Abstract
Individual donors in silicon chips are used as quantum bits with extremely low error rates. However, physical realizations have been limited to one donor because their atomic size causes fabrication challenges. Quantum dot qubits, in contrast, are highly adjustable using electrical gate voltages. This adjustability could be leveraged to deterministically couple donors to quantum dots in arrays of qubits. In this work, we demonstrate the coherent interaction of a 31P donor electron with the electron of a metal-oxide-semiconductor quantum dot. We form a logical qubit encoded in the spin singlet and triplet states of the two-electron system. We show that the donor nuclear spin drives coherent rotations between the electronic qubit states through the contact hyperfine interaction. This provides every key element for compact two-electron spin qubits requiring only a single dot and no additional magnetic field gradients, as well as a means to interact with the nuclear spin qubit.
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Introduction
The silicon industry’s fabrication capability promises to be a differentiating accelerator for the future development of quantum computers built with silicon quantum bits (qubits). Silicon is, furthermore, an appealing material for qubits because it provides an ultra low decoherence environment1. In particular, extremely high fidelities have been demonstrated for both the electron1,2,3,4,5 and nuclear spins6 of a single dopant atom in isotopically-enriched silicon nanostructures4. Assembling these exceptional solid-state qubits into a full quantum processor, as first envisioned by Kane7, will require coupling donor atoms to one another in a controllable way. This has proven extremely challenging, demanding near-atomic precision in the placement of the donors8,9,10,11,12. In contrast, single electron spins confined in quantum dots (QDs)13,14,15,16 are routinely coupled to one another since quantum dots are highly tunable and fabricated in engineered locations, allowing for controllable and scalable two-qubit interactions13, 17,18,19,20. For this reason, QDs have been theoretically discussed as intermediates to couple donor qubits7, 21,22,23,24,25. Recently, spin blockade has been observed in a silicon QD-donor device26. However, the coherent spin coupling between donor- and quantum dot-based qubits has remained elusive. It is the cornerstone advance necessary for exploiting the advantages of these two complementary qubit systems.
Here, we advance silicon-based quantum information processing by coherently coupling a phosphorus donor’s electron spin to a metal-oxide-semiconductor (MOS) QD. In our system, the QD is tuned to few-electron occupancy while simultaneously keeping a nearby donor (D) tunnel-coupled to the QD. The combination of the QD and donor electron qubits gives rise to a joint singlet-triplet (ST) logical encoding analogous to those in double-QD qubits27, 28. Specifically, the two logical states are the singlet \(\left| S \right\rangle = \left| { \uparrow \downarrow } \right\rangle \! - \! \left| { \downarrow \uparrow } \right\rangle \) and unpolarized triplet \(\left| {{T_0}} \right\rangle = \left| { \uparrow \downarrow } \right\rangle \! + \! \left| { \downarrow \uparrow } \right\rangle \). The encoding takes advantage of the contact hyperfine interaction between the donor electron spin and donor nuclear spin. This interaction makes the electron spin on the donor precess at a rate A/2 different from the QD electrons, where A is the hyperfine coupling strength. The hyperfine interaction thus amounts to an effective magnetic field gradient produced by the single phosphorus nucleus and drives rotations between singlet and triplet states29. By electrically controlling the donor charge configuration between ionized and neutral, the rotations can be turned off and on. The electron-electron exchange coupling and the hyperfine interaction with the donor nucleus define two orthogonal control axes for the qubit, and their relative strength is controlled using fast electrical pulses.
The electron qubit formed by the QD-D coupled system is analogous to other ST qubits, while introducing important advantages. It features full electrical control with a uniquely compact design requiring only one QD. The QD-D ST qubit avoids the integration complexities of other Si spin control schemes such as micromagnets30, 31, microwave striplines32, 33 or additional QDs for full electrical control14, 34. The hyperfine coupling to the single nuclear spin introduces a nature-defined and potentially very stable (i.e. low noise) rotation axis for the ST qubit. Furthermore, the system has a natural access to the nuclear spin, which is one of the highest performing solid state qubits4. Integration of a coil for nuclear magnetic resonance could enable full control over the nuclear spin qubit. Nuclear spin readout schemes based on ST interactions with the donor have already been proposed21, making complete control of these two coupled qubits foreseeable in the near future. The engineered coupling of the QD and D spins constitutes a possible path to realize over nineteen years of different theoretical proposals of donor qubit architectures7, 22, 24, 25, 35, 36. For example, the large lithographic quantum dot can facilitate the coupling of neighboring QD-D cells using capacitive coupling19, 20, 37 or exchange interaction13.
