1
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Badawy G, Bakkers EPAM. Electronic Transport and Quantum Phenomena in Nanowires. Chem Rev 2024; 124:2419-2440. [PMID: 38394689 PMCID: PMC10941195 DOI: 10.1021/acs.chemrev.3c00656] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2023] [Revised: 01/26/2024] [Accepted: 02/08/2024] [Indexed: 02/25/2024]
Abstract
Nanowires are natural one-dimensional channels and offer new opportunities for advanced electronic quantum transport experiments. We review recent progress on the synthesis of nanowires and methods for the fabrication of hybrid semiconductor/superconductor systems. We discuss methods to characterize their electronic properties in the context of possible future applications such as topological and spin qubits. We focus on group III-V (InAs and InSb) and group IV (Ge/Si) semiconductors, since these are the most developed, and give an outlook on other potential materials.
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Affiliation(s)
- Ghada Badawy
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
| | - Erik P. A. M. Bakkers
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
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2
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Li R. Spin-photon interaction in a nanowire quantum dot with asymmetrical confining potential. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:195302. [PMID: 38277684 DOI: 10.1088/1361-648x/ad22fa] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2023] [Accepted: 01/26/2024] [Indexed: 01/28/2024]
Abstract
The electron (hole) spin-photon interaction is studied in an asymmetrical InSb (Ge) nanowire quantum dot. The spin-orbit coupling in the quantum dot mediates not only a transverse spin-photon interaction, but also a longitudinal spin-photon interaction due to the asymmetry of the confining potential. Both the transverse and the longitudinal spin-photon interactions have non-monotonic dependence on the spin-orbit coupling. For realistic spin-orbit coupling in the quantum dot, the longitudinal spin-photon interaction is much (at least one order) smaller than the transverse spin-photon interaction. The order of the transverse spin-photon interaction is about 1 nm in terms of length|zeg|, or 0.1 MHz in terms of frequencyeE0|zeg|/hfor a moderate cavity electric field strengthE0=0.4V m-1.
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Affiliation(s)
- Rui Li
- Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao 066004, People's Republic of China
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3
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Li 李睿 R, Qi 齐新雨 XY. Two-band description of the strong 'spin'-orbit coupled one-dimensional hole gas in a cylindrical Ge nanowire. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:135302. [PMID: 36735991 DOI: 10.1088/1361-648x/acb8f5] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2022] [Accepted: 02/03/2023] [Indexed: 06/18/2023]
Abstract
The low-energy effective Hamiltonian of the strong 'spin'-orbit coupled one-dimensional hole gas in a cylindrical Ge nanowire in the presence of a strong magnetic field is studied both numerically and analytically. Basing on the Luttinger-Kohn Hamiltonian in the spherical approximation, we show this strong 'spin'-orbit coupled one-dimensional hole gas can be accurately described by an effective two-band HamiltonianHef=ℏ2kz2/(2mh∗)+ασxkz+gh∗μBBσz/2, as long as the magnetic field is purely longitudinal or purely transverse. The explicit magnetic field dependent expressions of the 'spin'-orbit couplingα≡α(B)and the effectiveg-factorgh∗≡gh∗(B)are given. When the magnetic field is applied in an arbitrary direction, the two-band Hamiltonian description is still a good approximation.
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Affiliation(s)
- Rui Li 李睿
- Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao 066004, People's Republic of China
| | - Xin-Yu Qi 齐新雨
- Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao 066004, People's Republic of China
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4
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Lu R, Liu K, Ban Y. Robust electron spin qubit control in a nanowire double quantum dot. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210270. [PMID: 36335949 DOI: 10.1098/rsta.2021.0270] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Accepted: 06/21/2022] [Indexed: 06/16/2023]
Abstract
Robust and efficient manipulation of electron spin qubits in quantum dots is of great significance for the reliable realization of quantum computers and execution of quantum algorithms. In this paper, we study the robust control on a singlet-triplet qubit based on inverse engineering, one technique of shortcuts to adiabaticity (STA), in a nanowire double quantum dot in the presence of magnetic field and strong spin-orbit coupling. The optimization of STA with respect to the systematic errors, contributed from the control field and the perturbative interaction, is explored. Moreover, we also apply optimal control techniques combining with STA, referred to as robust inverse optimization, to design optimal control fields and optimal operation time. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.
