1
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Huang JY, Su RY, Lim WH, Feng M, van Straaten B, Severin B, Gilbert W, Dumoulin Stuyck N, Tanttu T, Serrano S, Cifuentes JD, Hansen I, Seedhouse AE, Vahapoglu E, Leon RCC, Abrosimov NV, Pohl HJ, Thewalt MLW, Hudson FE, Escott CC, Ares N, Bartlett SD, Morello A, Saraiva A, Laucht A, Dzurak AS, Yang CH. High-fidelity spin qubit operation and algorithmic initialization above 1 K. Nature 2024; 627:772-777. [PMID: 38538941 PMCID: PMC10972758 DOI: 10.1038/s41586-024-07160-2] [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] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2023] [Accepted: 02/05/2024] [Indexed: 04/01/2024]
Abstract
The encoding of qubits in semiconductor spin carriers has been recognized as a promising approach to a commercial quantum computer that can be lithographically produced and integrated at scale1-10. However, the operation of the large number of qubits required for advantageous quantum applications11-13 will produce a thermal load exceeding the available cooling power of cryostats at millikelvin temperatures. As the scale-up accelerates, it becomes imperative to establish fault-tolerant operation above 1 K, at which the cooling power is orders of magnitude higher14-18. Here we tune up and operate spin qubits in silicon above 1 K, with fidelities in the range required for fault-tolerant operations at these temperatures19-21. We design an algorithmic initialization protocol to prepare a pure two-qubit state even when the thermal energy is substantially above the qubit energies and incorporate radiofrequency readout to achieve fidelities up to 99.34% for both readout and initialization. We also demonstrate single-qubit Clifford gate fidelities up to 99.85% and a two-qubit gate fidelity of 98.92%. These advances overcome the fundamental limitation that the thermal energy must be well below the qubit energies for the high-fidelity operation to be possible, surmounting a main obstacle in the pathway to scalable and fault-tolerant quantum computation.
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Affiliation(s)
- Jonathan Y Huang
- School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales, Australia.
| | - Rocky Y Su
- School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales, Australia
| | - Wee Han Lim
- School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales, Australia
- Diraq, Sydney, New South Wales, Australia
| | - MengKe Feng
- School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales, Australia
| | | | - Brandon Severin
- School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales, Australia
- Department of Engineering Science, University of Oxford, Oxford, UK
| | - Will Gilbert
- School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales, Australia
- Diraq, Sydney, New South Wales, Australia
| | - Nard Dumoulin Stuyck
- School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales, Australia
- Diraq, Sydney, New South Wales, Australia
| | - Tuomo Tanttu
- School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales, Australia
- Diraq, Sydney, New South Wales, Australia
| | - Santiago Serrano
- School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales, Australia
| | - Jesus D Cifuentes
- School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales, Australia
| | - Ingvild Hansen
- School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales, Australia
| | - Amanda E Seedhouse
- School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales, Australia
| | - Ensar Vahapoglu
- School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales, Australia
- Diraq, Sydney, New South Wales, Australia
| | - Ross C C Leon
- School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales, Australia
- Quantum Motion Technologies, London, UK
| | | | | | - Michael L W Thewalt
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada
| | - Fay E Hudson
- School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales, Australia
- Diraq, Sydney, New South Wales, Australia
| | - Christopher C Escott
- School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales, Australia
- Diraq, Sydney, New South Wales, Australia
| | - Natalia Ares
- Department of Engineering Science, University of Oxford, Oxford, UK
| | - Stephen D Bartlett
- Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney, New South Wales, Australia
| | - Andrea Morello
- School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales, Australia
| | - Andre Saraiva
- School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales, Australia
- Diraq, Sydney, New South Wales, Australia
| | - Arne Laucht
- School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales, Australia
- Diraq, Sydney, New South Wales, Australia
| | - Andrew S Dzurak
- School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales, Australia.
- Diraq, Sydney, New South Wales, Australia.
| | - Chih Hwan Yang
- School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales, Australia.
- Diraq, Sydney, New South Wales, Australia.
