A two-site Kitaev chain in a two-dimensional electron gas.

Artificial Kitaev chains can be used to engineer Majorana bound states (MBSs) in superconductor-semiconductor hybrids1-4. In this work, we realize a two-site Kitaev chain in a two-dimensional electron gas by coupling two quantum dots through a region proximitized by a superconductor. We demonstrate systematic control over inter-dot couplings through in-plane rotations of the magnetic field and via electrostatic gating of the proximitized region. This allows us to tune the system to sweet spots in parameter space, where robust correlated zero-bias conductance peaks are observed in tunnelling spectroscopy. To study the extent of hybridization between localized MBSs, we probe the evolution of the energy spectrum with magnetic field and estimate the Majorana polarization, an important metric for Majorana-based qubits5,6. The implementation of a Kitaev chain on a scalable and flexible two-dimensional platform provides a realistic path towards more advanced experiments that require manipulation and readout of multiple MBSs.

Realization of a minimal Kitaev chain in coupled quantum dots.

Majorana bound states constitute one of the simplest examples of emergent non-Abelian excitations in condensed matter physics. A toy model proposed by Kitaev shows that such states can arise at the ends of a spinless p-wave superconducting chain1. Practical proposals for its realization2,3 require coupling neighbouring quantum dots (QDs) in a chain through both electron tunnelling and crossed Andreev reflection4. Although both processes have been observed in semiconducting nanowires and carbon nanotubes5-8, crossed-Andreev interaction was neither easily tunable nor strong enough to induce coherent hybridization of dot states. Here we demonstrate the simultaneous presence of all necessary ingredients for an artificial Kitaev chain: two spin-polarized QDs in an InSb nanowire strongly coupled by both elastic co-tunnelling (ECT) and crossed Andreev reflection (CAR). We fine-tune this system to a sweet spot where a pair of poor man's Majorana states is predicted to appear. At this sweet spot, the transport characteristics satisfy the theoretical predictions for such a system, including pairwise correlation, zero charge and stability against local perturbations. Although the simple system presented here can be scaled to simulate a full Kitaev chain with an emergent topological order, it can also be used imminently to explore relevant physics related to non-Abelian anyons.

Singlet and triplet Cooper pair splitting in hybrid superconducting nanowires.

In most naturally occurring superconductors, electrons with opposite spins form Cooper pairs. This includes both conventional s-wave superconductors such as aluminium, as well as high-transition-temperature, d-wave superconductors. Materials with intrinsic p-wave superconductivity, hosting Cooper pairs made of equal-spin electrons, have not been conclusively identified, nor synthesized, despite promising progress1-3. Instead, engineered platforms where s-wave superconductors are brought into contact with magnetic materials have shown convincing signatures of equal-spin pairing4-6. Here we directly measure equal-spin pairing between spin-polarized quantum dots. This pairing is proximity-induced from an s-wave superconductor into a semiconducting nanowire with strong spin-orbit interaction. We demonstrate such pairing by showing that breaking a Cooper pair can result in two electrons with equal spin polarization. Our results demonstrate controllable detection of singlet and triplet pairing between the quantum dots. Achieving such triplet pairing in a sequence of quantum dots will be required for realizing an artificial Kitaev chain7-9.

Exploiting Light Polarization for Deep HDR Imaging from a Single Exposure.

In computational photography, high dynamic range (HDR) imaging refers to the family of techniques used to recover a wider range of intensity values compared to the limited range provided by standard sensors. Classical techniques consist of acquiring a scene-varying exposure to compensate for saturated and underexposed regions, followed by a non-linear compression of intensity values called tone mapping. Recently, there has been a growing interest in estimating HDR images from a single exposure. Some methods exploit data-driven models trained to estimate values outside the camera's visible intensity levels. Others make use of polarimetric cameras to reconstruct HDR information without exposure bracketing. In this paper, we present a novel HDR reconstruction method that employs a single PFA (polarimetric filter array) camera with an additional external polarizer to increase the scene's dynamic range across the acquired channels and to mimic different exposures. Our contribution consists of a pipeline that effectively combines standard HDR algorithms based on bracketing and data-driven solutions designed to work with polarimetric images. In this regard, we present a novel CNN (convolutional neural network) model that exploits the underlying mosaiced pattern of the PFA in combination with the external polarizer to estimate the original scene properties, and a second model designed to further improve the final tone mapping step. The combination of such techniques enables us to take advantage of the light attenuation given by the filters while producing an accurate reconstruction. We present an extensive experimental section in which we validate the proposed method on both synthetic and real-world datasets specifically acquired for the task. Quantitative and qualitative results show the effectiveness of the approach when compared to state-of-the-art methods. In particular, our technique exhibits a PSNR (peak signal-to-noise ratio) on the whole test set equal to 23 dB, which is 18% better with respect to the second-best alternative.