Results
Device description
The QD-D device is fabricated with isotopically-enriched 28Si and a foundry-compatible process (i.e. no lift-off processing). We use a poly-silicon gate stack, shown in Fig. 1a, that allows self-aligned ion implantation and subsequent activation annealing process. Phosphorus donors are implanted using the AG gate as a mask. This processing maximizes the probability of placing a D in a suitable location next to the QD. It also facilitates future multi-qubit fabrication that could take advantage of single ion implantation8 and a planar QD geometry24, 25. Fabrication details are found in the Supplementary Note 1 and are similar to ref. 38. A channel of electrons is formed at the MOS interface underneath the wire-shaped accumulation gate (AG) by applying a positive voltage, depicted as a blue overlay in Fig. 1a. Next, a QD island is isolated by applying suitable negative voltages on neighboring gates. A single-electron transistor (SET) is formed in the upper wire to monitor the electron occupation N of the QD and the relevant donor, denoted (N QD, N D). The SET charge sensor (CS) is also used for spin readout via spin-to-charge conversion. An in-plane magnetic field of 300 mT is applied throughout the experiments and the electron temperature is measured to be 215 mK. Detailed information about fabrication, gate biasing and electron counting is provided in the Supplementary Note 2.
To investigate coherent coupling dynamics between the donor and the QD, we first identify an effective (2, 0) ↔ (1, 1) QD-D charge transition with a total of four electrons, as shown in Fig. 1b–d 39, 40. We use the spin filling structure, measured through magnetic fields, to engineer a sufficiently large energy difference J (4,0) between the singlet and triplet states41, which we observe to be substantially larger for four electrons (~150 μeV) than for two electrons (~60 μeV). Details are available in the Supplementary Note 3. In Si MOS, the valley splitting can be tuned to large values by increasing the electric field perpendicular to the interface, which was verified in this device42. Simultaneously keeping the donor in resonance with the few electron QD states, however, constrained the available range of voltage in this design leading to the relatively small two-electron valley splitting. We note two general benefits of using the four-electron configuration: (i) filled shells might be a general approach to circumvent the obstacle of low valley splitting in any material with conduction band degeneracy14, 43; and (ii) increased electron numbers can extend the size of the QD due to the increased filling of the potential well, which in turn allows more range in selecting a suitable tunnel coupling to remote donor sites.
Hyperfine-driven spin rotations
Rotations between \(\left| S \right\rangle \) and \(\left| {{T_0}} \right\rangle \) can be driven by an effective magnetic field gradient ΔB z = ±A/2 between the QD and the donor (in the remainder of the text we will drop the ket notation). These rotations provide a signature of the single 31P donor. The source of the effective ΔB z is the contact hyperfine interaction \(A\widehat {\bf{S}} \cdot \widehat {\bf{I}}\) between the donor electron spin \(\widehat {\bf{S}}\) and the nuclear spin \(\widehat {\bf{I}}\). We expect the nuclear spin state to be projected onto a ±1/2 eigenstate by the repetitive experimental measurement. Rapidly separating a singlet state by pulling one electron onto the donor triggers coherent rotations between the S and T 0 states. Reuniting the electrons onto the QD projects the state onto S or T 0. We note that spin preparation, manipulations and readout act self-consistently with respect to a fixed but unknown state of the nuclear spin (i.e. the sign of ΔB z ) in sufficiently large magnetic fields such that the interaction with the polarized triplets is suppressed (which is the case in this experiment). Moreover, nuclear states are known to be long lived (~seconds) compared to the timescale of electron manipulations4, therefore, errors caused by random flips while an electron is on the donor are expected to be negligible. The nuclear state could still have implications for single or multi-qubit operation. In the future, this could be addressed by deterministically setting the nuclear state through various pulsing schemes, such as a single-spin version of dynamic nuclear polarization44. To demonstrate the hyperfine-driven rotations, we use the pulse sequence shown in Fig. 2. We prepare a (4, 0)S state by first emptying the QD and loading an electron between the singlet and triplet loading lines. Then, we plunge the system at point P (see Fig. 2b). Next, we rapidly separate the electrons by pulsing the system to point A with a 16 ns ramp time. After waiting for a given manipulation time, the system is pulsed back to point P in (4, 0). The ramp time is such that the charge transition is adiabatic, but fast enough to prepare a (3, 1)S. Finally, we use an enhanced latching readout developed for this experiment and described in the Supplementary Note 4 to measure the triplet return probability.
