Engineering Spin-Orbit Interactions in Silicon Qubits at the Atomic-Scale.

Spin-orbit interactions arise whenever the bulk inversion symmetry and/or structural inversion symmetry of a crystal is broken providing a bridge between a qubit's spin and orbital degree of freedom. While strong interactions can facilitate fast qubit operations by all-electrical control, they also provide a mechanism to couple charge noise thereby limiting qubit lifetimes. Previously believed to be negligible in bulk silicon, recent silicon nano-electronic devices have shown larger than bulk spin-orbit coupling strengths from Dresselhaus and Rashba couplings. Here, it is shown that with precision placement of phosphorus atoms in silicon along the [110] direction (without inversion symmetry) or [111] direction (with inversion symmetry), a wide range of Dresselhaus and Rashba coupling strength can be achieved from zero to 1113 × 10-13eV-cm. It is shown that with precision placement of phosphorus atoms, the local symmetry (C2v, D2d, and D3d) can be changed to engineer spin-orbit interactions. Since spin-orbit interactions affect both qubit operation and lifetimes, understanding their impact is essential for quantum processor design.

Atomic Engineering of Molecular Qubits for High-Speed, High-Fidelity Single Qubit Gates.

Universal quantum computing requires fast single- and two-qubit gates with individual qubit addressability to minimize decoherence errors during processor operation. Electron spin qubits using individual phosphorus donor atoms in silicon have demonstrated long coherence times with high fidelities, providing an attractive platform for scalable quantum computing. While individual qubit addressability has been demonstrated by controlling the hyperfine interaction between the electron and nuclear wave function in a global magnetic field, the small hyperfine Stark coefficient of 0.34 MHz/MV m-1 achieved to date has limited the speed of single quantum gates to ∼42 µs to avoid rotating neighboring qubits due to power broadening from the antenna. The use of molecular 2P qubits with more than one donor atom has not only demonstrated fast (0.8 ns) two-qubit SWAP gates and long spin relaxation times of ∼30 s but provides an alternate way to achieve high selectivity of the qubit resonance frequency. Here, we show in two different devices that by placing the donors with comparable interatomic spacings (∼0.8 nm) but along different crystallographic axes, either the [110] or [310] orientations using STM lithography, we can engineer the hyperfine Stark shift from 1 MHz/MV m-1 to 11.2 MHz/MV m-1, respectively, a factor of 10 difference. NEMO atomistic calculations show that larger hyperfine Stark coefficients of up to ∼70 MHz/MV m-1 can be achieved within 2P molecules by placing the donors ≥5 nm apart. When combined with Gaussian pulse shaping, we show that fast single qubit gates with 2π rotation times of 10 ns and ∼99% fidelity single qubit operations are feasible without affecting neighboring qubits. By increasing the single qubit gate time to ∼550 ns, two orders of magnitude faster than previously measured, our simulations confirm that >99.99% single qubit control fidelities are achievable.

The Use of Exchange Coupled Atom Qubits as Atomic-Scale Magnetic Field Sensors.

Phosphorus atoms in silicon offer a rich quantum computing platform where both nuclear and electron spins can be used to store and process quantum information. While individual control of electron and nuclear spins has been demonstrated, the interplay between them during qubit operations has been largely unexplored. This study investigates the use of exchange-based operation between donor bound electron spins to probe the local magnetic fields experienced by the qubits with exquisite precision at the atomic scale. To achieve this, coherent exchange oscillations are performed between two electron spin qubits, where the left and right qubits are hosted by three and two phosphorus donors, respectively. The frequency spectrum of exchange oscillations shows quantized changes in the local magnetic fields at the qubit sites, corresponding to the different hyperfine coupling between the electron and each of the qubit-hosting nuclear spins. This ability to sense the hyperfine fields of individual nuclear spins using the exchange interaction constitutes a unique metrology technique, which reveals the exact crystallographic arrangements of the phosphorus atoms in the silicon crystal for each qubit. The detailed knowledge obtained of the local magnetic environment can then be used to engineer hyperfine fields in multi-donor qubits for high-fidelity two-qubit gates.

Monolithic Three-Dimensional Tuning of an Atomically Defined Silicon Tunnel Junction.