Tunable Superconducting Coupling of Quantum Dots via Andreev Bound States in Semiconductor-Superconductor Nanowires.

Semiconductor quantum dots have proven to be a useful platform for quantum simulation in the solid state. However, implementing a superconducting coupling between quantum dots mediated by a Cooper pair has so far suffered from limited tunability and strong suppression. This has limited applications such as Cooper pair splitting and quantum dot simulation of topological Kitaev chains. In this Letter, we propose how to mediate tunable effective couplings via Andreev bound states in a semiconductor-superconductor nanowire connecting two quantum dots. We show that in this way it is possible to individually control both the coupling mediated by Cooper pairs and by single electrons by changing the properties of the Andreev bound states with easily accessible experimental parameters. In addition, the problem of coupling suppression is greatly mitigated. We also propose how to experimentally extract the coupling strengths from resonant current in a three-terminal junction. Our proposal will enable future experiments that have not been possible so far.

Locally Relevant High-Resolution Hydrodynamic Modeling of River Floods at the Regional Scale.

This paper deals with the simulation of inundated areas for a region of 84,000 km2 from estimated flood discharges at a resolution of 2 m. We develop a modeling framework that enables efficient parallel processing of the project region by splitting it into simulation tiles. For each simulation tile, the framework automatically calculates all input data and boundary conditions required for the hydraulic simulation on-the-fly. A novel method is proposed that ensures regionally consistent flood peak probabilities. Instead of simulating individual events, the framework simulates effective hydrographs consistent with the flood quantiles by adjusting streamflow at river nodes. The model accounts for local effects from buildings, culverts, levees, and retention basins. The two-dimensional full shallow water equations are solved by a second-order accurate scheme for all river reaches in Austria with catchment sizes over 10 km2, totaling 33,380 km. Using graphics processing units (GPUs), a single NVIDIA Titan RTX simulates a period of 3 days for a tile with 50 million wet cells in less than 3 days. We find good agreement between simulated and measured stage-discharge relationships at gauges. The simulated flood hazard maps also compare well with local high-quality flood maps, achieving critical success index scores of 0.6-0.79.

Enhanced Proximity Effect in Zigzag-Shaped Majorana Josephson Junctions.

High density superconductor-semiconductor-superconductor junctions have a small induced superconducting gap due to the quasiparticle trajectories with a large momentum parallel to the junction having a very long flight time. Because a large induced gap protects Majorana modes, these long trajectories constrain Majorana devices to a low electron density. We show that a zigzag-shaped geometry eliminates these trajectories, allowing the robust creation of Majorana states with both the induced gap E_{gap} and the Majorana size ξ_{M} improved by more than an order of magnitude for realistic parameters. In addition to the improved robustness of Majoranas, this new zigzag geometry is insensitive to the geometric details and the device tuning.

Spin-Orbit Protection of Induced Superconductivity in Majorana Nanowires.

Spin-orbit interaction (SOI) plays a key role in creating Majorana zero modes in semiconductor nanowires proximity coupled to a superconductor. We track the evolution of the induced superconducting gap in InSb nanowires coupled to a NbTiN superconductor in a large range of magnetic field strengths and orientations. Based on realistic simulations of our devices, we reveal SOI with a strength of 0.15-0.35 eV Å. Our approach identifies the direction of the spin-orbit field, which is strongly affected by the superconductor geometry and electrostatic gates.

Spin-Orbit Interaction and Induced Superconductivity in a One-Dimensional Hole Gas.

Low dimensional semiconducting structures with strong spin-orbit interaction (SOI) and induced superconductivity attracted great interest in the search for topological superconductors. Both the strong SOI and hard superconducting gap are directly related to the topological protection of the predicted Majorana bound states. Here we explore the one-dimensional hole gas in germanium silicon (Ge-Si) core-shell nanowires (NWs) as a new material candidate for creating a topological superconductor. Fitting multiple Andreev reflection measurements shows that the NW has two transport channels only, underlining its one-dimensionality. Furthermore, we find anisotropy of the Landé g-factor that, combined with band structure calculations, provides us qualitative evidence for the direct Rashba SOI and a strong orbital effect of the magnetic field. Finally, a hard superconducting gap is found in the tunneling regime and the open regime, where we use the Kondo peak as a new tool to gauge the quality of the superconducting gap.

h/e Superconducting Quantum Interference through Trivial Edge States in InAs.

