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Struck T, Volmer M, Visser L, Offermann T, Xue R, Tu JS, Trellenkamp S, Cywiński Ł, Bluhm H, Schreiber LR. Spin-EPR-pair separation by conveyor-mode single electron shuttling in Si/SiGe. Nat Commun 2024; 15:1325. [PMID: 38351007 PMCID: PMC10864332 DOI: 10.1038/s41467-024-45583-7] [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] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Accepted: 01/29/2024] [Indexed: 02/16/2024] Open
Abstract
Long-ranged coherent qubit coupling is a missing function block for scaling up spin qubit based quantum computing solutions. Spin-coherent conveyor-mode electron-shuttling could enable spin quantum-chips with scalable and sparse qubit-architecture. Its key feature is the operation by only few easily tuneable input terminals and compatibility with industrial gate-fabrication. Single electron shuttling in conveyor-mode in a 420 nm long quantum bus has been demonstrated previously. Here we investigate the spin coherence during conveyor-mode shuttling by separation and rejoining an Einstein-Podolsky-Rosen (EPR) spin-pair. Compared to previous work we boost the shuttle velocity by a factor of 10000. We observe a rising spin-qubit dephasing time with the longer shuttle distances due to motional narrowing and estimate the spin-shuttle infidelity due to dephasing to be 0.7% for a total shuttle distance of nominal 560 nm. Shuttling several loops up to an accumulated distance of 3.36 μm, spin-entanglement of the EPR pair is still detectable, giving good perspective for our approach of a shuttle-based scalable quantum computing architecture in silicon.
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Affiliation(s)
- Tom Struck
- JARA-FIT Institute for Quantum Information, Forschungszentrum Jülich GmbH and RWTH Aachen University, Aachen, Germany
- ARQUE Systems GmbH, Aachen, Germany
| | - Mats Volmer
- JARA-FIT Institute for Quantum Information, Forschungszentrum Jülich GmbH and RWTH Aachen University, Aachen, Germany
| | - Lino Visser
- JARA-FIT Institute for Quantum Information, Forschungszentrum Jülich GmbH and RWTH Aachen University, Aachen, Germany
| | - Tobias Offermann
- JARA-FIT Institute for Quantum Information, Forschungszentrum Jülich GmbH and RWTH Aachen University, Aachen, Germany
| | - Ran Xue
- JARA-FIT Institute for Quantum Information, Forschungszentrum Jülich GmbH and RWTH Aachen University, Aachen, Germany
| | - Jhih-Sian Tu
- Helmholtz Nano Facility (HNF), Forschungszentrum Jülich, Jülich, Germany
| | - Stefan Trellenkamp
- Helmholtz Nano Facility (HNF), Forschungszentrum Jülich, Jülich, Germany
| | - Łukasz Cywiński
- Institute of Physics, Polish Academy of Sciences, Warsaw, Poland
| | - Hendrik Bluhm
- JARA-FIT Institute for Quantum Information, Forschungszentrum Jülich GmbH and RWTH Aachen University, Aachen, Germany
- ARQUE Systems GmbH, Aachen, Germany
| | - Lars R Schreiber
- JARA-FIT Institute for Quantum Information, Forschungszentrum Jülich GmbH and RWTH Aachen University, Aachen, Germany.
- ARQUE Systems GmbH, Aachen, Germany.
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Smoleński T, Cywiński Ł, Kossacki P. Mechanisms of optical orientation of an individual Mn 2+ ion spin in a II-VI quantum dot. J Phys Condens Matter 2018; 30:055303. [PMID: 29315081 DOI: 10.1088/1361-648x/aaa20c] [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] [Indexed: 06/07/2023]
Abstract
We provide a theoretical description of the optical orientation of a single Mn2+ ion spin under quasi-resonant excitation demonstrated experimentally by Goryca et al (2009 Phys. Rev. Lett. 103 087401). We build and analyze a hierarchy of models by starting with the simplest assumptions (transfer of perfectly spin-polarized excitons from Mn-free dot to the other dot containing a single Mn2+ spin, followed by radiative recombination) and subsequently adding more features, such as spin relaxation of electrons and holes. Particular attention is paid to the role of the influx of the dark excitons and the process of biexciton formation, which are shown to contribute significantly to the orientation process in the quasi-resonant excitation case. Analyzed scenarios show how multiple features of the excitonic complexes in magnetically-doped quantum dots, such as the values of exchange integrals, spin relaxation times, etc, lead to a plethora of optical orientation processes, characterized by distinct dependencies on light polarization and laser intensity, and occurring on distinct timescales. Comparison with experimental data shows that the correct description of the optical orientation mechanism requires taking into account Mn2+ spin-flip processes occurring not only when the exciton is already in the orbital ground state of the light-emitting dot, but also those that happen during the exciton transfer from high-energy states to the ground state. Inspired by the experimental results on energy relaxation of electrons and holes in nonmagnetic dots, we focus on the process of biexciton creation allowed by mutual spin-flip of an electron and the Mn2+ spin, and we show that by including it in the model, we obtain good qualitative and quantitative agreement with the experimental data on quasi-resonantly driven Mn2+ spin orientation.