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2
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DeAbreu A, Bowness C, Alizadeh A, Chartrand C, Brunelle NA, MacQuarrie ER, Lee-Hone NR, Ruether M, Kazemi M, Kurkjian ATK, Roorda S, Abrosimov NV, Pohl HJ, Thewalt MLW, Higginbottom DB, Simmons S. Waveguide-integrated silicon T centres. Opt Express 2023; 31:15045-15057. [PMID: 37157355 DOI: 10.1364/oe.482008] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
The performance of modular, networked quantum technologies will be strongly dependent upon the quality of their quantum light-matter interconnects. Solid-state colour centres, and in particular T centres in silicon, offer competitive technological and commercial advantages as the basis for quantum networking technologies and distributed quantum computing. These newly rediscovered silicon defects offer direct telecommunications-band photonic emission, long-lived electron and nuclear spin qubits, and proven native integration into industry-standard, CMOS-compatible, silicon-on-insulator (SOI) photonic chips at scale. Here we demonstrate further levels of integration by characterizing T centre spin ensembles in single-mode waveguides in SOI. In addition to measuring long spin T1 times, we report on the integrated centres' optical properties. We find that the narrow homogeneous linewidth of these waveguide-integrated emitters is already sufficiently low to predict the future success of remote spin-entangling protocols with only modest cavity Purcell enhancements. We show that further improvements may still be possible by measuring nearly lifetime-limited homogeneous linewidths in isotopically pure bulk crystals. In each case the measured linewidths are more than an order of magnitude lower than previously reported and further support the view that high-performance, large-scale distributed quantum technologies based upon T centres in silicon may be attainable in the near term.
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3
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Gilbert W, Tanttu T, Lim WH, Feng M, Huang JY, Cifuentes JD, Serrano S, Mai PY, Leon RCC, Escott CC, Itoh KM, Abrosimov NV, Pohl HJ, Thewalt MLW, Hudson FE, Morello A, Laucht A, Yang CH, Saraiva A, Dzurak AS. On-demand electrical control of spin qubits. Nat Nanotechnol 2023; 18:131-136. [PMID: 36635331 DOI: 10.1038/s41565-022-01280-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2022] [Accepted: 10/24/2022] [Indexed: 06/17/2023]
Abstract
Once called a 'classically non-describable two-valuedness' by Pauli, the electron spin forms a qubit that is naturally robust to electric fluctuations. Paradoxically, a common control strategy is the integration of micromagnets to enhance the coupling between spins and electric fields, which, in turn, hampers noise immunity and adds architectural complexity. Here we exploit a switchable interaction between spins and orbital motion of electrons in silicon quantum dots, without a micromagnet. The weak effects of relativistic spin-orbit interaction in silicon are enhanced, leading to a speed up in Rabi frequency by a factor of up to 650 by controlling the energy quantization of electrons in the nanostructure. Fast electrical control is demonstrated in multiple devices and electronic configurations. Using the electrical drive, we achieve a coherence time T2,Hahn ≈ 50 μs, fast single-qubit gates with Tπ/2 = 3 ns and gate fidelities of 99.93%, probed by randomized benchmarking. High-performance all-electrical control improves the prospects for scalable silicon quantum computing.
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Affiliation(s)
- Will Gilbert
- School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales, Australia.
- Diraq, Sydney, New South Wales, Australia.
| | - Tuomo Tanttu
- School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales, Australia
- Diraq, Sydney, New South Wales, Australia
| | - Wee Han Lim
- School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales, Australia
- Diraq, Sydney, New South Wales, Australia
| | - MengKe Feng
- School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales, Australia
| | - Jonathan Y Huang
- School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales, Australia
| | - Jesus D Cifuentes
- School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales, Australia
| | - Santiago Serrano
- School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales, Australia
| | - Philip Y Mai
- School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales, Australia
| | - Ross C C Leon
- School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales, Australia
| | - Christopher C Escott
- School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales, Australia
- Diraq, Sydney, New South Wales, Australia
| | - Kohei M Itoh
- School of Fundamental Science and Technology, Keio University, Yokohama, Japan
| | | | | | - Michael L W Thewalt
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada
| | - Fay E Hudson
- School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales, Australia
- Diraq, Sydney, New South Wales, Australia
| | - Andrea Morello
- School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales, Australia
| | - Arne Laucht
- School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales, Australia
- Diraq, Sydney, New South Wales, Australia
| | - Chih Hwan Yang
- School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales, Australia
- Diraq, Sydney, New South Wales, Australia
| | - Andre Saraiva
- School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales, Australia.
