, China.,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, Anhui, China
| | - Lin Tian
- School of Nature Sciences, University of California, Merced, CA, 95343, USA.
| | - Guo-Ping Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, Anhui, China. .,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, Anhui, China.
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10
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Zhang ZZ, Song XX, Luo G, Deng GW, Mosallanejad V, Taniguchi T, Watanabe K, Li HO, Cao G, Guo GC, Nori F, Guo GP. Electrotunable artificial molecules based on van der Waals heterostructures. Sci Adv 2017; 3:e1701699. [PMID: 29062893 PMCID: PMC5650488 DOI: 10.1126/sciadv.1701699] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2017] [Accepted: 09/25/2017] [Indexed: 06/02/2023]
Abstract
Quantum confinement has made it possible to detect and manipulate single-electron charge and spin states. The recent focus on two-dimensional (2D) materials has attracted significant interests on possible applications to quantum devices, including detecting and manipulating either single-electron charging behavior or spin and valley degrees of freedom. However, the most popular model systems, consisting of tunable double-quantum-dot molecules, are still extremely difficult to realize in these materials. We show that an artificial molecule can be reversibly formed in atomically thin MoS2 sandwiched in hexagonal boron nitride, with each artificial atom controlled separately by electrostatic gating. The extracted values for coupling energies at different regimes indicate a single-electron transport behavior, with the coupling strength between the quantum dots tuned monotonically. Moreover, in the low-density regime, we observe a decrease of the conductance with magnetic field, suggesting the observation of Coulomb blockade weak anti-localization. Our experiments demonstrate for the first time the realization of an artificial quantum-dot molecule in a gated MoS2 van der Waals heterostructure, which could be used to investigate spin-valley physics. The compatibility with large-scale production, gate controllability, electron-hole bipolarity, and new quantum degrees of freedom in the family of 2D materials opens new possibilities for quantum electronics and its applications.
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Affiliation(s)
- Zhuo-Zhi Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiang-Xiang Song
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Gang Luo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Guang-Wei Deng
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Vahid Mosallanejad
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Takashi Taniguchi
- National Institute for Materials Science, Namiki 1-1, Ibaraki 305-0044, Japan
| | - Kenji Watanabe
- National Institute for Materials Science, Namiki 1-1, Ibaraki 305-0044, Japan
| | - Hai-Ou Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Gang Cao
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Franco Nori
- CEMS, RIKEN, Wako-shi, Saitama 351-0198, Japan
- Department of Physics, University of Michigan, Ann Arbor, MI 48109–1040, USA
| | - Guo-Ping Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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11
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Luo G, Zhang ZZ, Deng GW, Li HO, Cao G, Xiao M, Guo GC, Guo GP. Coupling graphene nanomechanical motion to a single-electron transistor. Nanoscale 2017; 9:5608-5614. [PMID: 28422197 DOI: 10.1039/c6nr09768e] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Graphene-based electromechanical resonators have attracted great interest recently because of the outstanding mechanical and electrical properties of graphene and their various applications. However, the coupling between mechanical motion and charge transport has not been explored in graphene. Herein, we studied the mechanical properties of a suspended 50 nm wide graphene nanoribbon, which also acts as a single-electron transistor (SET) at low temperatures. Using the SET as a sensitive detector, we found that the resonance frequency could be tuned from 82 MHz to 100 MHz and the quality factor exceeded 30 000. The strong charge-mechanical coupling was demonstrated by observing the SET induced ∼140 kHz resonance frequency shifts and mechanical damping. We also found that the SET can enhance the nonlinearity of the resonator. Our SET-coupled graphene mechanical resonator could approach an ultra-sensitive mass resolution of ∼0.55 × 10-21 g and a force sensitivity of ∼1.9 × 10-19 N (Hz)-1/2, and can be further improved. These properties indicate that our device is a good platform for both fundamental physical studies and potential applications.
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Affiliation(s)
- Gang Luo
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China.
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12
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Zhu D, Wang XH, Kong WC, Deng GW, Wang JT, Li HO, Cao G, Xiao M, Jiang KL, Dai XC, Guo GC, Nori F, Guo GP. Coherent Phonon Rabi Oscillations with a High-Frequency Carbon Nanotube Phonon Cavity. Nano Lett 2017; 17:915-921. [PMID: 28068098 DOI: 10.1021/acs.nanolett.6b04223] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
Phonon-cavity electromechanics allows the manipulation of mechanical oscillations similar to photon-cavity systems. Many advances on this subject have been achieved in various materials. In addition, the coherent phonon transfer (phonon Rabi oscillations) between the phonon cavity mode and another oscillation mode has attracted many interest in nanoscience. Here, we demonstrate coherent phonon transfer in a carbon nanotube phonon-cavity system with two mechanical modes exhibiting strong dynamical coupling. The gate-tunable phonon oscillation modes are manipulated and detected by extending the red-detuned pump idea of photonic cavity electromechanics. The first- and second-order coherent phonon transfers are observed with Rabi frequencies 591 and 125 kHz, respectively. The frequency quality factor product fQm ∼ 2 × 1012 Hz achieved here is larger than kBTbase/h, which may enable the future realization of Rabi oscillations in the quantum regime.
