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Dyte HE, Gillard G, Manna S, Covre da Silva SF, Rastelli A, Chekhovich EA. Is Wave Function Collapse Necessary? Explaining Quantum Nondemolition Measurement of a Spin Qubit within Linear Evolution. PHYSICAL REVIEW LETTERS 2024; 132:160804. [PMID: 38701456 DOI: 10.1103/physrevlett.132.160804] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2023] [Revised: 01/28/2024] [Accepted: 03/14/2024] [Indexed: 05/05/2024]
Abstract
The measurement problem dates back to the dawn of quantum mechanics. Here, we measure a quantum dot electron spin qubit through off-resonant coupling with a highly redundant ancilla, consisting of thousands of nuclear spins. Large redundancy allows for single-shot measurement with high fidelity ≈99.85%. Repeated measurements enable heralded initialization of the qubit and backaction-free detection of electron spin quantum jumps, attributed to burstlike fluctuations in a thermally populated phonon bath. Based on these results we argue that the measurement, linking quantum states to classical observables, can be made without any "wave function collapse" in agreement with the Quantum Darwinism concept.
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Affiliation(s)
- Harry E Dyte
- Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom
| | - George Gillard
- Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom
| | - Santanu Manna
- Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, Altenberger Strasse 69, 4040 Linz, Austria
| | - Saimon F Covre da Silva
- Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, Altenberger Strasse 69, 4040 Linz, Austria
| | - Armando Rastelli
- Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, Altenberger Strasse 69, 4040 Linz, Austria
| | - Evgeny A Chekhovich
- Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom
- Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, United Kingdom
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2
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Adambukulam C, Johnson BC, Morello A, Laucht A. Hyperfine Spectroscopy and Fast, All-Optical Arbitrary State Initialization and Readout of a Single, Ten-Level ^{73}Ge Vacancy Nuclear Spin Qudit in Diamond. PHYSICAL REVIEW LETTERS 2024; 132:060603. [PMID: 38394595 DOI: 10.1103/physrevlett.132.060603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2023] [Accepted: 01/11/2024] [Indexed: 02/25/2024]
Abstract
A high-spin nucleus coupled to a color center can act as a long-lived memory qudit in a spin-photon interface. The germanium vacancy (GeV) in diamond has attracted recent attention due to its excellent spectral properties and provides access to the ten-dimensional Hilbert space of the I=9/2 ^{73}Ge nucleus. Here, we observe the ^{73}GeV hyperfine structure, perform nuclear spin readout, and optically initialize the ^{73}Ge spin into any eigenstate on a μs timescale and with a fidelity of up to ∼84%. Our results establish ^{73}GeV as an optically addressable high-spin quantum platform for a high-efficiency spin-photon interface as well as for foundational quantum physics and metrology.
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Affiliation(s)
- C Adambukulam
- School of Electrical Engineering and Telecommunications, University of New South Wales, Kensington, NSW 2052, Australia
| | - B C Johnson
- School of Science, RMIT University, Melbourne, VIC 3001, Australia
| | - A Morello
- School of Electrical Engineering and Telecommunications, University of New South Wales, Kensington, NSW 2052, Australia
| | - A Laucht
- School of Electrical Engineering and Telecommunications, University of New South Wales, Kensington, NSW 2052, Australia
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3
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Kirstein E, Smirnov DS, Zhukov EA, Yakovlev DR, Kopteva NE, Dirin DN, Hordiichuk O, Kovalenko MV, Bayer M. The squeezed dark nuclear spin state in lead halide perovskites. Nat Commun 2023; 14:6683. [PMID: 37865649 PMCID: PMC10590392 DOI: 10.1038/s41467-023-42265-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2023] [Accepted: 10/04/2023] [Indexed: 10/23/2023] Open
Abstract
Coherent many-body states are highly promising for robust quantum information processing. While far-reaching theoretical predictions have been made for various implementations, direct experimental evidence of their appealing properties can be challenging. Here, we demonstrate optical manipulation of the nuclear spin ensemble in the lead halide perovskite semiconductor FAPbBr3 (FA = formamidinium), targeting a long-postulated collective dark state that is insensitive to optical pumping after its build-up. Via optical orientation of localized hole spins we drive the nuclear many-body system into this entangled state, requiring a weak magnetic field of only a few milli-Tesla strength at cryogenic temperatures. During its fast establishment, the nuclear polarization along the optical axis remains small, while the transverse nuclear spin fluctuations are strongly reduced, corresponding to spin squeezing as evidenced by a strong violation of the generalized nuclear squeezing-inequality with ξs < 0.5. The dark state corresponds to an ~35-body entanglement between the nuclei. Dark nuclear spin states can be exploited to store quantum information benefiting from their long-lived many-body coherence and to perform quantum measurements with a precision beyond the standard limit.