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Affiliation(s)
- Runyu Lu
- School of Materials Science and Engineering, Shanghai University, Shanghai 200444, People's Republic of China
| | - Kaipeng Liu
- International Center of Quantum Artificial Intelligence for Science and Technology (QuArtist) and Department of Physics, Shanghai University, Shanghai 200444, People's Republic of China
| | - Yue Ban
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 544, 48080 Bilbao, Spain
- EHU Quantum Center, University of the Basque Country UPV/EHU, Barrio Sarriena, s/n, 48940 Leioa, Biscay, Spain
- TECNALIA, Basque Research and Technology Alliance (BRTA), 48160 Derio, Spain
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5
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Li R. Searching strong 'spin'-orbit coupled one-dimensional hole gas in strong magnetic fields. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:075301. [PMID: 34753123 DOI: 10.1088/1361-648x/ac37da] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2021] [Accepted: 11/09/2021] [Indexed: 06/13/2023]
Abstract
We show that a strong 'spin'-orbit coupled one-dimensional hole gas is achievable via applying a strong magnetic field to the original two-fold degenerate (spin degeneracy) hole gas confined in a cylindrical Ge nanowire. Both strong longitudinal and strong transverse magnetic fields are feasible to achieve this goal. Based on quasi-degenerate perturbation calculations, we show the induced low-energy subband dispersion of the hole gas can be written asE=ℏ2kz2/(2mh*)+ασzkz+gh*μBBσx/2, a form exactly the same as that of the electron gas in the conduction band. Here the Pauli matricesσz,xrepresent a pseudo spin (or 'spin'), because the real spin degree of freedom has been split off from the subband dispersions by the strong magnetic field. Also, for a moderate nanowire radiusR= 10 nm, the induced effective hole massmh*(0.065∼0.08me)and the 'spin'-orbit couplingα(0.35 ∼ 0.8 eV Å) have a small magnetic field dependence in the studied magnetic field interval 1 <B< 15 T, while the effectiveg-factorgh*of the hole 'spin' only has a small magnetic field dependence in the large field region.
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Affiliation(s)
- Rui Li
- Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao 066004, People's Republic of China
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6
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Hai K, Wang Y, Chen Q, Hai W. Transparent qubit manipulations with spin-orbit coupled two-electron nanowire quantum dot. Sci Rep 2021; 11:18839. [PMID: 34552131 PMCID: PMC8458319 DOI: 10.1038/s41598-021-98152-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2021] [Accepted: 09/01/2021] [Indexed: 11/12/2022] Open
Abstract
We report on the first set of exact orthonormalized states to an ac driven one-dimensional (1D) two-electron nanowire quantum dot with the Rashba-Dresselhaus coexisted spin-orbit coupling (SOC) and the controlled magnetic field orientation and trapping frequency. In the ground state case, it is shown that the spatiotemporal evolutions of probability densities occupying internal spin states and the transfer rates between different spin states can be adjusted by the ac electric field and the intensities of SOC and magnetic field. Effects of the system parameters and initial-state-dependent constants on the mean entanglement are revealed, where the approximately maximal entanglement associated with the stronger SOC and its insensitivity to the initial and parametric perturbations are demonstrated numerically. A novel resonance transition mechanism is found, in which the ladder-like time-evolution process of expected energy and the transition time between two arbitrary exact states are controlled by the ac field strength. Using such maximally entangled exact states to encode qubits can render the qubit control more transparent and robust. The results could be extended to 2D case and to an array of two-electron quantum dots with weak neighboring coupling for quantum information processing.
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Affiliation(s)
- Kuo Hai
- Department of Physics and Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha, 410081, China.
| | - Yifan Wang
- Department of Physics and Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha, 410081, China
| | - Qiong Chen
- Department of Physics and Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha, 410081, China
| | - Wenhua Hai
- Department of Physics and Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha, 410081, China.