- Diraq, Sydney, New South Wales, Australia.
| | - Andrew S Dzurak
- School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales, Australia.
- Diraq, Sydney, New South Wales, Australia.
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4
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Mansir J, Conti P, Zeng Z, Pla JJ, Bertet P, Swift MW, Van de Walle CG, Thewalt MLW, Sklenard B, Niquet YM, Morton JJL. Linear Hyperfine Tuning of Donor Spins in Silicon Using Hydrostatic Strain. Phys Rev Lett 2018; 120:167701. [PMID: 29756909 DOI: 10.1103/physrevlett.120.167701] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2017] [Indexed: 06/08/2023]
Abstract
We experimentally study the coupling of group V donor spins in silicon to mechanical strain, and measure strain-induced frequency shifts that are linear in strain, in contrast to the quadratic dependence predicted by the valley repopulation model (VRM), and therefore orders of magnitude greater than that predicted by the VRM for small strains |ϵ|<10^{-5}. Through both tight-binding and first principles calculations we find that these shifts arise from a linear tuning of the donor hyperfine interaction term by the hydrostatic component of strain and achieve semiquantitative agreement with the experimental values. Our results provide a framework for making quantitative predictions of donor spins in silicon nanostructures, such as those being used to develop silicon-based quantum processors and memories. The strong spin-strain coupling we measure (up to 150 GHz per strain, for Bi donors in Si) offers a method for donor spin tuning-shifting Bi donor electron spins by over a linewidth with a hydrostatic strain of order 10^{-6}-as well as opportunities for coupling to mechanical resonators.
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Affiliation(s)
- J Mansir
- London Centre for Nanotechnology, UCL, 17-19 Gordon St, London WC1H 0AH, United Kingdom
| | - P Conti
- London Centre for Nanotechnology, UCL, 17-19 Gordon St, London WC1H 0AH, United Kingdom
| | - Z Zeng
- Université Grenoble Alpes, CEA, INAC-MEM, L_Sim, F-38000 Grenoble, France
| | - J J Pla
- School of Electrical Engineering & Telecommunications, University of New South Wales, Sydney, NSW 2052, Australia
| | - P Bertet
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - M W Swift
- Materials Department, University of California, Santa Barbara, California 93106-5050, USA
| | - C G Van de Walle
- Materials Department, University of California, Santa Barbara, California 93106-5050, USA
| | - M L W Thewalt
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
| | - B Sklenard
- Université Grenoble Alpes & CEA, LETI, MINATEC Campus, F-38000 Grenoble, France
| | - Y M Niquet
- Université Grenoble Alpes, CEA, INAC-MEM, L_Sim, F-38000 Grenoble, France
| | - J J L Morton
- London Centre for Nanotechnology, UCL, 17-19 Gordon St, London WC1H 0AH, United Kingdom
- Dept of Electronic and Electrical Engineering, UCL, London WC1E 7JE, United Kingdom
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5
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Morse KJ, Abraham RJS, DeAbreu A, Bowness C, Richards TS, Riemann H, Abrosimov NV, Becker P, Pohl HJ, Thewalt MLW, Simmons S. A photonic platform for donor spin qubits in silicon. Sci Adv 2017; 3:e1700930. [PMID: 28782032 PMCID: PMC5529058 DOI: 10.1126/sciadv.1700930] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2017] [Accepted: 06/19/2017] [Indexed: 05/25/2023]
Abstract
Donor spins in silicon are highly competitive qubits for upcoming quantum technologies, offering complementary metal-oxide semiconductor compatibility, coherence (T2) times of minutes to hours, and simultaneous initialization, manipulation, and readout fidelities near ~99.9%. This allows for many quantum error correction protocols, which will be essential for scale-up. However, a proven method of reliably coupling spatially separated donor qubits has yet to be identified. We present a scalable silicon-based platform using the unique optical properties of "deep" chalcogen donors. For the prototypical 77Se+ donor, we measure lower bounds on the transition dipole moment and excited-state lifetime, enabling access to the strong coupling limit of cavity quantum electrodynamics using known silicon photonic resonator technology and integrated silicon photonics. We also report relatively strong photon emission from this same transition. These results unlock clear pathways for silicon-based quantum computing, spin-to-photon conversion, photonic memories, integrated single-photon sources, and all-optical switches.