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Affiliation(s)
- T Smoleński
- Institute of Experimental Physics, Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warsaw, Poland
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Szańkowski P, Ramon G, Krzywda J, Kwiatkowski D, Cywiński Ł. Environmental noise spectroscopy with qubits subjected to dynamical decoupling. J Phys Condens Matter 2017; 29:333001. [PMID: 28569239 DOI: 10.1088/1361-648x/aa7648] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
A qubit subjected to pure dephasing due to classical Gaussian noise can be turned into a spectrometer of this noise by utilizing its readout under properly chosen dynamical decoupling (DD) sequences to reconstruct the power spectral density of the noise. We review the theory behind this DD-based noise spectroscopy technique, paying special attention to issues that arise when the environmental noise is non-Gaussian and/or it has truly quantum properties. While we focus on the theoretical basis of the method, we connect the discussed concepts with specific experiments, and provide an overview of environmental noise models relevant for solid-state based qubits, including quantum-dot based spin qubits, superconducting qubits, and NV centers in diamond.
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Affiliation(s)
- P Szańkowski
- Institute of Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, PL-02668 Warsaw, Poland
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Malinowski FK, Martins F, Cywiński Ł, Rudner MS, Nissen PD, Fallahi S, Gardner GC, Manfra MJ, Marcus CM, Kuemmeth F. Spectrum of the Nuclear Environment for GaAs Spin Qubits. Phys Rev Lett 2017; 118:177702. [PMID: 28498694 DOI: 10.1103/physrevlett.118.177702] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2017] [Indexed: 05/25/2023]
Abstract
Using a singlet-triplet spin qubit as a sensitive spectrometer of the GaAs nuclear spin bath, we demonstrate that the spectrum of Overhauser noise agrees with a classical spin diffusion model over 6 orders of magnitude in frequency, from 1 mHz to 1 kHz, is flat below 10 mHz, and falls as 1/f^{2} for frequency f≳1 Hz. Increasing the applied magnetic field from 0.1 to 0.75 T suppresses electron-mediated spin diffusion, which decreases the spectral content in the 1/f^{2} region and lowers the saturation frequency, each by an order of magnitude, consistent with a numerical model. Spectral content at megahertz frequencies is accessed using dynamical decoupling, which shows a crossover from the few-pulse regime (≲16π pulses), where transverse Overhauser fluctuations dominate dephasing, to the many-pulse regime (≳32 π pulses), where longitudinal Overhauser fluctuations with a 1/f spectrum dominate.
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Affiliation(s)
- Filip K Malinowski
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Frederico Martins
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Łukasz Cywiński
- Institute of Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, PL-02668 Warsaw, Poland
| | - Mark S Rudner
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Niels Bohr International Academy, Niels Bohr Institute, 2100 Copenhagen, Denmark
| | - Peter D Nissen
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Saeed Fallahi
- Department of Physics and Astronomy, Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - Geoffrey C Gardner
- Department of Physics and Astronomy, Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- School of Materials Engineering and School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - Michael J Manfra
- Department of Physics and Astronomy, Birck Nanotechnology Center, and Station Q Purdue, Purdue University, West Lafayette, Indiana 47907, USA
- School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - Charles M Marcus
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Ferdinand Kuemmeth
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
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Malinowski FK, Martins F, Nissen PD, Barnes E, Cywiński Ł, Rudner MS, Fallahi S, Gardner GC, Manfra MJ, Marcus CM, Kuemmeth F. Notch filtering the nuclear environment of a spin qubit. Nat Nanotechnol 2017; 12:16-20. [PMID: 27694847 DOI: 10.1038/nnano.2016.170] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2016] [Accepted: 08/12/2016] [Indexed: 06/06/2023]
Abstract
Electron spins in gate-defined quantum dots provide a promising platform for quantum computation. In particular, spin-based quantum computing in gallium arsenide takes advantage of the high quality of semiconducting materials, reliability in fabricating arrays of quantum dots and accurate qubit operations. However, the effective magnetic noise arising from the hyperfine interaction with uncontrolled nuclear spins in the host lattice constitutes a major source of decoherence. Low-frequency nuclear noise, responsible for fast (10 ns) inhomogeneous dephasing, can be removed by echo techniques. High-frequency nuclear noise, recently studied via echo revivals, occurs in narrow-frequency bands related to differences in Larmor precession of the three isotopes 69Ga, 71Ga and 75As (refs 15,16,17). Here, we show that both low- and high-frequency nuclear noise can be filtered by appropriate dynamical decoupling sequences, resulting in a substantial enhancement of spin qubit coherence times. Using nuclear notch filtering, we demonstrate a spin coherence time (T2) of 0.87 ms, five orders of magnitude longer than typical exchange gate times, and exceeding the longest coherence times reported to date in Si/SiGe gate-defined quantum dots.
