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The translational symmetry breaking of a crystal at its surface may form two-dimensional (2D) electronic states. We observed one-dimensional nonlinear optical edge states of a single atomic membrane of molybdenum disulfide (MoS 2 ), a transition metal dichalcogenide. The electronic structure changes at the edges of the 2D crystal result in strong resonant nonlinear optical susceptibilities, allowing direct optical imaging of the atomic edges and boundaries of a 2D material. Using the symmetry of the nonlinear optical responses, we developed a nonlinear optical imaging technique that allows rapid and all-optical determination of the crystal orientations of the 2D material at a large scale. Our technique provides a route toward understanding and making use of the emerging 2D materials and devices.T he structural discontinuity at the edges and boundaries of 2D atomic materials, such as graphene and transition metal dichalcogenides, leads to complex interplay between the atomic positions and the electronic structures. Subsequently, the atomic edges and boundaries reconstruct structurally and electronically. A broad range of exceptional physical behaviors and applications including widely tunable transport gaps (1, 2), unusual magnetic responses (3-5), and high-performance nanoelectronics (6, 7) have been discovered. However, experimental observations of these 1D structures have been limited to scanning tunneling microscopy and transmission electron microscopy. Here, we studied the second-order nonlinear optics on the 1D edges and boundaries of hexagonal molybdenum disulfide (MoS 2 ) atomic membranes. The broken inversion symmetry of the atomically thin monolayer shows strong second-harmonic generation (SHG), in contrast to the centrosymmetric bulk material, which is immune to the second-order nonlinear processes. The destructive interference and annihilation of nonlinear waves from neighboring atomic membranes reveals the few-atom-wide line defects that stitch different crystal grains together, and also allows the mapping of crystal grains and grain boundaries over large areas. Our optical imaging technique enables the nonlinear optical detection of the edge states at the atomic edges of 2D crystals where the translational symmetry is broken. The observed edge resonance of SHG clearly indicates the electronic structure variation at the atomic edges, which have long been suspected to be the active sites for electrocatalytic hydrogen evolution (8).Unlike gapless graphene, the monolayer form of transition metal dichalcogenides such as MoS 2 shows a direct band gap at visible frequencies, making them emergent semiconductors for nanoelectronics and optoelectronics involving photovoltaic and/or photoemission processes (9, 10). In MoS 2 , the unique local orbital properties of the heavy transition metal atoms and broken inversion symmetry of the monolayer crystal introduce an imbalanced charge carrier distribution in momentum space, giving rise to a novel valleyspecific circular dichroism (11)(12)13). Hexagonal bulk MoS 2 ...

Detecting single-photon level signals—carriers of both classical and quantum information—is particularly challenging for low-energy microwave frequency excitations. Here we introduce a superconducting amplifier based on a Josephson junction transmission line. Unlike current standing-wave parametric amplifiers, this traveling wave architecture robustly achieves high gain over a bandwidth of several gigahertz with sufficient dynamic range to read out 20 superconducting qubits. To achieve this performance, we introduce a subwavelength resonant phase-matching technique that enables the creation of nonlinear microwave devices with unique dispersion relations. We benchmark the amplifier with weak measurements, obtaining a high quantum efficiency of 75% (70% including noise added by amplifiers following the Josephson amplifier). With a flexible design based on compact lumped elements, this Josephson amplifier has broad applicability to microwave metrology and quantum optics.

The discovery of optical second harmonic generation in 1961 started modern nonlinear optics. Soon after, R. C. Miller found empirically that the nonlinear susceptibility could be predicted from the linear susceptibilities. This important relation, known as Miller's Rule, allows a rapid determination of nonlinear susceptibilities from linear properties. In recent years, metamaterials, artificial materials that exhibit intriguing linear optical properties not found in natural materials, have shown novel nonlinear properties such as phase-mismatch-free nonlinear generation, new quasi-phase matching capabilities and large nonlinear susceptibilities. However, the understanding of nonlinear metamaterials is still in its infancy, with no general conclusion on the relationship between linear and nonlinear properties. The key question is then whether one can determine the nonlinear behaviour of these artificial materials from their exotic linear behaviour. Here, we show that the nonlinear oscillator model does not apply in general to nonlinear metamaterials. We show, instead, that it is possible to predict the relative nonlinear susceptibility of large classes of metamaterials using a more comprehensive nonlinear scattering theory, which allows efficient design of metamaterials with strong nonlinearity for important applications such as coherent Raman sensing, entangled photon generation and frequency conversion.

Phase matching is a critical requirement for coherent nonlinear optical processes such as frequency conversion and parametric amplification. Phase mismatch prevents microscopic nonlinear sources from combining constructively, resulting in destructive interference and thus very low efficiency. We report the experimental demonstration of phase mismatch-free nonlinear generation in a zero-index optical metamaterial. In contrast to phase mismatch compensation techniques required in conventional nonlinear media, the zero index eliminates the need for phase matching, allowing efficient nonlinear generation in both forward and backward directions. We demonstrate phase mismatch-free nonlinear generation using intrapulse four-wave mixing, where we observed a forward-to-backward nonlinear emission ratio close to unity. The removal of phase matching in nonlinear optical metamaterials may lead to applications such as multidirectional frequency conversion and entangled photon generation.

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We propose a technique to overcome phase mismatch in Josephson-junction traveling wave parametric amplifiers in order to achieve high gain over a broad bandwidth. Using "resonant phase matching," we design a compact superconducting device consisting of a transmission line with subwavelength resonant inclusions that simultaneously achieves a gain of 20 dB, an instantaneous bandwidth of 3 GHz, and a saturation power of -98 dBm. Such an amplifier is well suited to cryogenic broadband microwave measurements such as the multiplexed readout of quantum coherent circuits based on superconducting, semiconducting, or nanomechanical elements, as well as traditional astronomical detectors.

Growth of vertically aligned carbon nanotube (CNT) carpets on metallic substrates at low temperatures was achieved by controlled thermal treatment of ethylene and hydrogen at a temperature higher than the substrate temperature. High-resolution transmission electron microscopy showed that nanotubes were crystalline for a preheating temperature of 770 degrees C and a substrate temperature of 500 degrees C. Conductive atomic force microscopy measurements indicated electrical contact through the CNT carpet to the metallic substrate with an approximate resistance of 35 kOmega for multiwall carpets taller than two micrometers. An analysis of the activation energies indicated that thermal decomposition of the hydrocarbon/hydrogen gas mixture was the rate-limiting step for low-temperature chemical vapor deposition growth of CNTs. These results represent a significant advance toward the goal of replacing copper interconnects with nanotubes using CMOS-compatible processes.