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Affiliation(s)
- Kevin J. Morse
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
| | - Rohan J. S. Abraham
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
| | - Adam DeAbreu
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
| | - Camille Bowness
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
| | - Timothy S. Richards
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
| | - Helge Riemann
- Leibniz-Institut für Kristallzüchtung, 12489 Berlin, Germany
| | | | - Peter Becker
- Physikalisch-Technische Bundesanstalt (PTB) Braunschweig, 38116 Braunschweig, Germany
| | | | - Michael L. W. Thewalt
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
| | - Stephanie Simmons
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
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6
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Bienfait A, Pla JJ, Kubo Y, Stern M, Zhou X, Lo CC, Weis CD, Schenkel T, Thewalt MLW, Vion D, Esteve D, Julsgaard B, Mølmer K, Morton JJL, Bertet P. Reaching the quantum limit of sensitivity in electron spin resonance. Nat Nanotechnol 2016; 11:253-257. [PMID: 26657787 DOI: 10.1038/nnano.2015.282] [Citation(s) in RCA: 58] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2015] [Accepted: 10/29/2015] [Indexed: 06/05/2023]
Abstract
The detection and characterization of paramagnetic species by electron spin resonance (ESR) spectroscopy is widely used throughout chemistry, biology and materials science, from in vivo imaging to distance measurements in spin-labelled proteins. ESR relies on the inductive detection of microwave signals emitted by the spins into a coupled microwave resonator during their Larmor precession. However, such signals can be very small, prohibiting the application of ESR at the nanoscale (for example, at the single-cell level or on individual nanoparticles). Here, using a Josephson parametric microwave amplifier combined with high-quality-factor superconducting microresonators cooled at millikelvin temperatures, we improve the state-of-the-art sensitivity of inductive ESR detection by nearly four orders of magnitude. We demonstrate the detection of 1,700 bismuth donor spins in silicon within a single Hahn echo with unit signal-to-noise ratio, reduced to 150 spins by averaging a single Carr-Purcell-Meiboom-Gill sequence. This unprecedented sensitivity reaches the limit set by quantum fluctuations of the electromagnetic field instead of thermal or technical noise, which constitutes a novel regime for magnetic resonance. The detection volume of our resonator is ∼ 0.02 nl, and our approach can be readily scaled down further to improve sensitivity, providing a new versatile toolbox for ESR at the nanoscale.