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Affiliation(s)
- Filip K Malinowski
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - Frederico Martins
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - Peter D Nissen
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - Edwin Barnes
- Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA
- Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA
| | - Łukasz Cywiński
- Institute of Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, PL-02668 Warsaw, Poland
| | - Mark S Rudner
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
- Niels Bohr International Academy, Niels Bohr Institute, Copenhagen 2100, Denmark
| | - Saeed Fallahi
- Department of Physics and Astronomy, Birck Nanotechnology Center, and Station Q Purdue, Purdue University, West Lafayette, Indiana 47907, USA
| | - Geoffrey C Gardner
- Department of Physics and Astronomy, Birck Nanotechnology Center, and Station Q Purdue, Purdue University, West Lafayette, Indiana 47907, USA
- School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - Michael J Manfra
- Department of Physics and Astronomy, Birck Nanotechnology Center, and Station Q Purdue, Purdue University, West Lafayette, Indiana 47907, USA
- School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - Charles M Marcus
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - Ferdinand Kuemmeth
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
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Barnes E, Cywiński Ł, Das Sarma S. Nonperturbative master equation solution of central spin dephasing dynamics. Phys Rev Lett 2012; 109:140403. [PMID: 23083231 DOI: 10.1103/physrevlett.109.140403] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2012] [Indexed: 06/01/2023]
Abstract
We solve the long-standing central spin problem for a general set of inhomogeneous bath couplings and a large class of initial bath states. We compute the time evolution of the coherence of a central spin coupled to a spin bath by resumming all orders of the time-convolutionless master equation, thus avoiding the need to assume weak coupling to the bath. The fully quantum, non-markovian solution is obtained in the large-bath limit and is valid up to a time scale set by the largest coupling constant. Our result captures the full decoherence of an electron spin qubit coupled to a nuclear spin bath in a GaAs quantum dot for experimentally relevant parameters. In addition, our solution is quite compact and can readily be used to make quantitative predictions for the decoherence process and to guide the design of nuclear state preparation protocols.
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Affiliation(s)
- Edwin Barnes
- Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA.
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Medford J, Cywiński Ł, Barthel C, Marcus CM, Hanson MP, Gossard AC. Scaling of dynamical decoupling for spin qubits. Phys Rev Lett 2012; 108:086802. [PMID: 22463554 DOI: 10.1103/physrevlett.108.086802] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2011] [Indexed: 05/31/2023]
Abstract
We investigate the scaling of coherence time T(2) with the number of π pulses n(π) in a singlet-triplet spin qubit using Carr-Purcell-Meiboom-Gill (CPMG) and concatenated dynamical decoupling (CDD) pulse sequences. For an even numbers of CPMG pulses, we find a power law T(2) is proportional to (n(π))(γ(e)), with γ(e)=0.72±0.01, essentially independent of the envelope function used to extract T(2). From this surprisingly robust value, a power-law model of the noise spectrum of the environment, S(ω)~ω(-β), yields β=γ(e)/(1-γ(e))=2.6±0.1. Model values for T(2)(n(π)) using β=2.6 for CPMG with both even and odd n(π) up to 32 and CDD orders 3 through 6 compare very well with the experiment.
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Affiliation(s)
- J Medford
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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Dery H, Dalal P, Cywiński Ł, Sham LJ. Spin-based logic in semiconductors for reconfigurable large-scale circuits. Nature 2007; 447:573-6. [PMID: 17538616 DOI: 10.1038/nature05833] [Citation(s) in RCA: 92] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2006] [Accepted: 04/10/2007] [Indexed: 11/08/2022]
Abstract
Research in semiconductor spintronics aims to extend the scope of conventional electronics by using the spin degree of freedom of an electron in addition to its charge. Significant scientific advances in this area have been reported, such as the development of diluted ferromagnetic semiconductors, spin injection into semiconductors from ferromagnetic metals and discoveries of new physical phenomena involving electron spin. Yet no viable means of developing spintronics in semiconductors has been presented. Here we report a theoretical design that is a conceptual step forward-spin accumulation is used as the basis of a semiconductor computer circuit. Although the giant magnetoresistance effect in metals has already been commercially exploited, it does not extend to semiconductor/ferromagnet systems, because the effect is too weak for logic operations. We overcome this obstacle by using spin accumulation rather than spin flow. The basic element in our design is a logic gate that consists of a semiconductor structure with multiple magnetic contacts; this serves to perform fast and reprogrammable logic operations in a noisy, room-temperature environment. We then introduce a method to interconnect a large number of these gates to form a 'spin computer'. As the shrinking of conventional complementary metal-oxide-semiconductor (CMOS) transistors reaches its intrinsic limit, greater computational capability will mean an increase in both circuit area and power dissipation. Our spin-based approach may provide wide margins for further scaling and also greater computational capability per gate.
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Affiliation(s)
- H Dery
- Department of Physics, University of California San Diego, La Jolla, California 92093-0319, USA.
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