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7
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Li R. Low-energy subband wave-functions and effective g-factor of one-dimensional hole gas. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:355302. [PMID: 34153960 DOI: 10.1088/1361-648x/ac0d18] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2021] [Accepted: 06/21/2021] [Indexed: 06/13/2023]
Abstract
One-dimensional (1D) hole gas confined in a cylindrical Ge nanowire has potential applications in quantum information technologies. Here, we analytically study the low-energy properties of this 1D hole gas. The subbands of the hole gas are two-fold degenerate. The low-energy subband wave-functions are obtained exactly, and the degenerate pairs are related to each other via a combination of the time-reversal and the spin-rotation transformations. In evaluating the effectiveg-factor of these low-energy subbands, the orbital effects of the magnetic field are shown to contribute as strongly as the Zeeman term. Also, near the center of thekzspace, there is a sharp dip or a sharp peak in the effectiveg-factor. At the sitekz= 0, the longitudinalg-factorglis much less than the transverseg-factorgtfor the lowest subband, while away from the sitekz= 0,glcan be comparable togt.
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Affiliation(s)
- Rui Li
- Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao 066004, People's Republic of China
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8
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Zhang T, Liu H, Gao F, Xu G, Wang K, Zhang X, Cao G, Wang T, Zhang J, Hu X, Li HO, Guo GP. Anisotropic g-Factor and Spin-Orbit Field in a Germanium Hut Wire Double Quantum Dot. NANO LETTERS 2021; 21:3835-3842. [PMID: 33914549 DOI: 10.1021/acs.nanolett.1c00263] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Holes in nanowires have drawn significant attention in recent years because of the strong spin-orbit interaction, which plays an important role in constructing Majorana zero modes and manipulating spin-orbit qubits. Here, from the strongly anisotropic leakage current in the spin blockade regime for a double dot, we extract the full g-tensor and find that the spin-orbit field is in plane with an azimuthal angle of 59° to the axis of the nanowire. The direction of the spin-orbit field indicates a strong spin-orbit interaction along the nanowire, which may have originated from the interface inversion asymmetry in Ge hut wires. We also demonstrate two different spin relaxation mechanisms for the holes in the Ge hut wire double dot: spin-flip co-tunneling to the leads, and spin-orbit interaction within the double dot. These results help establish feasibility of a Ge-based quantum processor.
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Affiliation(s)
- Ting Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - He Liu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Fei Gao
- Institute of Physics and CAS Center for Excellence in Topological Quantum Computation, Chinese Academy of Sciences, Beijing 100190, China
| | - Gang Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Ke Wang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xin Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in 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
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Ting Wang
- Institute of Physics and CAS Center for Excellence in Topological Quantum Computation, Chinese Academy of Sciences, Beijing 100190, China
| | - Jianjun Zhang
- Institute of Physics and CAS Center for Excellence in Topological Quantum Computation, Chinese Academy of Sciences, Beijing 100190, China
| | - Xuedong Hu
- Department of Physics, University at Buffalo, SUNY, Buffalo, New York 14260, United States
| | - Hai-Ou Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Guo-Ping Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Origin Quantum Computing Company Limited, Hefei, Anhui 230026, China
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9
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Li 李 睿 R. Charge noise induced spin dephasing in a nanowire double quantum dot with spin-orbit coupling. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:025305. [PMID: 31569076 DOI: 10.1088/1361-648x/ab4933] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Unexpected fluctuating charge field near a semiconductor quantum dot has severely limited the coherence time of the localized spin qubit. It is the interplay between the spin-orbit coupling and the asymmetrical confining potential in a quantum dot, that mediates the longitudinal interaction between the spin qubit and the fluctuating charge field. Here, we study the 1/f charge noise induced spin dephasing in a nanowire double quantum dot via exactly solving its eigen-energies and eigenfunctions. Our calculations demonstrate that the spin dephasing has a nonmonotonic dependence on the asymmetry of the double quantum dot confining potential. With the increase of the potential asymmetry, the dephasing rate first becomes stronger very sharply before reaching to a maximum, after that it becomes weaker softly. Also, we find that the applied external magnetic field contributes to the spin dephasing, the dephasing rate is strongest at the anti-crossing point B 0 in the double quantum dot.