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Affiliation(s)
- A Bienfait
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - J J Pla
- London Centre for Nanotechnology, University College London, London WC1H 0AH, UK
| | - Y Kubo
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - M Stern
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
- Quantum Nanoelectronics Laboratory, BINA, Bar Ilan University, Ramat Gan, Israel
| | - X Zhou
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
- ISEN Department, Institute of Electronics Microelectronics and Nanotechnology, CNRS UMR 8520, Avenue Poincaré, CS 60069, Villeneuve d'Ascq Cedex 59652, France
| | - C C Lo
- London Centre for Nanotechnology, University College London, London WC1H 0AH, UK
| | - C D Weis
- Accelerator Technology and Applied Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - T Schenkel
- Accelerator Technology and Applied Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - M L W Thewalt
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
| | - D Vion
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - D Esteve
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - B Julsgaard
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, Aarhus C DK-8000, Denmark
| | - K Mølmer
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, Aarhus C DK-8000, Denmark
| | - J J L Morton
- London Centre for Nanotechnology, University College London, London WC1H 0AH, UK
| | - P Bertet
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
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7
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Lo CC, Urdampilleta M, Ross P, Gonzalez-Zalba MF, Mansir J, Lyon SA, Thewalt MLW, Morton JJL. Hybrid optical-electrical detection of donor electron spins with bound excitons in silicon. Nat Mater 2015; 14:490-494. [PMID: 25799326 DOI: 10.1038/nmat4250] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2014] [Accepted: 02/12/2015] [Indexed: 06/04/2023]
Abstract
Electrical detection of spins is an essential tool for understanding the dynamics of spins, with applications ranging from optoelectronics and spintronics, to quantum information processing. For electron spins bound to donors in silicon, bulk electrically detected magnetic resonance has relied on coupling to spin readout partners such as paramagnetic defects or conduction electrons, which fundamentally limits spin coherence times. Here we demonstrate electrical detection of donor electron spin resonance in an ensemble by transport through a silicon device, using optically driven donor-bound exciton transitions. We measure electron spin Rabi oscillations, and obtain long electron spin coherence times, limited only by the donor concentration. We also experimentally address critical issues such as non-resonant excitation, strain, and electric fields, laying the foundations for realizing a single-spin readout method with relaxed magnetic field and temperature requirements compared with spin-dependent tunnelling, enabling donor-based technologies such as quantum sensing.
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Affiliation(s)
- C C Lo
- 1] London Centre for Nanotechnology, University College London, London WC1H 0AH, UK [2] Department of Electronic and Electrical Engineering, University College London, London WC1E 7JE, UK
| | - M Urdampilleta
- London Centre for Nanotechnology, University College London, London WC1H 0AH, UK
| | - P Ross
- London Centre for Nanotechnology, University College London, London WC1H 0AH, UK
| | - M F Gonzalez-Zalba
- Hitachi Cambridge Laboratory, J. J. Thomson Avenue Cambridge CB3 0HE, UK
| | - J Mansir
- London Centre for Nanotechnology, University College London, London WC1H 0AH, UK
| | - S A Lyon
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M L W Thewalt
- Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
| | - J J L Morton
- 1] London Centre for Nanotechnology, University College London, London WC1H 0AH, UK [2] Department of Electronic and Electrical Engineering, University College London, London WC1E 7JE, UK
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8
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Gumann P, Patange O, Ramanathan C, Haas H, Moussa O, Thewalt MLW, Riemann H, Abrosimov NV, Becker P, Pohl HJ, Itoh KM, Cory DG. Inductive measurement of optically hyperpolarized phosphorous donor nuclei in an isotopically enriched silicon-28 crystal. Phys Rev Lett 2014; 113:267604. [PMID: 25615386 DOI: 10.1103/physrevlett.113.267604] [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: 07/27/2014] [Indexed: 06/04/2023]
Abstract
We experimentally demonstrate the first inductive readout of optically hyperpolarized phosphorus-31 donor nuclear spins in an isotopically enriched silicon-28 crystal. The concentration of phosphorus donors in the crystal was 1.5×10(15) cm(-3), 3 orders of magnitude lower than has previously been detected via direct inductive detection. The signal-to-noise ratio measured in a single free induction decay from a 1 cm(3) sample (≈10(15) spins) was 113. By transferring the sample to an X-band ESR spectrometer, we were able to obtain a lower bound for the nuclear spin polarization at 1.7 K of ∼64%. The (31)P-T2 measured with a Hahn echo sequence was 420 ms at 1.7 K, which was extended to 1.2 s with a Carr Purcell cycle. The T1 of the (31)P nuclear spins at 1.7 K is extremely long and could not be determined, as no decay was observed even on a time scale of 4.5 h. Optical excitation was performed with a 1047 nm laser, which provided above-band-gap excitation of the silicon. The buildup of the hyperpolarization at 4.2 K followed a single exponential with a characteristic time of 577 s, while the buildup at 1.7 K showed biexponential behavior with characteristic time constants of 578 and 5670 s.