Figure 2c shows the triplet return probability as a function of the manipulation time. All the details on the pulse sequence can be found in the Supplementary Notes 5 and 6. We find a ST rotation frequency f = 57 MHz. This frequency is the vector sum of the exchange energy J(\(\epsilon \)) and A/2, such that \(hf = \sqrt {{J^2} + {{\left( {A{\rm{/}}2} \right)}^2}} \), where h is the Planck constant29. We estimate a residual exchange of J/h = 27 MHz for this detuning from numeric fits to the frequency dependence on detuning (described below). The inset shows that this frequency is very stable over time. Such behavior differs from GaAs systems, for which dynamic nuclear polarization must be used to generate and maintain a particular ΔB z of similar magnitude45. The magnitude and stability of f provides a strong indication that the rotations are driven by a single 31P. A small and relatively constant frequency drift of around 0.8 MHz is observed over a period of 3.5 h which is consistent with the drift in the electrostatics of the device through the experimentally measured dJ/d\(\epsilon \) relation. Additionally, the observed linewidth is less than natural silicon, which has linewidths greater than 8 MHz for single donors32 and is qualitatively consistent with an enriched 28Si background. Noise in J is believed to presently limit the linewidth, discussed below in terms of \(T_2^*\).
Characterization of exchange interaction
The detuning dependence of the ST rotations reveals additional information about this QD-D system. In Fig. 3a, we plot the triplet return probability against both detuning and manipulation time. As the detuning gets closer to zero, the frequency of the exchange rotations increases, as shown in Fig. 3c. This is consistent with a ST model where the exchange energy J between the S and T 0 states is not negligible and drives rotations around a tilted axis in the qubit Bloch sphere. To better understand the exact shape of the oscillations of Fig. 3a, we simulate the quantum dynamics of the system using a master equation approach and time-dependent controls. We describe the system using the basis states {(4, 0)S, (4, 0)T 0, (3, 1)S, (3, 1)T 0}, similarly to previous treatments such as Taylor et al.29. The details of the model are given in the Supplementary Note 7. The numerical simulation results are shown in Fig. 3b. The phase and shape of the oscillations is very well reproduced; however, the mechanisms limiting the visibility are numerous and detailed in the Supplementary Note 8. At the moment, we think that addressing the various causes could ultimately produce results on-a-par or even better than state-of-the-art ST qubits. The key fitting parameters of the model are the triplet tunnel coupling t T, singlet tunnel coupling t S, and hyperfine interaction A. We can determine these parameters using a fit to the data of Fig. 3c, knowing that hf equals the energy gap between the S and T 0 states. We find t S = 19 μeV, t T = 31 μeV and A/2h = 50 MHz. Shifts in A of this magnitude relative to the bulk value (of 58.5 MHz, ref. 32) have been reported in single donor electron spin resonance (ESR) experiments4 and have been attributed to Stark shifts of the contact hyperfine interaction due to the large electric fields in the vicinity of the neighboring QD. The measured value in this work is both consistent with a shallow phosphorus donor and is inconsistent with likely alternatives, such as arsenic. Following the fit procedure, we can extract J(\(\epsilon \)) by subtracting the A/2 contribution. The result is shown in Fig. 3c.