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Affiliation(s)
- Rui Li 李 睿
- Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao 066004, People's Republic of China
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10
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Li R. A spin dephasing mechanism mediated by the interplay between the spin-orbit coupling and the asymmetrical confining potential in a semiconductor quantum dot. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:395304. [PMID: 30141413 DOI: 10.1088/1361-648x/aadcb8] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Understanding the spin dephasing mechanism is of fundamental importance in all potential applications of the spin qubit. Here we demonstrate a spin dephasing mechanism in a semiconductor quantum dot due to the 1/f charge noise. The spin-charge interaction is mediated by the interplay between the spin-orbit coupling and the asymmetrical quantum dot confining potential. The dephasing rate is proportional to both the strength of the spin-orbit coupling and the degree of the asymmetry of the confining potential. For parameters typical of the InSb, InAs, and GaAs quantum dots with a moderate well-height [Formula: see text] meV, we find the spin dephasing times are [Formula: see text] μs, 275 μs, and 55 ms, respectively. In particular, the spin dephasing can be enhanced by lowering the well-height. When the well-height is as small as [Formula: see text] meV, the spin depahsing times in the InSb, InAs, and GaAs quantum dots are decreased to [Formula: see text] μs, 18 μs, and 9 ms, respectively.
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Affiliation(s)
- Rui Li
- Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao 066004, People's Republic of China
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11
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Li R, Liu ZH, Wu Y, Liu CS. The impacts of the quantum-dot confining potential on the spin-orbit effect. Sci Rep 2018; 8:7400. [PMID: 29743523 PMCID: PMC5943540 DOI: 10.1038/s41598-018-25692-2] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2018] [Accepted: 04/26/2018] [Indexed: 11/09/2022] Open
Abstract
For a nanowire quantum dot with the confining potential modeled by both the infinite and the finite square wells, we obtain exactly the energy spectrum and the wave functions in the strong spin-orbit coupling regime. We find that regardless of how small the well height is, there are at least two bound states in the finite square well: one has the σ x [Formula: see text] = -1 symmetry and the other has the σ x [Formula: see text] = 1 symmetry. When the well height is slowly tuned from large to small, the position of the maximal probability density of the first excited state moves from the center to x ≠ 0, while the position of the maximal probability density of the ground state is always at the center. A strong enhancement of the spin-orbit effect is demonstrated by tuning the well height. In particular, there exists a critical height [Formula: see text], at which the spin-orbit effect is enhanced to maximal.
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Affiliation(s)
- Rui Li
- Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao, 066004, China. .,Quantum Physics and Quantum Information Division, Beijing Computational Science Research Center, Beijing, 100193, China.
| | - Zhi-Hai Liu
- Quantum Physics and Quantum Information Division, Beijing Computational Science Research Center, Beijing, 100193, China
| | - Yidong Wu
- Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao, 066004, China
| | - C S Liu
- Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao, 066004, China
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12
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Li Y, Li SX, Gao F, Li HO, Xu G, Wang K, Liu D, Cao G, Xiao M, Wang T, Zhang JJ, Guo GC, Guo GP. Coupling a Germanium Hut Wire Hole Quantum Dot to a Superconducting Microwave Resonator. NANO LETTERS 2018; 18:2091-2097. [PMID: 29468882 DOI: 10.1021/acs.nanolett.8b00272] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Realizing a strong coupling between spin and resonator is an important issue for scalable quantum computation in semiconductor systems. Benefiting from the advantages of a strong spin-orbit coupling strength and long coherence time, the Ge hut wire, which is proposed to be site-controlled grown for scalability, is considered to be a promising candidate to achieve this goal. Here we present a hybrid architecture in which an on-chip superconducting microwave resonator is coupled to the holes in a Ge quantum dot. The charge stability diagram can be obtained from the amplitude and phase responses of the resonator independently from the DC transport measurement. Furthermore, we estimate the hole-resonator coupling rate of gc/2π = 148 MHz in the single quantum dot-resonator system and estimate the spin-resonator coupling rate gs/2π to be in the range 2-4 MHz. We anticipate that strong coupling between hole spins and microwave photons in a Ge hut wire is feasible with optimized schemes in the future.
