Analysis and Geometric Optimization of Single Electron Transistors for Read-Out in Solid-State Quantum Computing

The single electron transistor (SET) offers unparalled opportunities as a nano-scale electrometer, capable of measuring sub-electron charge variations. SETs have been proposed for read-out schema in solid-state quantum computing where quantum information processing outcomes depend on the location of a single electron on nearby quantum dots. In this paper we investigate various geometries of a SET in order to maximize the device's sensitivity to charge transfer between quantum dots. Through the use of finite element modeling we model the materials and geometries of an Al/Al2O3 SET measuring the state of quantum dots in the Si substrate beneath. The investigation is motivated by the quest to build a scalable quantum computer, though the methodology used is primarily that of circuit theory. As such we provide useful techniques for any electronic device operating at the classical/quantum interface.Comment: 13 pages, 17 figure

Development of outbred CD1 mouse colonies with distinct standardized gut microbiota profiles for use in complex microbiota targeted studies.

Studies indicate that the gut microbiota (GM) can significantly influence both local and systemic host physiologic processes. With rising concern for optimization of experimental reproducibility and translatability, it is essential to consider the GM in study design. However, GM profiles can vary between rodent producers making consistency between models challenging. To circumvent this, we developed outbred CD1 mouse colonies with stable, complex GM profiles that can be used as donors for a variety of GM transfer techniques including rederivation, co-housing, cross-foster, and fecal microbiota transfer (FMT). CD1 embryos were surgically transferred into CD1 or C57BL/6 surrogate dams that varied by GM composition and complexity to establish four separate mouse colonies harboring GM profiles representative of contemporary mouse producers. Using targeted 16S rRNA amplicon sequencing, subsequent female offspring were found to have similar GM profiles to surrogate dams. Furthermore, breeding colonies of CD1 mice with distinct GM profiles were maintained for nine generations, demonstrating GM stability within these colonies. To confirm GM stability, we shipped cohorts of these four colonies to collaborating institutions and found no significant variation in GM composition. These mice are an invaluable experimental resource that can be used to investigate GM effects on mouse model phenotype

Analytic Solution for the Ground State Energy of the Extensive Many-Body Problem

A closed form expression for the ground state energy density of the general extensive many-body problem is given in terms of the Lanczos tri-diagonal form of the Hamiltonian. Given the general expressions of the diagonal and off-diagonal elements of the Hamiltonian Lanczos matrix, $\alpha_n(N)$ and $\beta_n(N)$, asymptotic forms $\alpha(z)$ and $\beta(z)$ can be defined in terms of a new parameter $z\equiv n/N$ ($n$ is the Lanczos iteration and $N$ is the size of the system). By application of theorems on the zeros of orthogonal polynomials we find the ground-state energy density in the bulk limit to be given in general by ${\cal E}_0 = {\rm inf}\,\left[\alpha(z) - 2\,\beta(z)\right]$.Comment: 10 pages REVTex3.0, 3 PS figure

Chopping a Chebyshev series

Chebfun and related software projects for numerical computing with functions are based on the idea that at each step of a computation, a function f(x) defined on an interval [a, b] is “rounded” to a prescribed precision by constructing a Chebyshev series and chopping it at an appropriate point. Designing a chopping algorithm with the right properties proves to be a surprisingly complex and interesting problem. We describe the chopping algorithm introduced in Chebfun Version 5.3 in 2015 after\ud many years of discussion and the considerations that led to this design

Ground-layer wavefront reconstruction from multiple natural guide stars

Observational tests of ground layer wavefront recovery have been made in open loop using a constellation of four natural guide stars at the 1.55 m Kuiper telescope in Arizona. Such tests explore the effectiveness of wide-field seeing improvement by correction of low-lying atmospheric turbulence with ground-layer adaptive optics (GLAO). The wavefronts from the four stars were measured simultaneously on a Shack-Hartmann wavefront sensor (WFS). The WFS placed a 5 x 5 array of square subapertures across the pupil of the telescope, allowing for wavefront reconstruction up to the fifth radial Zernike order. We find that the wavefront aberration in each star can be roughly halved by subtracting the average of the wavefronts from the other three stars. Wavefront correction on this basis leads to a reduction in width of the seeing-limited stellar image by up to a factor of 3, with image sharpening effective from the visible to near infrared wavelengths over a field of at least 2 arc minutes. We conclude that GLAO correction will be a valuable tool that can increase resolution and spectrographic throughput across a broad range of seeing-limited observations.Comment: 25 pages, 8 figures, to be published in Astrophys.

Computation of 2D Stokes flows via lightning and AAA rational approximation

Low Reynolds number fluid flows are governed by the Stokes equations. In two dimensions, Stokes flows can be described by two analytic functions, known as Goursat functions. Brubeck and Trefethen (2022) recently introduced a lightning Stokes solver that uses rational functions to approximate the Goursat functions in polygonal domains. In this paper, we present a solver for computing 2D Stokes flows in domains with smooth boundaries and multiply-connected domains using lightning and AAA rational approximation (Nakatsukasa et al., 2018). This leads to a new rational approximation algorithm "LARS" that is suitable for computing many bounded 2D Stokes flow problems. After validating our solver against known analytical solutions, we solve a variety of 2D Stokes flow problems with physical and engineering applications. The computations take less than a second and give solutions with at least 6-digit accuracy