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A magnetic impurity coupled to a superconductor gives rise to a Yu-Shiba-Rusinov (YSR) state inside the superconducting energy gap. With increasing exchange coupling the excitation energy of this state eventually crosses zero and the system switches to a YSR groundstate with bound quasiparticles screening the impurity spin by $\hbar/2$. Here we explore InAs nanowire double quantum dots tunnel coupled to a superconductor and demonstrate YSR screening of spin-1/2 and spin-1 states. Gating the double dot through 9 different charge states, we show that the honeycomb pattern of zero-bias conductance peaks, archetypal of double dots coupled to normal leads, is replaced by lines of zero-energy YSR states. These enclose regions of YSR-screened dot spins displaying distinctive spectral features, and their characteristic shape and topology change markedly with tunnel coupling strengths. We find excellent agreement with a simple zero-bandwidth approximation, and with numerical renormalization group calculations for the two-orbital Anderson model., Comment: 6 pages, 4 figures. For Supplementary Information, see http://www.kaspergr.dk/YSRDQD/SupplementaryInformation.pdf

We present magnetoresistance (MR) experiments on an InAs nanowire quantum dot device with two ferromagnetic sidegates (FSGs) in a split-gate geometry. The wire segment can be electrically tuned to a single dot or to a double dot regime using the FSGs and a backgate. In both regimes we find a strong MR and a sharp MR switching of up to 25\% at the field at which the magnetizations of the FSGs are inverted by the external field. The sign and amplitude of the MR and the MR switching can both be tuned electrically by the FSGs. In a double dot regime close to pinch-off we find {\it two} sharp transitions in the conductance, reminiscent of tunneling MR (TMR) between two ferromagnetic contacts, with one transition near zero and one at the FSG switching fields. These surprisingly rich characteristics we explain in several simple resonant tunneling models. For example, the TMR-like MR can be understood as a stray-field controlled transition between singlet and a triplet double dot states. Such local magnetic fields are the key elements in various proposals to engineer novel states of matter and may be used for testing electron spin-based Bell inequalities., Comment: 7 pages, 6 figures

Majorana zero modes are quasiparticle excitations in condensed matter systems that have been proposed as building blocks of fault-tolerant quantum computers [1]. They are expected to exhibit non-Abelian particle statistics, in contrast to the usual statistics of fermions and bosons, enabling quantum operations to be performed by braiding isolated modes around one another. Quantum braiding operations are topologically protected insofar as these modes are pinned near zero energy, and the pinning is predicted to be exponential as the modes become spatially separated. Following theoretical proposals, several experiments have identified signatures of Majorana modes in proximitized nanowires and atomic chains, with small mode-splitting potentially explained by hybridization of Majoranas. Here, we use Coulomb-blockade spectroscopy in an InAs nanowire segment with epitaxial aluminum, which forms a proximity-induced superconducting Coulomb island (a Majorana island) that is isolated from normal-metal leads by tunnel barriers, to measure the splitting of near-zero-energy Majorana modes. We observe exponential suppression of energy splitting with increasing wire length. For short devices of a few hundred nanometers, sub-gap state energies oscillate as the magnetic field is varied, as is expected for hybridized Majorana modes. Splitting decreases by a factor of about ten for each half micrometer of increased wire length. For devices longer than about one micrometer, transport in strong magnetic fields occurs through a zero-energy state that is energetically isolated from a continuum, yielding uniformly spaced Coulomb-blockade conductance peaks, consistent with teleportation via Majorana modes. Our results help explain the trivial-to-topological transition in finite systems and to quantify the scaling of topological protection with end-mode separation., Comment: main text and methods section

The thermal gradient along indium-arsenide nanowires was engineered by a combination of fabricated micro- trenches in the supporting substrate and focused laser irradiation. This allowed local control of thermally activated oxidation reactions of the nanowire on the scale of the diffraction limit. The locality of the oxidation was detected by micro-Raman mapping, and the results were found consistent with numerical simulations of the temperature profile. Applying the technique to nanowires in electrical devices the locally oxidized nanowires remained conducting with a lower conductance as expected for an effectively thinner conducting core.

Semiconducting nanowires (NWs) are a versatile, highly tunable material platform at the heart of many new developments in nanoscale and quantum physics. Here, we demonstrate charge pumping, i.e., the controlled transport of individual electrons through an InAs NW quantum dot (QD) device at frequencies up to $1.3\,$GHz. The QD is induced electrostatically in the NW by a series of local bottom gates in a state of the art device geometry. A periodic modulation of a single gate is enough to obtain a dc current proportional to the frequency of the modulation. The dc bias, the modulation amplitude and the gate voltages on the local gates can be used to control the number of charges conveyed per cycle. Charge pumping in InAs NWs is relevant not only in metrology as a current standard, but also opens up the opportunity to investigate a variety of exotic states of matter, e.g. Majorana modes, by single electron spectroscopy and correlation experiments., Comment: 21 pages