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Affiliation(s)
- Yan Li
- Key Laboratory of Quantum Information, CAS , University of Science and Technology of China , Hefei , Anhui 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, CAS , University of Science and Technology of China , Hefei , Anhui 230026 , China
- Synergetic Innovation Center of Quantum Information & Quantum Physics , University of Science and Technology of China , Hefei , Anhui 230026 , China
| | - Fei Gao
- National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences , Beijing 100190 , China
- School of Physical Science, University of Chinese Academy of Sciences , Beijing 100190 , China
| | - Hai-Ou Li
- Key Laboratory of Quantum Information, CAS , University of Science and Technology of China , Hefei , Anhui 230026 , China
- Synergetic Innovation Center of Quantum Information & Quantum Physics , University of Science and Technology of China , Hefei , Anhui 230026 , China
| | - Gang Xu
- Key Laboratory of Quantum Information, CAS , University of Science and Technology of China , Hefei , Anhui 230026 , China
- Synergetic Innovation Center of Quantum Information & Quantum Physics , University of Science and Technology of China , Hefei , Anhui 230026 , China
| | - Ke Wang
- Key Laboratory of Quantum Information, CAS , University of Science and Technology of China , Hefei , Anhui 230026 , China
- Synergetic Innovation Center of Quantum Information & Quantum Physics , University of Science and Technology of China , Hefei , Anhui 230026 , China
| | - Di Liu
- Key Laboratory of Quantum Information, CAS , University of Science and Technology of China , Hefei , Anhui 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, CAS , University of Science and Technology of China , Hefei , Anhui 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, CAS , University of Science and Technology of China , Hefei , Anhui 230026 , China
- Synergetic Innovation Center of Quantum Information & Quantum Physics , University of Science and Technology of China , Hefei , Anhui 230026 , China
| | - Ting Wang
- National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences , Beijing 100190 , China
- School of Physical Science, University of Chinese Academy of Sciences , Beijing 100190 , China
| | - Jian-Jun Zhang
- National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences , Beijing 100190 , China
- School of Physical Science, University of Chinese Academy of Sciences , Beijing 100190 , China
| | - Guang-Can Guo
- Key Laboratory of Quantum Information, CAS , University of Science and Technology of China , Hefei , Anhui 230026 , China
- Synergetic Innovation Center of Quantum Information & Quantum Physics , University of Science and Technology of China , Hefei , Anhui 230026 , China
| | - Guo-Ping Guo
- Key Laboratory of Quantum Information, CAS , University of Science and Technology of China , Hefei , Anhui 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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13
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Liu ZH, Li R, Hu X, You JQ. Spin-orbit coupling and electric-dipole spin resonance in a nanowire double quantum dot. Sci Rep 2018; 8:2302. [PMID: 29396539 PMCID: PMC5797113 DOI: 10.1038/s41598-018-20706-5] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2017] [Accepted: 01/19/2018] [Indexed: 11/18/2022] Open
Abstract
We study the electric-dipole transitions for a single electron in a double quantum dot located in a semiconductor nanowire. Enabled by spin-orbit coupling (SOC), electric-dipole spin resonance (EDSR) for such an electron can be generated via two mechanisms: the SOC-induced intradot pseudospin states mixing and the interdot spin-flipped tunneling. The EDSR frequency and strength are determined by these mechanisms together. For both mechanisms the electric-dipole transition rates are strongly dependent on the external magnetic field. Their competition can be revealed by increasing the magnetic field and/or the interdot distance for the double dot. To clarify whether the strong SOC significantly impact the electron state coherence, we also calculate relaxations from excited levels via phonon emission. We show that spin-flip relaxations can be effectively suppressed by the phonon bottleneck effect even at relatively low magnetic fields because of the very large g-factor of strong SOC materials such as InSb.
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Affiliation(s)
- Zhi-Hai Liu
- Quantum Physics and Quantum Information Division, Beijing Computational Science Research Center, Beijing, 100193, China
| | - Rui Li
- Quantum Physics and Quantum Information Division, Beijing Computational Science Research Center, Beijing, 100193, China
| | - Xuedong Hu
- Department of Physics, University at Buffalo, SUNY, Buffalo, New York, 14260-1500, USA.
| | - J Q You
- Quantum Physics and Quantum Information Division, Beijing Computational Science Research Center, Beijing, 100193, China.
