Map to Majorana fermions in nanowires is revealed.

We propose a topological qubit in which braiding and readout are mediated by the 4π Majorana-Josephson effect. The braidonium device consists of three Majorana nanowires that come together to make a tri-junction. In order to control the superconducting phase differences at the tri-junction, the nanowires are enclosed in a ring made of a conventional superconductor. In order to perform initialization/readout, one of the nanowires is coupled to a fluxonium qubit through a topological Josephson junction. We analyze how flux-based control and readout protocols can be used to demonstrate braiding and qubit operation for realistic materials and circuit parameters.

We study the differential conductance for charge tunneling into a semiconductor wire--superconductor hybrid structure, which is actively investigated as a possible scheme for realizing topological superconductivity and Majorana zero modes. The calculations are done based on a tight-binding model of the heterostructure using both a Blonder-Tinkham-Klapwijk approach and a Keldysh non-equilibrium Green's function method. The dependence of various tunneling conductance features on the coupling strength between the semiconductor and the superconductor, the tunnel barrier height, and temperature is systematically investigated. We find that treating the parent superconductor as an active component of the system, rather than a passive source of Cooper pairs, has qualitative consequences regarding the low-energy behavior of the differential conductance. In particular, the presence of sub-gap states in the parent superconductor, due to disorder and finite magnetic fields, leads to characteristic particle-hole asymmetric features and to the breakdown of the quantization of the zero-bias peak associated with the presence of Majorana zero modes localized at the ends of the wire. The implications of these findings for the effort toward the realization of Majorana bound states with true non-Abelian properties are discussed.Comment: published version, 15+ pages, 12 figure

We study the low-energy physics of a one-dimensional array of superconducting quantum dots realized by proximity coupling a semiconductor nanowire to multiple superconducting islands separated by narrow uncovered regions. The effective electrostatic potential inside the quantum dots and the uncovered regions can be controlled using potential gates. By performing detailed numerical calculations based on effective tightbinding models, we find that multiple low-energy sub-gap states consisting of partially overlapping Majorana bound states emerge generically in the vicinity of the uncovered regions. Explicit differential conductance calculations show that a robust zero-bias conductance peak is not inconsistent with the presence of such states localized throughout the system, hence the observation of such a peak does not demonstrate the realization of well-separated Majorana zero modes. However, we find that creating effective potential wells in the uncovered regions traps pairs of nearby partially overlapping Majorana bound states, which become less separated and acquire a finite gap that protects the pair of Majorana zero modes localized at the ends of the system. This behavior persists over a significant parameter range, suggesting that proximitized quantum dot arrays could provide a platform for highly controllable Majorana devices. arXiv:1805.08119v2 [cond-mat.mes-hall]

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Lettuce is an important vegetable in the human diet and is commonly consumed for salad. It is a source of vitamin A, which plays a vital role in human health. Improvements in lettuce production will be needed to ensure a stable and economically available supply in the future. The influence of nitrogen (N), phosphorus (P), and potassium (K) compounds on the growth dynamics of four hydroponically grown lettuce (Lactuca sativa L.) cultivars (Black Seeded Simpson, Parris Island, Rex RZ, and Tacitus) in tubs and in a nutrient film technique (NFT) system were studied. Hyperspectral images (HSI) were captured at plant harvest. Models developed from the HSI data were used to estimate nutrient levels of leaf tissues by employing principal component analysis (PCA), partial least squares regression (PLSR), multivariate regression, and variable importance projection (VIP) methods. The optimal wavebands were found in six regions, including 390.57–438.02, 497–550, 551–600, 681.34–774, 802–821, and 822–838 nm for tub-grown lettuces and four regions, namely 390.57–438.02, 497–550, 551–600, and 681.34–774 nm for NFT-system-grown lettuces. These fitted models’ levels showed high accuracy (R2=0.85−0.99) in estimating the growth dynamics of the studied lettuce cultivars in terms of nutrient content. HSI data of the lettuce leaves and applied N solutions demonstrated a direct positive correlation with an accuracy of 0.82–0.99 for blue and green regions in 400–575 nm wavebands. The results proved that, in most of the tested multivariate regression models, HSI data of freshly cut leaves correlated well with laboratory-measured data.

Majorana zero modes are expected to arise in semiconductor-superconductor hybrid systems, with potential topological quantum computing applications. One limitation of this approach is the need for a relatively high external magnetic field that should also change direction at the nanoscale. This proposal considers devices that incorporate micromagnets to address this challenge. We perform numerical simulations of stray magnetic fields from different micromagnet configurations, which are then used to solve for Majorana wavefunctions. Several devices are proposed, starting with the basic four-magnet design to align magnetic field with the nanowire and scaling up to nanowire T-junctions. The feasibility of the approach is assessed by performing magnetic imaging of prototype patterns.