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Affiliation(s)
- E Kirstein
- Experimental Physics 2, Department of Physics, TU Dortmund, 44227, Dortmund, Germany.
| | - D S Smirnov
- Ioffe Institute, 194021, St. Petersburg, Russia.
| | - E A Zhukov
- Experimental Physics 2, Department of Physics, TU Dortmund, 44227, Dortmund, Germany
| | - D R Yakovlev
- Experimental Physics 2, Department of Physics, TU Dortmund, 44227, Dortmund, Germany
| | - N E Kopteva
- Experimental Physics 2, Department of Physics, TU Dortmund, 44227, Dortmund, Germany
| | - D N Dirin
- Laboratory of Inorganic Chemistry, Department of Chemistry and Applied Biosciences, ETH Zürich, 8093, Zürich, Switzerland
| | - O Hordiichuk
- Laboratory of Inorganic Chemistry, Department of Chemistry and Applied Biosciences, ETH Zürich, 8093, Zürich, Switzerland
- Laboratory for Thin Films and Photovoltaics, Department of Advanced Materials and Surfaces, Empa - Swiss Federal Laboratories for Materials Science and Technology, 8600, Dübendorf, Switzerland
| | - M V Kovalenko
- Laboratory of Inorganic Chemistry, Department of Chemistry and Applied Biosciences, ETH Zürich, 8093, Zürich, Switzerland
- Laboratory for Thin Films and Photovoltaics, Department of Advanced Materials and Surfaces, Empa - Swiss Federal Laboratories for Materials Science and Technology, 8600, Dübendorf, Switzerland
| | - M Bayer
- Experimental Physics 2, Department of Physics, TU Dortmund, 44227, Dortmund, Germany
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4
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Millington-Hotze P, Manna S, Covre da Silva SF, Rastelli A, Chekhovich EA. Nuclear spin diffusion in the central spin system of a GaAs/AlGaAs quantum dot. Nat Commun 2023; 14:2677. [PMID: 37160864 PMCID: PMC10170165 DOI: 10.1038/s41467-023-38349-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2022] [Accepted: 04/24/2023] [Indexed: 05/11/2023] Open
Abstract
The spin diffusion concept provides a classical description of a purely quantum-mechanical evolution in inhomogeneously polarized many-body systems such as nuclear spin lattices. The central spin of a localized electron alters nuclear spin diffusion in a way that is still poorly understood. Here, spin diffusion in a single GaAs/AlGaAs quantum dot is witnessed in the most direct manner from oscillatory spin relaxation dynamics. Electron spin is found to accelerate nuclear spin relaxation, from which we conclude that the long-discussed concept of a Knight-field-gradient diffusion barrier does not apply to GaAs epitaxial quantum dots. Our experiments distinguish between non-diffusion relaxation and spin diffusion, allowing us to conclude that diffusion is accelerated by the central electron spin. Such acceleration is observed up to unexpectedly high magnetic fields - we propose electron spin-flip fluctuations as an explanation. Diffusion-limited nuclear spin lifetimes range between 1 and 10 s, which is sufficiently long for quantum information storage and processing.
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Affiliation(s)
- Peter Millington-Hotze
- Department of Physics and Astronomy, University of Sheffield, Sheffield, S3 7RH, United Kingdom
| | - Santanu Manna
- Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, Altenberger Str. 69, Linz, 4040, Austria
- Department of Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, 110016, India
| | - Saimon F Covre da Silva
- Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, Altenberger Str. 69, Linz, 4040, Austria
| | - Armando Rastelli
- Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, Altenberger Str. 69, Linz, 4040, Austria
| | - Evgeny A Chekhovich
- Department of Physics and Astronomy, University of Sheffield, Sheffield, S3 7RH, United Kingdom.