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14
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Russ M, Burkard G. Three-electron spin qubits. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:393001. [PMID: 28562367 DOI: 10.1088/1361-648x/aa761f] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The goal of this article is to review the progress of three-electron spin qubits from their inception to the state of the art. We direct the main focus towards the exchange-only qubit (Bacon et al 2000 Phys. Rev. Lett. 85 1758-61, DiVincenzo et al 2000 Nature 408 339) and its derived versions, e.g. the resonant exchange (RX) qubit, but we also discuss other qubit implementations using three electron spins. For each three-spin qubit we describe the qubit model, the envisioned physical realization, the implementations of single-qubit operations, as well as the read-out and initialization schemes. Two-qubit gates and decoherence properties are discussed for the RX qubit and the exchange-only qubit, thereby completing the list of requirements for quantum computation for a viable candidate qubit implementation. We start by describing the full system of three electrons in a triple quantum dot, then discuss the charge-stability diagram, restricting ourselves to the relevant subsystem, introduce the qubit states, and discuss important transitions to other charge states (Russ et al 2016 Phys. Rev. B 94 165411). Introducing the various qubit implementations, we begin with the exchange-only qubit (DiVincenzo et al 2000 Nature 408 339, Laird et al 2010 Phys. Rev. B 82 075403), followed by the RX qubit (Medford et al 2013 Phys. Rev. Lett. 111 050501, Taylor et al 2013 Phys. Rev. Lett. 111 050502), the spin-charge qubit (Kyriakidis and Burkard 2007 Phys. Rev. B 75 115324), and the hybrid qubit (Shi et al 2012 Phys. Rev. Lett. 108 140503, Koh et al 2012 Phys. Rev. Lett. 109 250503, Cao et al 2016 Phys. Rev. Lett. 116 086801, Thorgrimsson et al 2016 arXiv:1611.04945). The main focus will be on the exchange-only qubit and its modification, the RX qubit, whose single-qubit operations are realized by driving the qubit at its resonant frequency in the microwave range similar to electron spin resonance. Two different types of two-qubit operations are presented for the exchange-only qubits which can be divided into short-ranged and long-ranged interactions. Both of these interaction types are expected to be necessary in a large-scale quantum computer. The short-ranged interactions use the exchange coupling by placing qubits next to each other and applying exchange-pulses (DiVincenzo et al 2000 Nature 408 339, Fong and Wandzura 2011 Quantum Inf. Comput. 11 1003, Setiawan et al 2014 Phys. Rev. B 89 085314, Zeuch et al 2014 Phys. Rev. B 90 045306, Doherty and Wardrop 2013 Phys. Rev. Lett. 111 050503, Shim and Tahan 2016 Phys. Rev. B 93 121410), while the long-ranged interactions use the photons of a superconducting microwave cavity as a mediator in order to couple two qubits over long distances (Russ and Burkard 2015 Phys. Rev. B 92 205412, Srinivasa et al 2016 Phys. Rev. B 94 205421). The nature of the three-electron qubit states each having the same total spin and total spin in z-direction (same Zeeman energy) provides a natural protection against several sources of noise (DiVincenzo et al 2000 Nature 408 339, Taylor et al 2013 Phys. Rev. Lett. 111 050502, Kempe et al 2001 Phys. Rev. A 63 042307, Russ and Burkard 2015 Phys. Rev. B 91 235411). The price to pay for this advantage is an increase in gate complexity. We also take into account the decoherence of the qubit through the influence of magnetic noise (Ladd 2012 Phys. Rev. B 86 125408, Mehl and DiVincenzo 2013 Phys. Rev. B 87 195309, Hung et al 2014 Phys. Rev. B 90 045308), in particular dephasing due to the presence of nuclear spins, as well as dephasing due to charge noise (Medford et al 2013 Phys. Rev. Lett. 111 050501, Taylor et al 2013 Phys. Rev. Lett. 111 050502, Shim and Tahan 2016 Phys. Rev. B 93 121410, Russ and Burkard 2015 Phys. Rev. B 91 235411, Fei et al 2015 Phys. Rev. B 91 205434), fluctuations of the energy levels on each dot due to noisy gate voltages or the environment. Several techniques are discussed which partly decouple the qubit from magnetic noise (Setiawan et al 2014 Phys. Rev. B 89 085314, West and Fong 2012 New J. Phys. 14 083002, Rohling and Burkard 2016 Phys. Rev. B 93 205434) while for charge noise it is shown that it is favorable to operate the qubit on the so-called '(double) sweet spots' (Taylor et al 2013 Phys. Rev. Lett. 111 050502, Shim and Tahan 2016 Phys. Rev. B 93 121410, Russ and Burkard 2015 Phys. Rev. B 91 235411, Fei et al 2015 Phys. Rev. B 91 205434, Malinowski et al 2017 arXiv: 1704.01298), which are least susceptible to noise, thus providing a longer lifetime of the qubit.
