High Precision Quantum Control of Single Donor Spins in Silicon

Rahman, Rajib; Wellard, Cameron; Bradbury, F. R.; Prada, Marta; Cole, Jared H.; Klimeck, Gerhard; Hollenberg, Lloyd C. L.

doi:10.1103/physrevlett.99.036403

Cited by 119 publications

(154 citation statements)

References 29 publications

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“…The strength of the hyperfine coupling between the electron and the two P nuclear spins (A i (E)) (ref. 19), as well as the electronic g factor (g e (E)) (ref. 20), has been calculated within the tight-binding formalism (see Methods).…”

Section: Discussionmentioning

confidence: 99%

“…The strength of hyperfine coupling, A, is proportional to the probability density j Cðr i Þ j 2 of the electron wavefunction at the site of the donor atom r i (ref. 19). An applied electric field (E) distorts the wavefunction and, therefore, modifies A.…”

Section: Methodsmentioning

confidence: 99%

“…To calculate the E dependence of A, the electron wavefunctions were first obtained from the semi-empirical tight-binding method in the Nanoelectronic Modeling tool (NEMO-3D), as described in ref. 19. In addition to the contact hyperfine components A, we also calculate the anisotropic components of the full hyperfine tensor B (as described in ref.…”

Section: Methodsmentioning

confidence: 99%

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Spin readout and addressability of phosphorus-donor clusters in silicon

et al. 2013

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The spin states of an electron bound to a single phosphorus donor in silicon show remarkably long coherence and relaxation times, which makes them promising building blocks for the realization of a solid-state quantum computer. Here we demonstrate, by high-fidelity (93%) electrical spin readout, that a long relaxation time T 1 of about 2 s, at B ¼ 1.2 T and TE100 mK, is also characteristic of electronic spin states associated with a cluster of few phosphorus donors, suggesting their suitability as hosts for spin qubits. Owing to the difference in the hyperfine coupling, electronic spin transitions of such clusters can be sufficiently distinct from those of a single phosphorus donor. Our atomistic tight-binding calculations reveal that when neighbouring qubits are hosted by a single phosphorus atom and a cluster of two phosphorus donors, the difference in their electron spin resonance frequencies allows qubit rotations with error rates E10 À 4 . These results provide a new approach to achieving individual qubit addressability.

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Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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Spin readout and addressability of phosphorus-donor clusters in silicon

et al. 2013

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“…The tight-binding Hamiltonian of 1.4 million silicon atoms with a boron acceptor was represented with a 20-orbital sp3d5s* basis per atom including nearestneighbor and spin-orbit interactions. An acceptor was represented by a Coulomb potential of a negative charge screened by the dielectric constant of Si and subjected to an onsite cutoff potential U 0 [20]. The model provides an accurate solution for the single-hole eigenstates of a bulk acceptor, and an acceptor near an interface.…”

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confidence: 99%

Interface-induced heavy-hole/light-hole splitting of acceptors in silicon

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Salfi

Rahman

et al. 2015

Applied Physics Letters

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The energy spectrum of spin-orbit coupled states of individual sub-surface boron acceptor dopants in silicon have been investigated using scanning tunneling spectroscopy (STS) at cryogenic temperatures. The spatially resolved tunnel spectra show two resonances which we ascribe to the heavyand light-hole Kramers doublets. This type of broken degeneracy has recently been argued to be advantageous for the lifetime of acceptor-based qubits [Phys. Rev. B 88 064308 (2013)]. The depth dependent energy splitting between the heavy-and light-hole Kramers doublets is consistent with tight binding calculations, and is in excess of 1 meV for all acceptors within the experimentally accessible depth range (< 2 nm from the surface). These results will aid the development of tunable acceptor-based qubits in silicon with long coherence times and the possibility for electrical manipulation. Meanwhile, rapid progress in scanning tunnelling microscopy (STM) based lithography has paved the way towards atomically precise placement of dopant atoms [3]. While phosphorous donors in silicon remains among the most compelling candidates for dopant-based quantum computing to date, other impurity systems have recently drawn considerable attention. In particular, boron acceptors could provide a pathway towards electrically addressable spin-qubits via spin-orbit coupling [4] analogues to electrically driven spin manipulation in gate defined electron [5,6] and hole [7] quantum dots in III-V materials. Compared with other spin-orbit qubits, acceptors in silicon have several advantages: gates are not required for hole confinement and each qubit experiences the same confinement potential; furthermore the holespin decoherence, due to the nuclear spin bath, can be effectively eliminated by isotope purification of the silicon host.Unlike the ground state of donor-bound electrons in silicon, the acceptor-bound hole ground state is four-fold degenerate, reflecting the heavy-hole/light-hole degeneracy of the silicon valence band. Recent theoretical work has suggested the regime of long lifetimes for acceptors with a four-fold degenerate ground state is only accessible for small magnetic fields [4]. Interestingly, this work also suggests that symmetry breaking due to strain or electric fields could yield longer-lived qubits based on acceptor-bound holes at higher magnetic fields. The symmetry breaking perturbation of biaxial strain [4] renders the lowest two (qubit) levels within a Kramers degenerate pair, such that they do not directly couple to electric fields. Quantum confinement could provide a similar form of protection. In this Letter we demonstrate that the symmetry-reduction of a potential boundary renders the lowest two levels Kramers degenerate and heavy-hole like. Recent transport spectroscopy studies of an individual acceptor embedded in nano-scale transistors have shown that for acceptors ∼10 nm away from an interface the bulk-like four-fold degeneracy is maintained [8]. Here we demonstrate that the presence of a nearby interface (<2 nm) lift...

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“…This scaling method is also used in the literature to study the Stark shift of the HFS in Si:P devices [39,50] …”

Section: Donor Electron Wave Function Simulationsmentioning

confidence: 99%

A computational workflow for designing silicon donor qubits

et al. 2016

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Developing devices that can reliably and accurately demonstrate the principles of superposition and entanglement is an on-going challenge for the quantum computing community. Modeling and simulation offer attractive means of testing early device designs and establishing expectations for operational performance. However, the complex integrated material systems required by quantum device designs are not captured by any single existing computational modeling method. We examine the development and analysis of a multi-staged computational workflow that can be used to design and characterize silicon donor qubit systems with modeling and simulation. Our approach integrates quantum chemistry calculations with electrostatic field solvers to perform detailed simulations of a phosphorus dopant in silicon. We show how atomistic details can be synthesized into an operational model for the logical gates that define quantum computation in this particular technology. The resulting computational workflow realizes a design tool for silicon donor qubits that can help verify and validate current and nearterm experimental devices.

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High Precision Quantum Control of Single Donor Spins in Silicon

Cited by 119 publications

References 29 publications

Spin readout and addressability of phosphorus-donor clusters in silicon

Spin readout and addressability of phosphorus-donor clusters in silicon

Interface-induced heavy-hole/light-hole splitting of acceptors in silicon

A computational workflow for designing silicon donor qubits

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