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5
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Zaporski L, Shofer N, Bodey JH, Manna S, Gillard G, Appel MH, Schimpf C, Covre da Silva SF, Jarman J, Delamare G, Park G, Haeusler U, Chekhovich EA, Rastelli A, Gangloff DA, Atatüre M, Le Gall C. Ideal refocusing of an optically active spin qubit under strong hyperfine interactions. NATURE NANOTECHNOLOGY 2023; 18:257-263. [PMID: 36702953 DOI: 10.1038/s41565-022-01282-2] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2022] [Accepted: 10/28/2022] [Indexed: 06/18/2023]
Abstract
Combining highly coherent spin control with efficient light-matter coupling offers great opportunities for quantum communication and computing. Optically active semiconductor quantum dots have unparalleled photonic properties but also modest spin coherence limited by their resident nuclei. The nuclear inhomogeneity has thus far bound all dynamical decoupling measurements to a few microseconds. Here, we eliminate this inhomogeneity using lattice-matched GaAs-AlGaAs quantum dot devices and demonstrate dynamical decoupling of the electron spin qubit beyond 0.113(3) ms. Leveraging the 99.30(5)% visibility of our optical π-pulse gates, we use up to Nπ = 81 decoupling pulses and find a coherence time scaling of [Formula: see text]. This scaling manifests an ideal refocusing of strong interactions between the electron and the nuclear spin ensemble, free of extrinsic noise, which holds the promise of lifetime-limited spin coherence. Our findings demonstrate that the most punishing material science challenge for such quantum dot devices has a remedy and constitute the basis for highly coherent spin-photon interfaces.
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Affiliation(s)
- Leon Zaporski
- Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom.
| | - Noah Shofer
- Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
| | - Jonathan H Bodey
- Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
| | - Santanu Manna
- Institute of Semiconductor and Solid State Physics, Johannes Kepler University, Linz, Austria
- Department of Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, India
| | - George Gillard
- Department of Physics and Astronomy, University of Sheffield, Sheffield, United Kingdom
| | | | - Christian Schimpf
- Institute of Semiconductor and Solid State Physics, Johannes Kepler University, Linz, Austria
| | | | - John Jarman
- Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
| | - Geoffroy Delamare
- Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
| | - Gunhee Park
- Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
| | - Urs Haeusler
- Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
| | - Evgeny A Chekhovich
- Department of Physics and Astronomy, University of Sheffield, Sheffield, United Kingdom
| | - Armando Rastelli
- Institute of Semiconductor and Solid State Physics, Johannes Kepler University, Linz, Austria
| | - Dorian A Gangloff
- Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
- Department of Engineering Science, University of Oxford, Oxford, United Kingdom
| | - Mete Atatüre
- Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom.
| | - Claire Le Gall
- Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom.
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6
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Gillard G, Clarke E, Chekhovich EA. Harnessing many-body spin environment for long coherence storage and high-fidelity single-shot qubit readout. Nat Commun 2022; 13:4048. [PMID: 35831368 PMCID: PMC9279416 DOI: 10.1038/s41467-022-31618-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2022] [Accepted: 06/23/2022] [Indexed: 11/09/2022] Open
Abstract
There is a growing interest in hybrid solid-state quantum systems where nuclear spins, interfaced to the electron spin qubit, are used as quantum memory or qubit register. These approaches require long nuclear spin coherence, which until now seemed impossible owing to the disruptive effect of the electron spin. Here we study InGaAs semiconductor quantum dots, demonstrating millisecond-long collective nuclear spin coherence even under inhomogeneous coupling to the electron central spin. We show that the underlying decoherence mechanism is spectral diffusion induced by a fluctuating electron spin. These results provide new understanding of the many-body coherence in central spin systems, required for development of electron-nuclear spin qubits. As a demonstration, we implement a conditional gate that encodes electron spin state onto collective nuclear spin coherence, and use it for a single-shot readout of the electron spin qubit with >99% fidelity.
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Affiliation(s)
- George Gillard
- Department of Physics and Astronomy, University of Sheffield, Sheffield, S3 7RH, UK.
| | - Edmund Clarke
- Department of Electronic and Electrical Engineering, University of Sheffield, Sheffield, S1 3JD, UK
| | - Evgeny A Chekhovich
- Department of Physics and Astronomy, University of Sheffield, Sheffield, S3 7RH, UK.
