Publications

Abstract not provided.

Abstract not provided.

Abstract not provided.

The attachment of dopant precursor molecules to depassivated areas of hydrogen-terminated silicon templated with a scanning tunneling microscope (STM) has been used to create electronic devices with sub-nanometer precision, typically for quantum physics demonstrations, and to dope silicon past the solid-solubility limit, with potential applications in microelectronics and plasmonics. However, this process, which we call atomic precision advanced manufacturing (APAM), currently lacks the throughput required to develop sophisticated applications because there is no proven scalable hydrogen lithography pathway. Here, we demonstrate and characterize an APAM device workflow where STM lithography has been replaced with photolithography. An ultraviolet laser is shown to locally heat silicon controllably above the temperature required for hydrogen depassivation. STM images indicate a narrow range of laser energy density where hydrogen has been depassivated, and the surface remains well-ordered. A model for photothermal heating of silicon predicts a local temperature which is consistent with atomic-scale STM images of the photo-patterned regions. Finally, a simple device made by exposing photo-depassivated silicon to phosphine is found to have a carrier density and mobility similar to that produced by similar devices patterned by STM.

A number of applications in basic science and technology would benefit from high-fidelity photon-number-resolving photodetectors. While some recent experimental progress has been made in this direction, the requirements for true photon number resolution are stringent, and no design currently exists that achieves this goal. Here we employ techniques from fundamental quantum optics to demonstrate that detectors composed of subwavelength elements interacting collectively with the photon field can achieve high-performance photon number resolution. We propose a new design that simultaneously achieves photon number resolution, high efficiency, low jitter, low dark counts, and high count rate. We discuss specific systems that satisfy the design requirements, pointing to the important role of nanoscale device elements.

Nuclear spins are highly coherent quantum objects. In large ensembles, their control and detection via magnetic resonance is widely exploited, for example, in chemistry, medicine, materials science and mining. Nuclear spins also featured in early proposals for solid-state quantum computers1 and demonstrations of quantum search2 and factoring3 algorithms. Scaling up such concepts requires controlling individual nuclei, which can be detected when coupled to an electron4–6. However, the need to address the nuclei via oscillating magnetic fields complicates their integration in multi-spin nanoscale devices, because the field cannot be localized or screened. Control via electric fields would resolve this problem, but previous methods7–9 relied on transducing electric signals into magnetic fields via the electron–nuclear hyperfine interaction, which severely affects nuclear coherence. Here we demonstrate the coherent quantum control of a single 123Sb (spin-7/2) nucleus using localized electric fields produced within a silicon nanoelectronic device. The method exploits an idea proposed in 196110 but not previously 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 results in coherent nuclear spin transitions that are uniquely addressable owing to lattice strain. The spin dephasing time, 0.1 seconds, is orders of magnitude longer than those obtained by methods that require a coupled electron spin to achieve electrical driving. These results show that high-spin quadrupolar nuclei could be deployed as chaotic models, strain sensors and hybrid spin-mechanical quantum systems using all-electrical controls. Integrating electrically controllable nuclei with quantum dots11,12 could pave the way to scalable, nuclear- and electron-spin-based quantum computers in silicon that operate without the need for oscillating magnetic fields.

Abstract not provided.

The fractional Laplacian in Rd, which we write as (−Δ)α/2 with α∈(0,2), has multiple equivalent characterizations. Moreover, in bounded domains, boundary conditions must be incorporated in these characterizations in mathematically distinct ways, and there is currently no consensus in the literature as to which definition of the fractional Laplacian in bounded domains is most appropriate for a given application. The Riesz (or integral) definition, for example, admits a nonlocal boundary condition, where the value of a function must be prescribed on the entire exterior of the domain in order to compute its fractional Laplacian. In contrast, the spectral definition requires only the standard local boundary condition. These differences, among others, lead us to ask the question: “What is the fractional Laplacian?” Beginning from first principles, we compare several commonly used definitions of the fractional Laplacian theoretically, through their stochastic interpretations as well as their analytical properties. Then, we present quantitative comparisons using a sample of state-of-the-art methods. We discuss recent advances on nonzero boundary conditions and present new methods to discretize such boundary value problems: radial basis function collocation (for the Riesz fractional Laplacian) and nonharmonic lifting (for the spectral fractional Laplacian). In our numerical studies, we aim to compare different definitions on bounded domains using a collection of benchmark problems. We consider the fractional Poisson equation with both zero and nonzero boundary conditions, where the fractional Laplacian is defined according to the Riesz definition, the spectral definition, the directional definition, and the horizon-based nonlocal definition. We verify the accuracy of the numerical methods used in the approximations for each operator, and we focus on identifying differences in the boundary behaviors of solutions to equations posed with these different definitions. Through our efforts, we aim to further engage the research community in open problems and assist practitioners in identifying the most appropriate definition and computational approach to use for their mathematical models in addressing anomalous transport in diverse applications.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.