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Affiliation(s)
- Maximilian Russ
- Department of Physics, University of Konstanz, D-78457 Konstanz, Germany
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15
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Fan J, Chen Y, Chen G, Xiao L, Jia S, Nori F. Electric-field-induced interferometric resonance of a one-dimensional spin-orbit-coupled electron. Sci Rep 2016; 6:38851. [PMID: 27966598 PMCID: PMC5155278 DOI: 10.1038/srep38851] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2016] [Accepted: 11/15/2016] [Indexed: 11/10/2022] Open
Abstract
The efficient control of electron spins is of crucial importance for spintronics, quantum metrology, and quantum information processing. We theoretically formulate an electric mechanism to probe the electron spin dynamics, by focusing on a one-dimensional spin-orbit-coupled nanowire quantum dot. Owing to the existence of spin-orbit coupling and a pulsed electric field, different spin-orbit states are shown to interfere with each other, generating intriguing interference-resonant patterns. We also reveal that an in-plane magnetic field does not affect the interval of any neighboring resonant peaks, but contributes a weak shift of each peak, which is sensitive to the direction of the magnetic field. We find that this proposed external-field-controlled scheme should be regarded as a new type of quantum-dot-based interferometry. This interferometry has potential applications in precise measurements of relevant experimental parameters, such as the Rashba and Dresselhaus spin-orbit-coupling strengths, as well as the Landé factor.
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Affiliation(s)
- Jingtao Fan
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser spectroscopy, Shanxi University, Taiyuan 030006, China.,Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Yuansen Chen
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China.,State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opt-Electronics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Gang Chen
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser spectroscopy, Shanxi University, Taiyuan 030006, China.,Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Liantuan Xiao
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser spectroscopy, Shanxi University, Taiyuan 030006, China.,Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Suotang Jia
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser spectroscopy, Shanxi University, Taiyuan 030006, China.,Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Franco Nori
- CEMS, RIKEN, Saitama 351-0198, Japan.,Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
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16
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Ban Y, Chen X. Counter-diabatic driving for fast spin control in a two-electron double quantum dot. Sci Rep 2014; 4:6258. [PMID: 25174453 PMCID: PMC4150114 DOI: 10.1038/srep06258] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2014] [Accepted: 08/08/2014] [Indexed: 12/04/2022] Open
Abstract
The techniques of shortcuts to adiabaticity have been proposed to accelerate the "slow" adiabatic processes in various quantum systems with the applications in quantum information processing. In this paper, we study the counter-diabatic driving for fast adiabatic spin manipulation in a two-electron double quantum dot by designing time-dependent electric fields in the presence of spin-orbit coupling. To simplify implementation and find an alternative shortcut, we further transform the Hamiltonian in term of Lie algebra, which allows one to use a single Cartesian component of electric fields. In addition, the relation between energy and time is quantified to show the lower bound for the operation time when the maximum amplitude of electric fields is given. Finally, the fidelity is discussed with respect to noise and systematic errors, which demonstrates that the decoherence effect induced by stochastic environment can be avoided in speeded-up adiabatic control.