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Affiliation(s)
- Dong Zhu
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Xin-He Wang
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics and Tsinghua-Foxconn Nanotechnology Research Center, Tsinghua University , Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter , Beijing 100084, China
| | - Wei-Cheng Kong
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Guang-Wei Deng
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Jiang-Tao Wang
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics and Tsinghua-Foxconn Nanotechnology Research Center, Tsinghua University , Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter , Beijing 100084, China
| | - Hai-Ou Li
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Gang Cao
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Ming Xiao
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Kai-Li Jiang
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics and Tsinghua-Foxconn Nanotechnology Research Center, Tsinghua University , Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter , Beijing 100084, China
| | - Xing-Can Dai
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics and Tsinghua-Foxconn Nanotechnology Research Center, Tsinghua University , Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter , Beijing 100084, China
| | - Guang-Can Guo
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Franco Nori
- CEMS, RIKEN , Wako-shi, Saitama 351-0198, Japan
- Physics Department, University of Michigan , Ann Arbor, Michigan 48109-1040, United States
| | - Guo-Ping Guo
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
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13
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Deng GW, Zhu D, Wang XH, Zou CL, Wang JT, Li HO, Cao G, Liu D, Li Y, Xiao M, Guo GC, Jiang KL, Dai XC, Guo GP. Strongly Coupled Nanotube Electromechanical Resonators. Nano Lett 2016; 16:5456-62. [PMID: 27487412 DOI: 10.1021/acs.nanolett.6b01875] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
Coupling an electromechanical resonator with carbon-nanotube quantum dots is a significant method to control both the electronic charge and the spin quantum states. By exploiting a novel microtransfer technique, we fabricate two separate strongly coupled and electrically tunable mechanical resonators for the first time. The frequency of the two resonators can be individually tuned by the bottom gates, and in each resonator, the electron transport through the quantum dot can be strongly affected by the phonon mode and vice versa. Furthermore, the conductance of either resonator can be nonlocally modulated by the other resonator through phonon-phonon interaction between the two resonators. Strong coupling is observed between the phonon modes of the two resonators, where the coupling strength larger than 200 kHz can be reached. This strongly coupled nanotube electromechanical resonator array provides an experimental platform for future studies of the coherent electron-phonon interaction, the phonon-mediated long-distance electron interaction, and entanglement state generation.
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Affiliation(s)
- Guang-Wei Deng
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Dong Zhu
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Xin-He Wang
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics and Tsinghua-Foxconn Nanotechnology Research Center, Tsinghua University , Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter , Beijing 100084, China
| | - Chang-Ling Zou
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Jiang-Tao Wang
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics and Tsinghua-Foxconn Nanotechnology Research Center, Tsinghua University , Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter , Beijing 100084, China
| | - Hai-Ou Li
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Gang Cao
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Di Liu
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Yan Li
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Ming Xiao
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Guang-Can Guo
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Kai-Li Jiang
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics and Tsinghua-Foxconn Nanotechnology Research Center, Tsinghua University , Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter , Beijing 100084, China
| | - Xing-Can Dai
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics and Tsinghua-Foxconn Nanotechnology Research Center, Tsinghua University , Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter , Beijing 100084, China
| | - Guo-Ping Guo
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
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14
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Li SX, Zhu D, Wang XH, Wang JT, Deng GW, Li HO, Cao G, Xiao M, Guo GC, Jiang KL, Dai XC, Guo GP. Parametric strong mode-coupling in carbon nanotube mechanical resonators. Nanoscale 2016; 8:14809-14813. [PMID: 27447924 DOI: 10.1039/c6nr02853e] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Carbon nanotubes (CNTs) have attracted much attention for use in nanomechanical devices because of their exceptional properties, such as large resonant frequencies, low mass, and high quality factors. Here, we report the first experimental realization of parametric strong coupling between two mechanical modes on a single CNT nanomechanical resonator, by applying an extra microwave pump. This parametric pump method can be used to couple mechanical modes with arbitrary frequency differences. The properties of the mechanical resonator are detected by single-electron tunneling at low temperature, which is found to be strongly coupled to both modes. The coupling strength between the two modes can be tuned by the pump power, setting the coupling regime from weak to strong. This tunability may be useful in further phonon manipulations in carbon nanotubes.