Josephson junctions defined in strong spin orbit semiconductors are highly interesting for the search for topological systems. However, next to topological edge states that emerge in a sufficient magnetic field, trivial edge states can also occur. We study the trivial edge states with superconducting quantum interference measurements on nontopological InAs Josephson junctions. We observe a SQUID pattern, an indication of superconducting edge transport. Also, a remarkable h/e SQUID signal is observed that, as we find, stems from crossed Andreev states.

InSb Nanowires with Built-In GaxIn1-xSb Tunnel Barriers for Majorana Devices.

Majorana zero modes (MZMs), prime candidates for topological quantum bits, are detected as zero bias conductance peaks (ZBPs) in tunneling spectroscopy measurements. Implementation of a narrow and high tunnel barrier in the next generation of Majorana devices can help to achieve the theoretically predicted quantized height of the ZBP. We propose a material-oriented approach to engineer a sharp and narrow tunnel barrier by synthesizing a thin axial segment of GaxIn1-xSb within an InSb nanowire. By varying the precursor molar fraction and the growth time, we accurately control the composition and the length of the barriers. The height and the width of the GaxIn1-xSb tunnel barrier are extracted from the Wentzel-Kramers-Brillouin (WKB) fits to the experimental I-V traces.

Orbital Contributions to the Electron g Factor in Semiconductor Nanowires.

Recent experiments on Majorana fermions in semiconductor nanowires [S. M. Albrecht, A. P. Higginbotham, M. Madsen, F. Kuemmeth, T. S. Jespersen, J. Nygård, P. Krogstrup, and C. M. Marcus, Nature (London) 531, 206 (2016)NATUAS0028-083610.1038/nature17162] revealed a surprisingly large electronic Landé g factor, several times larger than the bulk value-contrary to the expectation that confinement reduces the g factor. Here we assess the role of orbital contributions to the electron g factor in nanowires and quantum dots. We show that an L·S coupling in higher subbands leads to an enhancement of the g factor of an order of magnitude or more for small effective mass semiconductors. We validate our theoretical finding with simulations of InAs and InSb, showing that the effect persists even if cylindrical symmetry is broken. A huge anisotropy of the enhanced g factors under magnetic field rotation allows for a straightforward experimental test of this theory.

Giant Spin-Orbit Splitting in Inverted InAs/GaSb Double Quantum Wells.

Transport measurements in inverted InAs/GaSb quantum wells reveal a giant spin-orbit splitting of the energy bands close to the hybridization gap. The splitting results from the interplay of electron-hole mixing and spin-orbit coupling, and can exceed the hybridization gap. We experimentally investigate the band splitting as a function of top gate voltage for both electronlike and holelike states. Unlike conventional, noninverted two-dimensional electron gases, the Fermi energy in InAs/GaSb can cross a single spin-resolved band, resulting in full spin-orbit polarization. In the fully polarized regime we observe exotic transport phenomena such as quantum Hall plateaus evolving in e^{2}/h steps and a nontrivial Berry phase.

Quantized Conductance and Large g-Factor Anisotropy in InSb Quantum Point Contacts.

Because of a strong spin-orbit interaction and a large Landé g-factor, InSb plays an important role in research on Majorana fermions. To further explore novel properties of Majorana fermions, hybrid devices based on quantum wells are conceived as an alternative approach to nanowires. In this work, we report a pronounced conductance quantization of quantum point contact devices in InSb/InAlSb quantum wells. Using a rotating magnetic field, we observe a large in-plane (|g1| = 26) and out-of-plane (|g1| = 52) g-factor anisotropy. Additionally, we investigate crossings of subbands with opposite spins and extract the electron effective mass from magnetic depopulation of one-dimensional subbands.

Electric and Magnetic Tuning Between the Trivial and Topological Phases in InAs/GaSb Double Quantum Wells.

Among the theoretically predicted two-dimensional topological insulators, InAs/GaSb double quantum wells (DQWs) have a unique double-layered structure with electron and hole gases separated in two layers, which enables tuning of the band alignment via electric and magnetic fields. However, the rich trivial-topological phase diagram has yet to be experimentally explored. We present an in situ and continuous tuning between the trivial and topological insulating phases in InAs/GaSb DQWs through electrical dual gating. Furthermore, we show that an in-plane magnetic field shifts the electron and hole bands relatively to each other in momentum space, functioning as a powerful tool to discriminate between the topologically distinct states.

RSVP for VPSA : A Meta Design Study on Rapid Suggestive Visualization Prototyping for Visual Parameter Space Analysis.