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Affiliation(s)
- Yue Ban
- Department of Electronic Information Materials, Shanghai University, 200444 Shanghai, People's Republic of China
| | - Xi Chen
- Department of Physics, Shanghai University, 200444 Shanghai, People's Republic of China
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17
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Pawłowski J, Szumniak P, Skubis A, Bednarek S. Electron spin separation without magnetic field. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:345302. [PMID: 25106038 DOI: 10.1088/0953-8984/26/34/345302] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
A nanodevice capable of separating spins of two electrons confined in a quantum dot formed in a gated semiconductor nanowire is proposed. Two electrons confined initially in a single quantum dot in the singlet state are transformed into the system of two electrons confined in two spatially separated quantum dots with opposite spins. In order to separate the electrons' spins we exploit transitions between the singlet and the triplet state, which are induced by resonantly oscillating Rashba spin-orbit coupling strength. The proposed device is all electrically controlled and the electron spin separation can be realized within tens of picoseconds. The results are supported by solving numerically the quasi-one-dimensional time-dependent Schroedinger equation for two electrons, where the electron-electron correlations are taken into account in the exact manner.
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Affiliation(s)
- J Pawłowski
- Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Kraków, Poland
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18
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Li J, Yu T, Lin HQ, You JQ. Probing the non-locality of Majorana fermions via quantum correlations. Sci Rep 2014; 4:4930. [PMID: 24816484 PMCID: PMC4017219 DOI: 10.1038/srep04930] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2014] [Accepted: 04/23/2014] [Indexed: 11/27/2022] Open
Abstract
Majorana fermions (MFs) are exotic particles that are their own anti-particles. Recently, the search for the MFs occurring as quasi-particle excitations in solid-state systems has attracted widespread interest, because of their fundamental importance in fundamental physics and potential applications in topological quantum computation based on solid-state devices. Here we study the quantum correlations between two spatially separate quantum dots induced by a pair of MFs emerging at the two ends of a semiconductor nanowire, in order to develop a new method for probing the MFs. We find that without the tunnel coupling between these paired MFs, quantum entanglement cannot be induced from an unentangled (i.e., product) state, but quantum discord is observed due to the intrinsic nonlocal correlations of the paired MFs. This finding reveals that quantum discord can indeed demonstrate the intrinsic non-locality of the MFs formed in the nanowire. Also, quantum discord can be employed to discriminate the MFs from the regular fermions. Furthermore, we propose an experimental setup to measure the onset of quantum discord due to the nonlocal correlations. Our approach provides a new, and experimentally accessible, method to study the Majorana bound states by probing their intrinsic non-locality signature.
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Affiliation(s)
- Jun Li
- 1] Beijing Computational Science Research Center, Beijing 100084, China [2] College of Physics and Electronic Engineering, Dezhou University, Dezhou 253023, China
| | - Ting Yu
- Center for Controlled Quantum Systems and Department of Physics and Engineering Physics, Stevens Institute of Technology, Hoboken, New Jersey 07030, USA
| | - Hai-Qing Lin
- Beijing Computational Science Research Center, Beijing 100084, China
| | - J Q You
- Beijing Computational Science Research Center, Beijing 100084, China
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19
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Čadež T, Jefferson JH, Ramšak A. Exact nonadiabatic holonomic transformations of spin-orbit qubits. PHYSICAL REVIEW LETTERS 2014; 112:150402. [PMID: 24785014 DOI: 10.1103/physrevlett.112.150402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2014] [Indexed: 06/03/2023]
Abstract
An exact analytical solution is derived for the wave function of an electron in a one-dimensional moving quantum dot in a nanowire, in the presence of time-dependent spin-orbit coupling. For cyclic evolutions we show that the spin of the electron is rotated by an angle proportional to the area of a closed loop in the parameter space of the time-dependent quantum dot position and the amplitude of a fictitious classical oscillator driven by time-dependent spin-orbit coupling. By appropriate choice of parameters, we show that the spin may be rotated by an arbitrary angle on the Bloch sphere. Exact expressions for dynamical and geometrical phases are also derived.
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Affiliation(s)
- T Čadež
- Jožef Stefan Institute, 1000 Ljubljana, Slovenia and Institute of Mathematics, Physics and Mechanics, 1000 Ljubljana, Slovenia
| | - J H Jefferson
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, United Kingdom
| | - A Ramšak
- Jožef Stefan Institute, 1000 Ljubljana, Slovenia and Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia
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