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Affiliation(s)
- P Gumann
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada and Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - O Patange
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada and Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - C Ramanathan
- Department of Physics and Astronomy, Wilder Laboratory, Dartmouth College, Hanover, New Hampshire 03755, USA
| | - H Haas
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - O Moussa
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - M L W Thewalt
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
| | - H Riemann
- Leibniz-Institut fuer Kristallzuechtung, 12489 Berlin, Germany
| | - N V Abrosimov
- Leibniz-Institut fuer Kristallzuechtung, 12489 Berlin, Germany
| | - P Becker
- PTB Braunschweig, 38116 Braunschweig, Germany
| | - H-J Pohl
- VITCON Projectconsult GmbH, 07743 Jena, Germany
| | - K M Itoh
- School of Fundamental Science and Technology, Keio University, Yokohama, 3-14-1 Hiyoshi 223-8522, Japan
| | - D G Cory
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada and Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada and Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada and Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada and Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
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9
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Steger M, Saeedi K, Thewalt MLW, Morton JJL, Riemann H, Abrosimov NV, Becker P, Pohl HJ. Quantum information storage for over 180 s using donor spins in a 28Si "semiconductor vacuum". Science 2012; 336:1280-3. [PMID: 22679091 DOI: 10.1126/science.1217635] [Citation(s) in RCA: 228] [Impact Index Per Article: 19.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
A quantum computer requires systems that are isolated from their environment, but can be integrated into devices, and whose states can be measured with high accuracy. Nuclear spins in solids promise long coherence lifetimes, but they are difficult to initialize into known states and to detect with high sensitivity. We show how the distinctive optical properties of enriched (28)Si enable the use of hyperfine-resolved optical transitions, as previously applied to great effect for isolated atoms and ions in vacuum. Together with efficient Auger photoionization, these resolved hyperfine transitions permit rapid nuclear hyperpolarization and electrical spin-readout. We combine these techniques to detect nuclear magnetic resonance from dilute (31)P in the purest available sample of (28)Si, at concentrations inaccessible to conventional measurements, measuring a solid-state coherence time of over 180 seconds.
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Affiliation(s)
- M Steger
- Department of Physics, Simon Fraser University, Burnaby, BC, Canada
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Tyryshkin AM, Tojo S, Morton JJL, Riemann H, Abrosimov NV, Becker P, Pohl HJ, Schenkel T, Thewalt MLW, Itoh KM, Lyon SA. Electron spin coherence exceeding seconds in high-purity silicon. Nat Mater 2011; 11:143-7. [PMID: 22138791 DOI: 10.1038/nmat3182] [Citation(s) in RCA: 191] [Impact Index Per Article: 14.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2011] [Accepted: 10/24/2011] [Indexed: 05/05/2023]
Abstract
Silicon is one of the most promising semiconductor materials for spin-based information processing devices. Its advanced fabrication technology facilitates the transition from individual devices to large-scale processors, and the availability of a (28)Si form with no magnetic nuclei overcomes a primary source of spin decoherence in many other materials. Nevertheless, the coherence lifetimes of electron spins in the solid state have typically remained several orders of magnitude lower than that achieved in isolated high-vacuum systems such as trapped ions. Here we examine electron spin coherence of donors in pure (28)Si material (residual (29)Si concentration <50 ppm) with donor densities of 10(14)-10(15) cm(-3). We elucidate three mechanisms for spin decoherence, active at different temperatures, and extract a coherence lifetime T(2) up to 2 s. In this regime, we find the electron spin is sensitive to interactions with other donor electron spins separated by ~200 nm. A magnetic field gradient suppresses such interactions, producing an extrapolated electron spin T(2) of 10 s at 1.8 K. These coherence lifetimes are without peer in the solid state and comparable to high-vacuum qubits, making electron spins of donors in silicon ideal components of quantum computers, or quantum memories for systems such as superconducting qubits.