Discussion
Decoherence of MOS QDs33 and single donors4 has been characterized in separate systems, but the charge noise and magnetic noise properties of strongly hybridized QD-D systems are not well established. Our system provides a unique platform to study these important properties in an effective two-electron case where entanglement is delocalized in the form of a spatially separated singlet or triplet. We measure long time traces and plot the visibility of the oscillations vs. manipulation time t in Fig. 4a. The data and method are presented in the Supplementary Note 9. We then fit the decay using a slow detuning noise model that produces a Gaussian decay of the visibility \(v = {v_0}\,{\rm{exp}}\left[ { - {{\left( {t{\rm{/}}T_2^*} \right)}^2}} \right]\), where v 0 is an arbitrary initial visibility. We find that \(T_2^*\) depends on the detuning (Fig. 4b). To understand this dependence, we use a charge noise model represented by \(\epsilon \) noise with a characteristic standard deviation \({\sigma _\epsilon }\) and producing decoherence through J(\(\epsilon \))46. Details about the model are given in the Supplementary Note 10. We find that \({\sigma _\epsilon }\) = 9 μeV is consistent with the observed \(T_2^*\). In this model, we neglect magnetic noise that could be caused by residual 29Si or other sources. Our observations are consistent with \(T_2^*\) being limited by charge noise, a mechanism that is expected to play an important role when J varies as a function of \(\epsilon \) 46. We note that 2\({\sigma _\epsilon }\) is approximately the electronic temperature k B T e. The noise magnitude has previously been correlated with the electronic temperature46. We further tabulate noise magnitudes in a variety of material systems, like GaAs/AlGaAs heterostructures47, Si/SiGe heterostructures14, 48 and MOS (this work), and show the results in Fig. 4c.
In summary, we have demonstrated coherent coupling between the electrons of two very different qubit systems: a donor atom (natural atom) and a MOS quantum dot (artificial atom49). The coherent rotations between the singlet and triplet are driven by a nuclear spin qubit through the contact hyperfine interaction, and produce 10 ns X(π) rotations with a \(T_2^*\) of 1.3 ± 0.7 μs, thus allowing over 100 rotations within the coherence time. A charge noise magnitude of 9 μeV fits the stationary noise model and is a characterization of the MOS interface noise properties, which are found to be of similar magnitude to other common QD material systems. Assuming this model, the \(T_2^*\) could possibly be improved by a factor 10 or more by operating at larger detunings where the exchange is negligible, hence taking full advantage of isotopically pure silicon. Our experiments demonstrate the feasibility of using the QD-D system as a compact ST qubit with no additional micromagnets30, 31 or QDs (as in all-exchange qubits14, 50, 51), and avoid the decoherence mechanisms associated with GaAs or Si host nuclear species28, 52. More sophisticated ST qubit control approaches53, 54 and optimized preparation/readout parameters will likely increase the visibility and reduce errors of future two-axis QD-D qubit demonstrations. To further speed up the operations compared to the coherence time, it could be possible to use other donor species that have stronger contact hyperfine strengths. Beyond individual ST qubits, this work opens-up compelling possibilities. One such example is the coupling of donor-based qubits without atomic precision placement through, for example, electrostatic coupling between ST qubits19, 20, 37. Another example is all-electrical nuclear spin readout21 and electric/nuclear magnetic resonance control without high magnetic fields or ESR, thus introducing a nuclear spin qubit as an additional resource.
Data availability
The authors declare that the data supporting the findings of this study are available within the paper and its Supplementary Information files. Additional data (e.g. source data for figures) are available from the corresponding author upon reasonable request.
References
Tyryshkin, A. M. et al. Electron spin coherence exceeding seconds in high-purity silicon. Nat. Mater. 11, 143–147 (2012).
Witzel, W. M., Carroll, M. S., Morello, A., Cywiński, L. & Das Sarma, S. Electron spin decoherence in isotope-enriched silicon. Phys. Rev. Lett. 105, 187602 (2010).
Zwanenburg, F. A. et al. Silicon quantum electronics. Rev. Mod. Phys. 85, 961–1019 (2013).
Muhonen, J. T. et al. Storing quantum information for 30 seconds in a nanoelectronic device. Nat. Nano 9, 986–991 (2014).
Tracy, L. A. et al. Single shot spin readout using a cryogenic high-electron-mobility transistor amplifier at sub-kelvin temperatures. Appl. Phys. Lett. 108, 063101 (2016).
Pla, J. J. et al. High-fidelity readout and control of a nuclear spin qubit in silicon. Nature 496, 334–338 (2013).
Kane, B. E. A silicon-based nuclear spin quantum computer. Nature 393, 133–137 (1998).
Bielejec, E., Seamons, J. A. & Carroll, M. S. Single ion implantation for single donor devices using Geiger mode detectors. Nanotechnology 21, 085201 (2010).
Weber, B. et al. Spin blockade and exchange in coulomb-confined silicon double quantum dots. Nat. Nano 9, 430–435 (2014).
