Measurement of classical entanglement using interference fringes

Classical entanglement refers to non-separable correlations between the polarization direction and the polarization amplitude of a light field. The degree of entanglement is quantified by the Schmidt number, taking the value of unity for a separable state and two for a maximally entangled state. We propose two detection methods to determine this number based on the distinguishable patterns of interference between four light sources derived from the unknown laser beam to be detected. The second method being a modification of the first one has the interference fringes form discernable angles uniquely related to the entangled state. The maximally entangled state corresponds to fringes symmetric about the diagonal axis at either 45{\deg} or 135{\deg} direction while the separable state corresponds to fringes symmetric either about the X- or Y-axis or both simultaneously. States with Schmidt number between unity and two have fringes of symmetric angles between these two extremes. The detection methods would be beneficial to constructing transmission channels of information contained in the classically entangled states

Computing Shor's algorithmic steps with classical light beams

When considered as orthogonal bases in distinct vector spaces, the unit vectors of polarization directions and the Laguerre-Gaussian modes of polarization amplitude are inseparable, constituting a so-called classical entangled light beam. Equating this classical entanglement to quantum entanglement necessary for computing purpose, we show that the parallelism featured in Shor's factoring algorithm is equivalent to the concurrent light-path propagation of an entangled beam or pulse train. A gedanken experiment is proposed for executing the key algorithmic steps of modular exponentiation and Fourier transform on a target integer $N$ using only classical manipulations on the amplitudes and polarization directions. The multiplicative order associated with the sought-after integer factors is identified through a four-hole diffraction interference from sources obtained from the entangled beam profile. The unique mapping from the fringe patterns to the computed order is demonstrated through simulations for the case $N=15$

Resistance Switching and Failure Behavior of the MoO_<i>x</i>/Mo₂C Heterostructure

With the rapid demand for high-performance and power-efficient memristive and synaptic systems, more 2D heterostructures with improved resistance switching (RS) properties are still urgently in need for next-generation devices. Here, we report the RS behaviors of vertical MoOx/Mo2C heterostructures fabricated by controllable thermal oxidation and uncover the failure behavior for the first time. It is found that the MoOx/Mo2C heterostructure exhibits bipolar RS with a low set/reset voltage of +0.5/–0.3 V, an ultralow power consumption of 5 × 10–8 W, and an on/off ratio of 102, which is ascribed to the transport of the internal oxygen ions of MoOx. Furthermore, the failure behavior of RS behaviors of the MoOx/Mo2C heterostructure under a higher work voltage is revealed. It indicates that the amorphization of the pristine crystalline MoOx layer could block the movement of the internal oxygen ions in the vertical direction. The excellent RS performance induced by the synergy of MoOx and Mo2C and the demonstration of the failure behavior enable the potential applications of the 2D heterostructure in related memory devices and biological neural networks

Field Electron Emission Characteristics and Physical Mechanism of Individual Single-Layer Graphene

Due to its difficulty, experimental measurement of field emission from a single-layer graphene has not been reported, although field emission from a two-dimensional (2D) regime has been an attractive topic. The open surface and sharp edge of graphene are beneficial for field electron emission. A 2D geometrical effect, such as massless Dirac fermion, can lead to new mechanisms in field emission. Here, we report our findings from in situ field electron emission characterization on an individual singe-layer graphene and the understanding of the related mechanism. The measurement of field emission from the edges was done using a microanode probe equipped in a scanning electron microscope. We show that repeatable stable field emission current can be obtained after a careful conditioning process. This enables us to examine experimentally the typical features of the field emission from a 2D regime. We plot current versus applied field data, respectively, in ln(I/E3/2) ∼ 1/E and ln(I/E3) ∼ 1/E2 coordinates, which have recently been proposed for field emission from graphene in high- and low-field regimes. It is observed that the plots all exhibit an upward bending feature, revealing that the field emission processes undergo from a low- to high-field transition. We discuss with theoretical analysis the physical mechanism responsible for the new phenomena