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7
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Mantsevich VN, Smirnov DS. Current-induced hole spin polarization in a quantum dot via a chiral quasi bound state. NANOSCALE HORIZONS 2022; 7:752-758. [PMID: 35593642 DOI: 10.1039/d1nh00685a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
We put forward a mechanism for the current-induced spin polarization in semiconductor heterostructures, which is based on the complex structure of the valence band. It takes place for a light hole in a quantum dot side-coupled to a quantum wire with heavy holes. In stark contrast with the traditional mechanisms based on the linear in momentum spin-orbit coupling, an exponentially small bias applied to this structure is enough to create the 100% spin polarization in the quantum dot. Microscopically, this effect is related to the formation of the chiral quasi bound states and the spin-dependent tunneling of holes from the quantum wire to the quantum dot. This new concept is equally valid for the GaAs-, Si- and Ge-based nanostructures.
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Affiliation(s)
- V N Mantsevich
- Chair of Semiconductors and Cryoelectronics & Quantum Technology Center, Physics department, Lomonosov Moscow State University, 119991 Moscow, Russia
| | - D S Smirnov
- Ioffe Institute, 194021 St. Petersburg, Russia.
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8
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Eckstein M, Horodecki P. Probing the limits of quantum theory with quantum information at subnuclear scales. Proc Math Phys Eng Sci 2022. [DOI: 10.1098/rspa.2021.0806] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Modern quantum engineering techniques enabled successful foundational tests of quantum mechanics. Yet, the universal validity of quantum postulates is an open question. Here we propose a new theoretical framework of Q-data tests, which recognizes the established validity of quantum theory, but allows for more general—‘post-quantum’—scenarios in certain physical regimes. It can accommodate a large class of models with modified quantum wave dynamics, correlations beyond entanglement or general probabilistic postulates. We discuss its experimental implementation suited to probe the nature of strong nuclear interactions. In contrast to the present accelerator experiments, it shifts the focus from high-luminosity beam physics to individual particle coherent control.
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Affiliation(s)
- Michał Eckstein
- Institute of Theoretical Physics, Jagiellonian University, ul. Łojasiewicza 11, 30–348 Kraków, Poland
- Copernicus Center for Interdisciplinary Studies, ul. Szczepańska 1/5, 31-011 Kraków, Poland
| | - Paweł Horodecki
- International Centre for Theory of Quantum Technologies, University of Gdańsk, Wita Stwosza 63, 80-308 Gdańsk, Poland
- Faculty of Applied Physics and Mathematics, National Quantum Information Centre, Gdańsk University of Technology, Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland
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9
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Podemski P, Gawełczyk M, Wyborski P, Salamon H, Burakowski M, Musiał A, Reithmaier JP, Benyoucef M, Sęk G. Spin memory effect in charged single telecom quantum dots. OPTICS EXPRESS 2021; 29:34024-34034. [PMID: 34809201 DOI: 10.1364/oe.438708] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2021] [Accepted: 09/24/2021] [Indexed: 06/13/2023]
Abstract
Single InP-based quantum dots emitting in the third telecom window are probed quasi-resonantly in polarization-resolved microphotoluminescence experiments. For charged quantum dots we observe negative circular polarization being a fingerprint of the optical spin writing of the carriers within the quantum dots. The investigated quantum dots have a very dense ladder of excited states providing relatively easy quasi-resonant optical excitation, and together with telecom wavelengths emission they bring quantum gates and memories closer to compatibility with fiber-optic communication.
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10
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Phonon-assisted relaxation between triplet and singlet states in a self-assembled double quantum dot. Sci Rep 2021; 11:15256. [PMID: 34315967 PMCID: PMC8316559 DOI: 10.1038/s41598-021-94621-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2021] [Accepted: 07/07/2021] [Indexed: 11/08/2022] Open
Abstract
We study theoretically phonon-induced spin dynamics of two electrons confined in a self-assembled double quantum dot. We calculate the transition rates and time evolution of occupations for the spin-triplet and spin-singlet states. We characterize the relative importance of various relaxation channels, including two-phonon processes, as a function of the electric and magnetic fields. The simulations are based on a model combining the eight-band [Formula: see text] method and configuration-interaction approach. We show that the electron g-factor mismatch between the Zeeman doublets localized on different dots opens a relatively fast triplet-singlet phonon-assisted relaxation channel. We also demonstrate, that the relaxation near the triplet-singlet anticrossing is slowed down up to several orders of magnitude due to vanishing of some relaxation channels.