A requirement for quantum information processors is the in situ tunability of the tunnel rates and the exchange interaction energy within the device. The large energy level separation for atom qubits in silicon is well suited for qubit operation but limits device tunability using in-plane gate architectures, requiring vertically separated top-gates to control tunnelling within the device. In this paper, we address control of the simplest tunnelling device in Si:P, the tunnel junction. Here we demonstrate that we can tune its conductance by using a vertically separated top-gate aligned with ±5 nm precision to the junction. We show that a monolithic 3D epitaxial top-gate increases the capacitive coupling by a factor of 3 compared to in-plane gates, resulting in a tunnel barrier height tunability of 0-186 meV. By combining multiple gated junctions in series we extend our monolithic 3D gating technology to implement nanoscale logic circuits including AND and OR gates.

Coherent control of a donor-molecule electron spin qubit in silicon.

Donor spins in silicon provide a promising material platform for large scale quantum computing. Excellent electron spin coherence times of [Formula: see text] µs with fidelities of 99.9% have been demonstrated for isolated phosphorus donors in isotopically pure 28Si, where donors are local-area-implanted in a nanoscale MOS device. Despite robust single qubit gates, realising two-qubit exchange gates using this technique is challenging due to the statistical nature of the dopant implant and placement process. In parallel a precision scanning probe lithography route has been developed to place single donors and donor molecules on one atomic plane of silicon with high accuracy aligned to heavily phosphorus doped silicon in-plane gates. Recent results using this technique have demonstrated a fast (0.8 ns) two-qubit gate with two P donor molecules placed 13 nm apart in natSi. In this paper we demonstrate a single qubit gate with coherent oscillations of the electron spin on a P donor molecule in natSi patterned by scanning tunneling microscope (STM) lithography. The electron spin exhibits excellent coherence properties, with a [Formula: see text] decoherence time of 298 ± 30 µs, and [Formula: see text] dephasing time of 295 ± 23 ns.

Spin read-out in atomic qubits in an all-epitaxial three-dimensional transistor.

The realization of the surface code for topological error correction is an essential step towards a universal quantum computer1-3. For single-atom qubits in silicon4-7, the need to control and read out qubits synchronously and in parallel requires the formation of a two-dimensional array of qubits with control electrodes patterned above and below this qubit layer. This vertical three-dimensional device architecture8 requires the ability to pattern dopants in multiple, vertically separated planes of the silicon crystal with nanometre precision interlayer alignment. Additionally, the dopants must not diffuse or segregate during the silicon encapsulation. Critical components of this architecture-such as nanowires9, single-atom transistors4 and single-electron transistors10-have been realized on one atomic plane by patterning phosphorus dopants in silicon using scanning tunnelling microscope hydrogen resist lithography11,12. Here, we extend this to three dimensions and demonstrate single-shot spin read-out with 97.9% measurement fidelity of a phosphorus dopant qubit within a vertically gated single-electron transistor with <5 nm interlayer alignment accuracy. Our strategy ensures the formation of a fully crystalline transistor using just two atomic species: phosphorus and silicon.

Addressable electron spin resonance using donors and donor molecules in silicon.

Phosphorus donor impurities in silicon are a promising candidate for solid-state quantum computing due to their exceptionally long coherence times and high fidelities. However, individual addressability of exchange coupled donors with separations ~15 nm is challenging. We show that by using atomic precision lithography, we can place a single P donor next to a 2P molecule 16 ± 1 nm apart and use their distinctive hyperfine coupling strengths to address qubits at vastly different resonance frequencies. In particular, the single donor yields two hyperfine peaks separated by 97 ± 2.5 MHz, in contrast to the donor molecule that exhibits three peaks separated by 262 ± 10 MHz. Atomistic tight-binding simulations confirm the large hyperfine interaction strength in the 2P molecule with an interdonor separation of ~0.7 nm, consistent with lithographic scanning tunneling microscopy images of the 2P site during device fabrication. We discuss the viability of using donor molecules for built-in addressability of electron spin qubits in silicon.

Suppressing Segregation in Highly Phosphorus Doped Silicon Monolayers.

