Nuclear spins are highly coherent quantum objects. In large ensembles, their control and detection via magnetic resonance is widely exploited, e.g. in chemistry, medicine, materials science and mining. Nuclear spins also featured in early ideas [1] and demonstrations [2] of quantum information processing. Scaling up these ideas requires controlling individual nuclei, which can be detected when coupled to an electron [3, 4, 5]. However, the need to address the nuclei via oscillating magnetic fields complicates their integration in multispin nanoscale devices, because the field cannot be localized or screened. Control via electric fields would resolve this problem, but previous methods [6, 7, 8] relied upon transducing electric signals into magnetic fields via the electron-nuclear hyperfine interaction, which severely affects the nuclear coherence. Here we demonstrate the coherent quantum control of a single antimony (spin-7/2) nucleus, using localized electric fields produced within a silicon nanoelectronic device. The method exploits an idea first proposed in 1961 [9] but never realized experimentally with a single nucleus. Our results are quantitatively supported by a microscopic theoretical model that reveals how the purely electrical modulation of the nuclear electric quadrupole interaction, in the presence of lat- † To whom correspondence should be addressed;
to new applications arising from the control of single charges and spins on individual dopants in silicon. Promi sing applications are where the donors function as quantum bits (qubits). How ever, configuring materials with arrays of single donor qubits in the solid state is a formidable challenge. It has been proposed that noisy, intermediatescale quantum (NISQ) [1] devices with ≈50-100 qubits can surpass classical supercom puters in executing some specific algo rithms. [2] Even for NISQ devices, the error budgets for the physical qubits are strict, requiring errors well below 1% in order to achieve sufficient circuit depths. Beyond NISQ, errorcorrected, universal quantum processors of the kind necessary to run Shor's factoring algorithm on a 2000 bit classical key will require upwards of 4000 logical qubits. Using a 2D surface code architecture, this would translate to about 200 mil lion physical qubits with present error rates of around 0.1%. [3] Future devices with lower error rates [4] will reduce the required number of physical qubits. The surface code is also able to tolerate 5-10% physically nonfunctional (absent or faulty) qubits in the architecture. [5,6] Silicon chips containing arrays of single dopant atoms can be the material of choice for classical and quantum devices that exploit single donor spins. For example, group-V donors implanted in isotopically purified 28 Si crystals are attractive for large-scale quantum computers. Useful attributes include long nuclear and electron spin lifetimes of 31 P, hyperfine clock transitions in 209 Bi or electrically controllable 123 Sb nuclear spins. Promising architectures require the ability to fabricate arrays of individual near-surface dopant atoms with high yield. Here, an on-chip detector electrode system with 70 eV root-mean-square noise (≈20 electrons) is employed to demonstrate near-room-temperature implantation of single 14 keV 31 P + ions. The physics model for the ion-solid interaction shows an unprecedented upper-bound single-ion-detection confidence of 99.85 ± 0.02% for near-surface implants. As a result, the practical controlled silicon doping yield is limited by materials engineering factors including surface gate oxides in which detected ions may stop. For a device with 6 nm gate oxide and 14 keV 31 P + implants, a yield limit of 98.1% is demonstrated. Thinner gate oxides allow this limit to converge to the upper-bound. Deterministic single-ion implantation can therefore be a viable materials engineering strategy for scalable dopant architectures in silicon devices.The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adma.202103235.
Most classical dynamical systems are chaotic. The trajectories of two identical systems prepared in infinitesimally different initial conditions diverge exponentially with time. Quantum systems, instead, exhibit quasi-periodicity due to their discrete spectrum. Nonetheless, the dynamics of quantum systems whose classical counterparts are chaotic are expected to show some features that resemble chaotic motion. Among the many controversial aspects of the quantum-classical boundary, the emergence of chaos remains among the least experimentally verified. Time-resolved observations of quantum chaotic dynamics are particularly rare, and as yet unachieved in a single particle, where the subtle interplay between chaos and quantum measurement could be explored at its deepest levels. We present here a realistic proposal to construct a chaotic driven top from the nuclear spin of a single donor atom in silicon, in the presence of a nuclear quadrupole interaction. This system is exquisitely measurable and controllable, and possesses extremely long intrinsic quantum coherence times, allowing for the observation of subtle dynamical behavior over extended periods. We show that signatures of chaos are expected to arise for experimentally realizable parameters of the system, allowing the study of the relation between quantum decoherence and classical chaos, and the observation of dynamical tunneling.
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