Dehollain, J. P. et al. Single-shot readout and relaxation of singlet and triplet states in exchange-coupled 31P electron spins in silicon. Phys. Rev. Lett. 112, 236801 (2014).
Singh, M. et al. Electrostatically defined silicon quantum dots with counted antimony donor implants. Appl. Phys. Lett. 108, 062101 (2016).
Gamble, J. K. et al. Multivalley effective mass theory simulation of donors in silicon. Phys. Rev. B 91, 235318 (2015).
Veldhorst, M. et al. A two-qubit logic gate in silicon. Nature 526, 410–414 (2015).
Eng, K. et al. Isotopically enhanced triple-quantum-dot qubit. Science Advances 1, e1500214 (2015).
Kim, D. et al. Quantum control and process tomography of a semiconductor quantum dot hybrid qubit. Nature 511, 70–74 (2014).
Takeda, K. et al. A fault-tolerant addressable spin qubit in a natural silicon quantum dot. Science Advances 2, e1600694 (2016).
Nowack, K. C. et al. Single-shot correlations and two-qubit gate of solid-state spins. Science 333, 1269–1272 (2011).
Brunner, R. et al. Two-qubit gate of combined single-spin rotation and interdot spin exchange in a double quantum dot. Phys. Rev. Lett. 107, 146801 (2011).
Shulman, M. D. et al. Demonstration of entanglement of electrostatically coupled singlet-triplet qubits. Science 336, 202–205 (2012).
Nichol, J. M. et al. High-fidelity entangling gate for double-quantum-dot spin qubits. npj Quantum Information 3, 3 (2017).
Kane, B. E. et al. Single-spin measurement using single-electron transistors to probe two-electron systems. Phys. Rev. B 61, 2961–2972 (2000).
Skinner, A. J., Davenport, M. E. & Kane, B. E. Hydrogenic spin quantum computing in silicon: A digital approach. Phys. Rev. Lett. 90, 087901 (2003).
Srinivasa, V., Xu, H. & Taylor, J. M. Tunable spin-qubit coupling mediated by a multielectron quantum dot. Phys. Rev. Lett. 114, 226803 (2015).
Pica, G., Lovett, B. W., Bhatt, R. N., Schenkel, T. & Lyon, S. A. Surface code architecture for donors and dots in silicon with imprecise and nonuniform qubit couplings. Phys. Rev. B 93, 035306 (2016).
Tosi, G. et al. Silicon quantum processor with robust long-distance qubit couplings. Nat. Commun. 8, 450 (2017).
Urdampilleta, M. et al. Charge dynamics and spin blockade in a hybrid double quantum dot in silicon. Phys. Rev. X 5, 031024 (2015).
Levy, J. Universal quantum computation with spin-1/2 pairs and Heisenberg exchange. Phys. Rev. Lett. 89, 147902 (2002).
Petta, J. R. et al. Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180–2184 (2005).
Taylor, J. M. et al. Relaxation, dephasing, and quantum control of electron spins in double quantum dots. Phys. Rev. B 76, 035315 (2007).
Pioro-Ladrière, M. et al. Electrically driven single-electron spin resonance in a slanting Zeeman field. Nat. Phys. 4, 776–779 (2008).
Wu, X. et al. Two-axis control of a singlet-triplet qubit with an integrated micromagnet. Proceedings of the National Academy of Sciences 111, 11938–11942 (2014).
Pla, J. J. et al. A single-atom electron spin qubit in silicon. Nature 489, 541–545 (2012).
Veldhorst, M. et al. An addressable quantum dot qubit with fault-tolerant control-fidelity. Nat. Nano 9, 981–985 (2014).
Medford, J. et al. Self-consistent measurement and state tomography of an exchange-only spin qubit. Nat. Nano 8, 654–659 (2013).
Vrijen, R. et al. Electron-spin-resonance transistors for quantum computing in silicon-germanium heterostructures. Phys. Rev. A. 62, 012306 (2000).
Calderón, M. J., Saraiva, A., Koiller, B. & Sarma, S. D. Quantum control and manipulation of donor electrons in Si-based quantum computing. J. Appl. Phys. 105, 122410 (2009).
Levy, J. E. et al. Implications of electronics constraints for solid-state quantum error correction and quantum circuit failure probability. New. J. Phys. 13, 083021 (2011).