Sharply defined dopant profiles and low resistivity are highly desired qualities in the microelectronic industry, and more recently, in the development of an all epitaxial Si:P based quantum computer. In this work, we use thin (monolayers thick) room temperature grown silicon layers, so-called locking layers, to limit dopant segregation in highly phosphorus doped silicon monolayers. We present secondary ion mass spectroscopy and atom probe tomography measurements that demonstrate the effectiveness of locking layers in suppressing P segregation. Scanning tunneling micrographs of the surface of the locking layer show that the growth is epitaxial, despite the low growth temperature, while magnetotransport measurements reveal a 50% decrease in the active carrier density. We show that applying a finely tuned rapid thermal anneal can restore the active carrier density to 3.4 × 10(14) cm(-2) while maintaining ultra sharp dopant profiles. In particular, 75% of the initial deposited P is confined in a layer with a full width at half-maximum thickness of 1.0 nm and a peak P concentration of 1.2 × 10(21) cm(-3) (2.5 atom %).

The Impact of Dopant Segregation on the Maximum Carrier Density in Si:P Multilayers.

Abrupt dopant profiles and low resistivity are highly sought after qualities in the silicon microelectronics industry and, more recently, in the development of an all epitaxial Si:P based quantum computer. If we increase the active carrier density in silicon to the point where the material becomes superconducting, while maintaining a low thermal budget, it will be possible to fabricate nanoscale superconducting devices using the highly successful technique of depassivation lithography. In this work, we investigate the dopant profile and activation in multiple high density Si:P δ-layers fabricated by stacking individual layers with intervening silicon growth. We determine that dopant activation is ultimately limited by the formation of P-P dimers due to the segregation of dopants between multilayers. By increasing the encapsulation thickness between subsequent layers, thereby minimizing the formation of these deactivating defects, we are able to achieve an active carrier density of ns = 4.5 ×10(14) cm(-2) for a triple layer. The results of electrical characterization are combined with those of secondary ion mass spectroscopy to construct a model that accurately describes the impact of P segregation on the final active carrier density in Si:P multilayers. Our model predicts that a 3D active carrier density of 8.5 × 10(20) cm(-3) (1.7 atom %) can be achieved.

A comparison of the physical properties of four new generation flexible ureteroscopes: (de)flection, flow properties, torsion stiffness, and optical characteristics.

BACKGROUND AND PURPOSE: Several kinds of flexible ureteroscopes are in use for the removal of kidney stones. This study evaluated and compared the characteristics of four new-generation flexible ureteroscopes. MATERIALS AND METHODS: The flexible ureteroscopes studied were: the ACMI Dur-8 Elite, the Storz Flex-X2 the Olympus XURF-P5, and the Wolf 7325.076. Measured properties included (de)flection, instrument insertion, flow properties, torsion stiffness, and optical characteristics. Active tip deflection and irrigation flow rates with and without various endoscopic tools were assessed. RESULTS: All ureteroscopes score better on (de)flection with an empty working channel, compared with a channel when tools are inserted (differences minimum 0.3 degrees--maximum 80.6 degrees). The Olympus XURF-P5 is the only ureteroscope with passive (de)flection capability, whereas the ACMI DUR-8 Elite is the only ureteroscope that has a secondary active (de)flection capability. The Storz Flex-X2 and the Wolf 7325.076 ureteroscopes show nearly identical best deflection capabilities with and without tools inserted in the working channel. The longest (Olympus XURF-P5, 70 cm) and shortest (ACMI DUR-8 Elite, 64 cm) ureteroscopes have, respectively, the lowest and highest flow rates. Best optical quality is offered by the Olympus XURF-P5 and Wolf 7325.076 ureteroscopes, which have low optical distortion (-9.7; -7.7%), high resolving power (17.95; 16.00 line pairs per millimeter), and a large field of view (62.9; 63.2 degrees). The Storz Flex-X2 and Wolf 7325.076 ureteroscopes have lowest torsion stiffness. CONCLUSIONS: The ex vivo evaluation of the deflection capabilities, passage of instruments, flow properties, torsion stiffness, and optical characteristics yielded quantitative measures of the in vivo performance capabilities of four new-generation flexible ureteroscopes. New ureteroscopes should be subjected to this or similar evaluation and comparison. Only in this way can the urologist make an informed and objective decision regarding appropriate instrument choice.