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11
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Shumilin AV, Smirnov DS. Nuclear Spin Dynamics, Noise, Squeezing, and Entanglement in Box Model. PHYSICAL REVIEW LETTERS 2021; 126:216804. [PMID: 34114866 DOI: 10.1103/physrevlett.126.216804] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2020] [Revised: 03/24/2021] [Accepted: 04/27/2021] [Indexed: 06/12/2023]
Abstract
We obtain a compact analytical solution for the nonlinear equation for the nuclear spin dynamics in the central spin box model in the limit of many nuclear spins. The total nuclear spin component along the external magnetic field is conserved and the two perpendicular components precess or oscillate depending on the electron spin polarization, with the frequency, determined by the nuclear spin polarization. As applications of our solution, we calculate the nuclear spin noise spectrum and describe the effects of nuclear spin squeezing and many body entanglement in the absence of a system excitation.
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Affiliation(s)
| | - D S Smirnov
- Ioffe Institute, 194021 St. Petersburg, Russia
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12
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Fataftah MS, Bayliss SL, Laorenza DW, Wang X, Phelan BT, Wilson CB, Mintun PJ, Kovos BD, Wasielewski MR, Han S, Sherwin MS, Awschalom DD, Freedman DE. Trigonal Bipyramidal V 3+ Complex as an Optically Addressable Molecular Qubit Candidate. J Am Chem Soc 2020; 142:20400-20408. [PMID: 33210910 DOI: 10.1021/jacs.0c08986] [Citation(s) in RCA: 33] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Abstract
Synthetic chemistry enables a bottom-up approach to quantum information science, where atoms can be deterministically positioned in a quantum bit or qubit. Two key requirements to realize quantum technologies are qubit initialization and read-out. By imbuing molecular spins with optical initialization and readout mechanisms, analogous to solid-state defects, molecules could be integrated into existing quantum infrastructure. To mimic the electronic structure of optically addressable defect sites, we designed the spin-triplet, V3+ complex, (C6F5)3trenVCNtBu (1). We measured the static spin properties as well as the spin coherence time of 1 demonstrating coherent control of this spin qubit with a 240 GHz electron paramagnetic resonance spectrometer powered by a free electron laser. We found that 1 exhibited narrow, near-infrared photoluminescence (PL) from a spin-singlet excited state. Using variable magnetic field PL spectroscopy, we resolved emission into each of the ground-state spin sublevels, a crucial component for spin-selective optical initialization and readout. This work demonstrates that trigonally symmetric, heteroleptic V3+ complexes are candidates for optical spin addressability.
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Affiliation(s)
- Majed S Fataftah
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| | - Sam L Bayliss
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Daniel W Laorenza
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| | - Xiaoling Wang
- Institute for Terahertz Science and Technology, University of California, Santa Barbara, Santa Barbara, California 93106, United States
- Department of Physics, University of California, Santa Barbara, Santa Barbara, California 93106, United States
| | - Brian T Phelan
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
- The Institute for Sustainability and Energy at Northwestern, Northwestern University, Evanston, Illinois 60208, United States
| | - C Blake Wilson
- Institute for Terahertz Science and Technology, University of California, Santa Barbara, Santa Barbara, California 93106, United States
- Department of Physics, University of California, Santa Barbara, Santa Barbara, California 93106, United States
| | - Peter J Mintun
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Berk D Kovos
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Michael R Wasielewski
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
- The Institute for Sustainability and Energy at Northwestern, Northwestern University, Evanston, Illinois 60208, United States
| | - Songi Han
- Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, California 93106, United States
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, Santa Barbara, California 93106, United States
- Institute for Terahertz Science and Technology, University of California, Santa Barbara, Santa Barbara, California 93106, United States
| | - Mark S Sherwin
- Institute for Terahertz Science and Technology, University of California, Santa Barbara, Santa Barbara, California 93106, United States
- Department of Physics, University of California, Santa Barbara, Santa Barbara, California 93106, United States
| | - David D Awschalom
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
- Department of Physics, University of Chicago, Chicago, Illinois 60637, United States
- Center for Molecular Engineering and Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Danna E Freedman
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
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