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Affiliation(s)
- Alexei M Tyryshkin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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Sekiguchi T, Steger M, Saeedi K, Thewalt MLW, Riemann H, Abrosimov NV, Nötzel N. Hyperfine structure and nuclear hyperpolarization observed in the bound exciton luminescence of Bi donors in natural Si. Phys Rev Lett 2010; 104:137402. [PMID: 20481913 DOI: 10.1103/physrevlett.104.137402] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2009] [Indexed: 05/29/2023]
Abstract
As the deepest group-V donor in Si, Bi has by far the largest hyperfine interaction and also a large I = 9/2 nuclear spin. At zero field this splits the donor ground state into states having total spin 5 and 4, which are fully resolved in the photoluminescence spectrum of Bi donor bound excitons. Under a magnetic field, the 60 expected allowed transitions cannot be individually resolved, but the effects of the nuclear spin distribution, -9/2 < or = I(z) < or = 9/2, are clearly observed. A strong hyperpolarization of the nuclear spin towards I(z) = -9/2 is observed to result from the nonresonant optical excitation. This is very similar to the recently reported optical hyperpolarization of P donors observed by EPR at higher magnetic fields. We introduce a new model to explain this effect, and predict that it may be very fast.
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Affiliation(s)
- T Sekiguchi
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
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Yang A, Steger M, Sekiguchi T, Thewalt MLW, Ladd TD, Itoh KM, Riemann H, Abrosimov NV, Becker P, Pohl HJ. Simultaneous subsecond hyperpolarization of the nuclear and electron spins of phosphorus in silicon by optical pumping of exciton transitions. Phys Rev Lett 2009; 102:257401. [PMID: 19659118 DOI: 10.1103/physrevlett.102.257401] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2009] [Indexed: 05/28/2023]
Abstract
We demonstrate a method which can hyperpolarize both the electron and nuclear spins of 31P donors in Si at low field, where both would be essentially unpolarized in equilibrium. It is based on the selective ionization of donors in a specific hyperfine state by optically pumping donor bound exciton hyperfine transitions, which can be spectrally resolved in 28Si. Electron and nuclear polarizations of 90% and 76%, respectively, are obtained in less than a second, providing an initialization mechanism for qubits based on these spins, and enabling further ESR and NMR studies on dilute 31P in 28Si.
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Affiliation(s)
- A Yang
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
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Steger M, Yang A, Stavrias N, Thewalt MLW, Riemann H, Abrosimov NV, Churbanov MF, Gusev AV, Bulanov AD, Kovalev ID, Kaliteevskii AK, Godisov ON, Becker P, Pohl HJ. Reduction of the linewidths of deep luminescence centers in 28Si reveals fingerprints of the isotope constituents. Phys Rev Lett 2008; 100:177402. [PMID: 18518336 DOI: 10.1103/physrevlett.100.177402] [Citation(s) in RCA: 2] [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] [Received: 01/08/2008] [Indexed: 05/26/2023]
Abstract
Dramatic reductions of the linewidths of well-known deep centers in 28Si reveal "isotopic fingerprints" of the constituents. The approximately 1014 meV Cu center, thought to be either a Cu pair or an isolated Cu, is shown to contain four Cu atoms, and the approximately 780 meV Ag center is shown to contain four Ag. The approximately 944 meV ;{*}Cu center, thought to be a different configuration of a Cu pair, in fact contains three Cu and one Ag, and a new two-Cu two-Ag center is found. The approximately 735 meV center, previously assigned to Fe, actually contains Au and three Cu. This suggests a family of four-atom (Cu, Ag, Au) centers.
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Affiliation(s)
- M Steger
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
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14
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Yang A, Steger M, Karaiskaj D, Thewalt MLW, Cardona M, Itoh KM, Riemann H, Abrosimov NV, Churbanov MF, Gusev AV, Bulanov AD, Kaliteevskii AK, Godisov ON, Becker P, Pohl HJ, Ager JW, Haller EE. Optical detection and ionization of donors in specific electronic and nuclear spin States. Phys Rev Lett 2006; 97:227401. [PMID: 17155840 DOI: 10.1103/physrevlett.97.227401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2006] [Indexed: 05/12/2023]
Abstract
We resolve the remarkably sharp bound exciton transitions of highly enriched 28Si using a single-frequency laser and photoluminescence excitation spectroscopy, as well as photocurrent spectroscopy. Well-resolved doublets in the spectrum of the 31P donor reflect the hyperfine coupling of the electronic and nuclear donor spins. The optical detection of the nuclear spin state, and selective pumping and ionization of donors in specific electronic and nuclear spin states, suggests a number of new possibilities which could be useful for the realization of silicon-based quantum computers.