Visual Parameter Space Analysis (VPSA) enables domain scientists to explore input-output relationships of computational models. Existing VPSA applications often feature multi-view visualizations designed by visualization experts for a specific scenario, making it hard for domain scientists to adapt them to their problems without professional help. We present RSVP, the Rapid Suggestive Visualization Prototyping system encoding VPSA knowledge to enable domain scientists to prototype custom visualization dashboards tailored to their specific needs. The system implements a task-oriented, multi-view visualization recommendation strategy over a visualization design space optimized for VPSA to guide users in meeting their analytical demands. We derived the VPSA knowledge implemented in the system by conducting an extensive meta design study over the body of work on VPSA. We show how this process can be used to perform a data and task abstraction, extract a common visualization design space, and derive a task-oriented VisRec strategy. User studies indicate that the system is user-friendly and can uncover novel insights.

Multimodal decoding of error processing in a virtual reality flight simulation.

Technological advances in head-mounted displays (HMDs) facilitate the acquisition of physiological data of the user, such as gaze, pupil size, or heart rate. Still, interactions with such systems can be prone to errors, including unintended behavior or unexpected changes in the presented virtual environments. In this study, we investigated if multimodal physiological data can be used to decode error processing, which has been studied, to date, with brain signals only. We examined the feasibility of decoding errors solely with pupil size data and proposed a hybrid decoding approach combining electroencephalographic (EEG) and pupillometric signals. Moreover, we analyzed if hybrid approaches can improve existing EEG-based classification approaches and focused on setups that offer increased usability for practical applications, such as the presented game-like virtual reality flight simulation. Our results indicate that classifiers trained with pupil size data can decode errors above chance. Moreover, hybrid approaches yielded improved performance compared to EEG-based decoders in setups with a reduced number of channels, which is crucial for many out-of-the-lab scenarios. These findings contribute to the development of hybrid brain-computer interfaces, particularly in combination with wearable devices, which allow for easy acquisition of additional physiological data.

Robust poor man's Majorana zero modes using Yu-Shiba-Rusinov states.

Kitaev chains in quantum dot-superconductor arrays are a promising platform for the realization of topological superconductivity. As recently demonstrated, even a two-site chain can host Majorana zero modes known as "poor man's Majorana". Harnessing the potential of these states for quantum information processing, however, requires increasing their robustness to external perturbations. Here, we form a two-site Kitaev chain using Yu-Shiba-Rusinov states in proximitized quantum dots. By deterministically tuning the hybridization between the quantum dots and the superconductor, we observe poor man's Majorana states with a gap larger than 70 µeV. The sensitivity to charge fluctuations is also greatly reduced compared to Kitaev chains made with non-proximitized dots. The systematic control and improved energy scales of poor man's Majorana states realized with Yu-Shiba-Rusinov states will benefit the realization of longer Kitaev chains, parity qubits, and the demonstration of non-Abelian physics.

Neural and Pupillometric Correlates of Error Perception in an Immersive VR Flight Simulation.

Algorithms detecting erroneous events, as used in brain-computer interfaces, usually rely solely on neural correlates of error perception. The increasing availability of wearable displays with built-in pupillometric sensors enables access to additional physiological data, potentially improving error detection. Hence, we measured both electroencephalographic (EEG) and pupillometric signals of 19 participants while performing a navigation task in an immersive virtual reality (VR) setting. We found EEG and pupillometric correlates of error perception and significant differences between distinct error types. Further, we found that actively performing tasks delays error perception. We believe that the results of this work could contribute to improving error detection, which has rarely been studied in the context of immersive VR.

Measuring Spinal Cord Potentials and Cortico-Spinal Interactions After Wrist Movements Induced by Neuromuscular Electrical Stimulation.

Electroencephalographic (EEG) correlates of movement have been studied extensively over many years. In the present work, we focus on investigating neural correlates that originate from the spine and study their connectivity to corresponding signals from the sensorimotor cortex using multivariate autoregressive (MVAR) models. To study cortico-spinal interactions, we simultaneously measured spinal cord potentials (SCPs) and somatosensory evoked potentials (SEPs) of wrist movements elicited by neuromuscular electrical stimulation. We identified directional connections between spine and cortex during both the extension and flexion of the wrist using only non-invasive recording techniques. Our connectivity estimation results are in alignment with various studies investigating correlates of movement, i.e., we found the contralateral side of the sensorimotor cortex to be the main sink of information as well as the spine to be the main source of it. Both types of movement could also be clearly identified in the time-domain signals.