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Affiliation(s)
- Shu-Xiao Li
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China.
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15
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Deng GW, Wei D, Li SX, Johansson JR, Kong WC, Li HO, Cao G, Xiao M, Guo GC, Nori F, Jiang HW, Guo GP. Coupling Two Distant Double Quantum Dots with a Microwave Resonator. Nano Lett 2015; 15:6620-6625. [PMID: 26327140 DOI: 10.1021/acs.nanolett.5b02400] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We fabricated a hybrid device with two distant graphene double quantum dots (DQDs) and a microwave resonator. A nonlinear response is observed in the resonator reflection amplitude when the two DQDs are jointly tuned to the vicinity of the degeneracy points. This observation can be well fitted by the Tavis-Cummings (T-C) model which describes two two-level systems coupling with one photonic field. Furthermore, the correlation between the DC currents in the two DQDs is studied. A nonzero cross-current correlation is observed which has been theoretically predicted to be an important sign of nonlocal coupling between two distant systems. Our results explore T-C physics in electronic transport and also contribute to the study of nonlocal transport and future implementations of remote electronic entanglement.
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Affiliation(s)
- Guang-Wei Deng
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Da Wei
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Shu-Xiao Li
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | | | - Wei-Cheng Kong
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Hai-Ou Li
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Gang Cao
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Ming Xiao
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Guang-Can Guo
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Franco Nori
- Physics Department, The University of Michigan , Ann Arbor, Michigan 48109-1040, United States
| | - Hong-Wen Jiang
- Department of Physics and Astronomy, University of California at Los Angeles , Los Angeles, California 90095, United States
| | - Guo-Ping Guo
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences , Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
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16
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Deng GW, Wei D, Johansson JR, Zhang ML, Li SX, Li HO, Cao G, Xiao M, Tu T, Guo GC, Jiang HW, Nori F, Guo GP. Charge Number Dependence of the Dephasing Rates of a Graphene Double Quantum Dot in a Circuit QED Architecture. Phys Rev Lett 2015; 115:126804. [PMID: 26431005 DOI: 10.1103/physrevlett.115.126804] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2015] [Indexed: 05/27/2023]
Abstract
We use an on-chip superconducting resonator as a sensitive meter to probe the properties of graphene double quantum dots at microwave frequencies. Specifically, we investigate the charge dephasing rates in a circuit quantum electrodynamics architecture. The dephasing rates strongly depend on the number of charges in the dots, and the variation has a period of four charges, over an extended range of charge numbers. Although the exact mechanism of this fourfold periodicity in dephasing rates is an open problem, our observations hint at the fourfold degeneracy expected in graphene from its spin and valley degrees of freedom.
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Affiliation(s)
- Guang-Wei Deng
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Da Wei
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | | | - Miao-Lei Zhang
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Shu-Xiao Li
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Hai-Ou Li
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Gang Cao
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Ming Xiao
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Tao Tu
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Guang-Can Guo
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Hong-Wen Jiang
- Department of Physics and Astronomy, University of California at Los Angeles, California 90095, USA
| | - Franco Nori
- CEMS, RIKEN, Wako-shi, Saitama 351-0198, Japan
- Physics Department, The University of Michigan, Ann Arbor, Michigan 48109-1040, USA
| | - Guo-Ping Guo
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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17
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Kong WC, Deng GW, Li SX, Li HO, Cao G, Xiao M, Guo GP. Introduction of DC line structures into a superconducting microwave 3D cavity. Rev Sci Instrum 2015; 86:023108. [PMID: 25725824 DOI: 10.1063/1.4913252] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We report a technique that can noninvasively add multiple DC wires into a 3D superconducting microwave cavity for electronic devices that require DC electrical terminals. We studied the influence of our DC lines on the cavity performance systematically. We found that the quality factor of the cavity is reduced if any of the components of the electrical wires cross the cavity equipotential planes. Using this technique, we were able to incorporate a quantum dot (QD) device into a 3D cavity. We then controlled and measured the QD transport signal using the DC lines. We have also studied the heating effects of the QD by the microwave photons in the cavity.
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Affiliation(s)
- Wei-Cheng Kong
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Guang-Wei Deng
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Shu-Xiao Li
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Hai-Ou Li
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Gang Cao
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Ming Xiao
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Guo-Ping Guo
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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