Diameter Modulation of Vertically Aligned Single-Walled Carbon Nanotubes

We demonstrate wide-range diameter modulation of vertically aligned single-walled carbon nanotubes (SWNTs) using a wet chemistry prepared catalyst. In order to ensure compatibility to electronic applications, the current minimum mean diameter of 2 nm for vertically aligned SWNTs is challenged. The mean diameter is decreased to about 1.4 nm by reducing Co catalyst concentrations to 1/100 or by increasing Mo catalyst concentrations by five times. We also propose a novel spectral analysis method that allows one to distinguish absorbance contributions from the upper, middle, and lower parts of a nanotube array. We use this method to quantitatively characterize the slight diameter change observed along the array height. On the basis of further investigation of the array and catalyst particles, we conclude that catalyst aggregationrather than Ostwald ripeningdominates the growth of metal particles

Controllable Fabrication of Large-Area Wrinkled Graphene on a Solution Surface

It is unavoidable to form wrinkles, which are folds or creases in a material, in graphene, whenever the graphene is prepared by micromechanical exfoliation from graphite or chemical vapor deposition (CVD). However, the controllable formation and structures of graphene with nanoscale wrinkles remains a big challenge. Here, we report a liquid-phase shrink method to controllably fabricate large-area wrinkled graphene (WG). The CVD-prepared graphene self-shrinks into a WG on an ethanol solution surface. By modifying the concentration of the ethanol solution, we can easily and efficiently obtain WG with a uniform distribution of wrinkles with different heights. The WG shows high stretchability and can withstand more than 100% tensile strain and up to 720° twist. Furthermore, electromechanical response sensors based on double-layer stacking of WG show ultrahigh sensitivity. This simple, effective, and environmentally friendly liquid-phase shrink method will pave a way for the controllable formation of WG, which is an ideal candidate for application in highly stretchable and highly sensitive electronic devices

Single Crystalline Trigonal Selenium Nanotubes and Nanowires Synthesized by Sonochemical Process

One-dimensional (1D) nanostructures of trigonal selenium (t-Se) were synthesized by the reduction of H2SeO3 in different solvents with a sonochemical method. The 1D structure of t-Se was formed by the anisotropic growth of selenium crystalline, and the morphology of the products highly depends on the reaction conditions including ultrasonic mode (e.g., frequency, power, and time), aging time, and solvent. Single crystalline trigonal selenium nanotubes with diameters of less than 200 nm and nanowires with diameters of 20−50 nm have been synthesized. X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), high-resolution TEM (HRTEM), energy-dispersive spectrometry (EDS), and Raman spectra were used to characterize the products. The formation process of t-Se nanotubes and nanowires were investigated. A sonication-induced directional growth mechanism was proposed for the formation of nanotubes. The further aging of tubes in solution leads to the collapse of the tubular structure and the formation of nanowires

Graphene Magnetoresistance Device in van der Pauw Geometry

We have fabricated extraordinary magnetoresistance (EMR) device, comprising a monolayer graphene with an embedded metallic disk, that exhibits large room temperature magnetoresistance (MR) enhancement of up to 55 000% at 9 T. Finite element simulations yield predictions in excellent agreement with the experiment and show possibility for even better performance. Simplicity, ease of implementation and high sensitivity of this device imply great potential for practical applications

Manipulation of Surface Plasmon Resonance in Sub-Stoichiometry Molybdenum Oxide Nanodots through Charge Carrier Control Technique

Semiconductor nanocrystals are intriguing because they show surface plasmon absorption features like noble metallic nanoparticles. In contrast with metal, manipulation of their unique plasmonic resonance could be easily realized by the free-carrier concentration. Here, it is demonstrated that MoO_3–<i>x</i> nanodots can exhibit striking surface plasmon resonance located at near-infrared region under treatment of two different reducing agents. Furthermore, the tunable resonance mode has been achieved through appropriate redox processes. Refractive index sensing has been demonstrated by monitoring the plasmonic peak. The improved sensing application is ascribed to the enhanced electric field in the plasmonic nanocrystals. These new insights into MoO_3–<i>x</i> nanodots pave a way to develop novel plasmonic applications such as photothermal therapy, light harvesting, and sensing