Tracy, L. A. et al. Electron spin lifetime of a single antimony donor in silicon. Appl. Phys. Lett. 103, 143115 (2013).
Nielsen, E., Barnes, E., Kestner, J. P. & Das Sarma, S. Six-electron semiconductor double quantum dot qubits. Phys. Rev. B 88, 195131 (2013).
Higginbotham, A. P., Kuemmeth, F., Hanson, M. P., Gossard, A. C. & Marcus, C. M. Coherent operations and screening in multielectron spin qubits. Phys. Rev. Lett. 112, 026801 (2014).
Johnson, A. C. et al. Triplet-singlet spin relaxation via nuclei in a double quantum dot. Nature 435, 925–928 (2005).
Gamble, J. K. et al. Valley splitting of single-electron Si MOS quantum dots. Appl. Phys. Lett. 109, 253101 (2016).
Kawakami, E. et al. Electrical control of a long-lived spin qubit in a Si/SiGe quantum dot. Nat. Nano 9, 666–670 (2014).
Nichol, J. M. et al. Quenching of dynamic nuclear polarization by spin-orbit coupling in GaAs quantum dots. Nat. Commun. 6, 7682 (2015).
Barthel, C. et al. Relaxation and readout visibility of a singlet-triplet qubit in an Overhauser field gradient. Phys. Rev. B 85, 035306 (2012).
Dial, O. E. et al. Charge noise spectroscopy using coherent exchange oscillations in a singlet-triplet qubit. Phys. Rev. Lett. 110, 146804 (2013).
Petersson, K. D., Petta, J. R., Lu, H. & Gossard, A. C. Quantum coherence in a one-electron semiconductor charge qubit. Phys. Rev. Lett. 105, 246804 (2010).
Shi, Z. et al. Coherent quantum oscillations and echo measurements of a Si charge qubit. Phys. Rev. B 88, 075416 (2013).
Kastner, M. A. Artificial atoms. Phys. Today 46, 24–31 (1993).
Gaudreau, L. et al. Coherent control of three-spin states in a triple quantum dot. Nat. Phys. 8, 54–58 (2012).
Medford, J. et al. Quantum-dot-based resonant exchange qubit. Phys. Rev. Lett. 111, 050501 (2013).
Maune, B. M. et al. Coherent singlet-triplet oscillations in a silicon-based double quantum dot. Nature 481, 344–347 (2012).
Shulman, M. D. et al. Suppressing qubit dephasing using real-time Hamiltonian estimation. Nat. Commun. 5, 233101 (2014).
Cerfontaine, P., Botzem, T., DiVincenzo, D. P. & Bluhm, H. High-fidelity single-qubit gates for two-electron spin qubits in GaAs. Phys. Rev. Lett. 113, 150501 (2014).
Acknowledgements
The authors would like to thank Erik Nielsen, Andrew D. Baczewski, Matthew J. Curry and Stephen Carr for valuable help and discussions regarding this work; B. Silva for support on device fabrication and room temperature measurements; and Benjamin D'Anjou and William A. Coish for discussions on readout fidelity. This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. DOE’s National Nuclear Security Administration under contract DE-NA0003525.
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P.H.-C. and M.S.C. designed the experiments. P.H.-C. performed the central measurements and analysis presented in this work. M.R. performed supporting measurements on similar “control” samples that establish repeatability of many observations in this work. N.T.J., P.H.-C., M.R. and J.K.G. modelled key elements of the device structure providing critical insights. P.H.-C., M.S.C., N.T.J. and M.P.-L. analyzed and discussed central results throughout the project, including designing models for observations. J.D., T.P., G.A.T.E. and M.S.C. designed process flow, fabricated devices and designed/characterized the 28Si material growth for this work. J.R.W. provided critical nanolithography steps. M.L. supplied critical laboratory set-up for the work. M.S.C. supervised combined effort including coordinating fab and identifying modelling needs for experimental path. P.H.-C., M.S.C. and M.P.-L. wrote the manuscript with input from all co-authors.
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Harvey-Collard, P., Jacobson, N., Rudolph, M. et al. Coherent coupling between a quantum dot and a donor in silicon. Nat Commun 8, 1029 (2017). https://doi.org/10.1038/s41467-017-01113-2
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DOI: https://doi.org/10.1038/s41467-017-01113-2
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