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Affiliation(s)
- A Yang
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, V5A 1S6 Canada
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Cardona M, Meyer TA, Thewalt MLW. Temperature dependence of the energy gap of semiconductors in the low-temperature limit. Phys Rev Lett 2004; 92:196403. [PMID: 15169425 DOI: 10.1103/physrevlett.92.196403] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2003] [Indexed: 05/24/2023]
Abstract
The temperature dependence of the electronic states and energy gaps of semiconductors is an old but still important experimental and theoretical topic. Remarkably, extant results do not clarify the asymptotic T-->0 behavior. Recent breakthroughs in the spectroscopy of enriched 28Si allow us to measure changes in the band gap over the liquid 4He temperature range with an astounding precision of one part in 10(8), revealing a T4.0+/-0.2 decrease with increasing T. This is in excellent agreement with a theoretical argument predicting an exponent of 4. This power law should apply, in the low temperature limit, to the temperature dependence of the energies of all electronic states in semiconductors and insulators.
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Affiliation(s)
- Manuel Cardona
- Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, 70569 Stuttgart, Germany.
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Karaiskaj D, Stotz JAH, Meyer T, Thewalt MLW, Cardona M. Impurity absorption spectroscopy in 28Si: the importance of inhomogeneous isotope broadening. Phys Rev Lett 2003; 90:186402. [PMID: 12786030 DOI: 10.1103/physrevlett.90.186402] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2003] [Indexed: 05/24/2023]
Abstract
We report high-resolution infrared absorption spectra of the neutral donors phosphorus and lithium, and the neutral acceptor boron, in isotopically pure 28Si crystals. Surprisingly, many of the transitions are much sharper than previously reported in natural Si. In particular, the 2p(0) line of phosphorus in 28Si has a full width at half maximum of only 4.2 microeV, about 5 times less than the narrowest 2p(0) line previously reported for natural Si, making it the narrowest shallow impurity transition yet observed. The widely held assumptions that the impurity transitions previously reported in high quality samples of natural Si revealed the true, homogeneous linewidths, are thus shown to be incorrect. The sharper transitions in 28Si also reveal new substructures in the boron and lithium spectra.
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Affiliation(s)
- D Karaiskaj
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
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Karaiskaj D, Kirczenow G, Thewalt MLW, Buczko R, Cardona M. Origin of the residual acceptor ground-state splitting in silicon. Phys Rev Lett 2003; 90:016404. [PMID: 12570637 DOI: 10.1103/physrevlett.90.016404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2002] [Indexed: 05/24/2023]
Abstract
The residual ground-state splitting of acceptors in high-quality silicon has been studied intensely by different experimental techniques for several decades. Recently, photoluminescence studies of isotopically pure silicon revealed the ground-state splitting to result from the random distribution of isotopes in natural silicon. Here we present a new model that explains these surprising experimental results, and discuss the implications for acceptor ground-state splittings observed in other isotopically mixed semiconductors, as well as for the acceptor ground state in semiconductor alloys.
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Affiliation(s)
- D Karaiskaj
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
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Karaiskaj D, Thewalt MLW, Ruf T, Cardona M, Konuma M. "Intrinsic" acceptor ground state splitting in silicon: an isotopic effect. Phys Rev Lett 2002; 89:016401. [PMID: 12097056 DOI: 10.1103/physrevlett.89.016401] [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: 03/13/2002] [Indexed: 05/23/2023]
Abstract
One of the oldest open questions in semiconductor physics is the origin of the small splittings of the neutral acceptor ground state in silicon which lead to a distribution of doublet splittings rather than the fourfold-degenerate state of Gamma(8) symmetry expected in the absence of perturbations. Here we show that these acceptor ground state splittings are absent in the photoluminescence spectra of acceptor bound excitons in isotopically purified 28Si, demonstrating conclusively the surprising result that the splittings previously observed in natural Si result from the randomness of the Si isotopic composition.
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Affiliation(s)
- D Karaiskaj
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
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