Cooper pair splitting (CPS) is a process in which the electrons of naturally occurring spin-singlet pairs in a superconductor are spatially separated using two quantum dots. Here we investigate the evolution of the conductance correlations in an InAs CPS device in the presence of an external magnetic field. In our experiments the gate dependence of the signal that depends on both quantum dots continuously evolves from a slightly asymmetric Lorentzian to a strongly asymmetric Fano-type resonance with increasing field. These experiments can be understood in a simple three - site model, which shows that the nonlocal CPS leads to symmetric line shapes, while the local transport processes can exhibit an asymmetric shape due to quantum interference. These findings demonstrate that the electrons from a Cooper pair splitter can propagate coherently after their emission from the superconductor and how a magnetic field can be used to optimize the performance of a CPS device. In addition, the model calculations suggest that the estimate of the CPS efficiency in the experiments is a lower bound for the actual efficiency., Comment: 5 pages + 4 pages supplementary information

Controlling the properties of semiconductor/metal interfaces is a powerful method for designing functionality and improving the performance of electrical devices. Recently semiconductor/superconductor hybrids have appeared as an important example where the atomic scale uniformity of the interface plays a key role for the quality of the induced superconducting gap. Here we present epitaxial growth of semiconductor-metal core-shell nanowires by molecular beam epitaxy, a method that provides a conceptually new route to controlled electrical contacting of nanostructures and for designing devices for specialized applications such as topological and gate-controlled superconducting electronics. Our materials of choice, InAs/Al, are grown with epitaxially matched single plane interfaces, and alternative semiconductor/metal combinations allowing epitaxial interface matching in nanowires are discussed. We formulate the grain growth kinetics of the metal phase in general terms of continuum parameters and bicrystal symmetries. The method realizes the ultimate limit of uniform interfaces and appears to solve the soft-gap problem in superconducting hybrid structures., Comment: Combined text and Supplementary Information

A Cooper pair splitter consists of a central superconducting contact, S, from which electrons are injected into two parallel, spatially separated quantum dots (QDs). This geometry and electron interactions can lead to correlated electrical currents due to the spatial separation of spin-singlet Cooper pairs from S. We present experiments on such a device with a series of bottom gates, which allows for spatially resolved tuning of the tunnel couplings between the QDs and the electrical contacts and between the QDs. Our main findings are gate-induced transitions between positive conductance correlation in the QDs due to Cooper pair splitting and negative correlations due to QD dynamics. Using a semi-classical rate equation model we show that the experimental findings are consistent with in-situ electrical tuning of the local and nonlocal quantum transport processes. In particular, we illustrate how the competition between Cooper pair splitting and local processes can be optimized in such hybrid nanostructures., Comment: 9 pages, 6 figures, 2 tables

We report a method for making epitaxial superconducting contacts to semiconducting nanowires. The temperature and gate characteristics demonstrate barrier-free electrical contact, and the properties in the superconducting state are investigated at low temperature. Half-covering aluminum contacts are realized without the need of lithography and we demonstrate how to controllably insert high-band gap layers in the interface region. These developments are relevant to hybrid superconductor-nanowire devices that support Majorana zero energy states.

The use of compressed air cannons in an undergraduate lab provides a way to illustrate the cooperation of diverse physics concepts, such as conservation of momentum, the work-kinetic energy theorem, expansion of gas, air drag, and elementary Newtonian mechanics. However, recent proposals have disagreed as to whether the expansion of the gas in the cannon should be modeled as an adiabatic or an isothermal process. We built an air cannon that utilized a diaphragm valve to release our pressurized gas and found that neither model accurately predicted the exit velocity of our projectile. We present a new model, based on the flow of air through the valve, that is in much better agreement with our data.

We present the design of a new type of compact toroidal, or "halo", ion trap. Such traps may be useful for mass spectrometry, studying small Coulomb cluster rings, quantum information applications, or other quantum simulations where a ring topology is of interest. We present results from a Monte Carlo optimization of the trap design parameters using finite-element analysis simulations that minimizes higher-order anharmonic terms in the trapping pseudopotential, while maintaining complete control over ion placement at the pseudopotential node in 3D using static bias fields. These simulations are based on a practical electrode design using readily-available parts, yet can be easily scaled to any size trap with similar electrode spacings. We also derive the conditions for a crystal phase transition for two ions in the compact halo trap, the first non-trivial phase transition for Coulomb crystals in this geometry., Comment: 8 pages, 9 figures

We investigate the angular normal modes for small oscillations about an equilibrium of a single-component coulomb cluster confined by a radially symmetric external potential to a circle. The dynamical matrix for this system is a Laplacian symmetrically circulant matrix and this result leads to an analytic solution for the eigenfrequencies of the angular normal modes. We also show the limiting dependence of the largest eigenfrequency for large numbers of particles.

We present an update of the "refractive index of air" experiment commonly used in optics and undergraduate advanced labs. The refractive index of air is based on the average molecular polarizability, which we measured from the period of the phase shift in a Michelson interferometer as a function of pressure. Our value of the average molecular polarizability of air is \gamma_mol = 2.133 \pm 0.032 \times 10^{-29} m^3 (95% CI) and from this we find the refractive index of air at atmospheric pressure to be n = 1.0002651(66), which is in agreement with the accepted value of n=1.000271375(6).

We collect the fluorescence from two trapped atomic ions, and measure quantum interference between photons emitted from the ions. The interference of two photons is a crucial component of schemes to entangle atomic qubits based on a photonic coupling. The ability to preserve the generated entanglement and to repeat the experiment with the same ions is necessary to implement entangling quantum gates between atomic qubits, and allows the implementation of protocols to efficiently scale to larger numbers of atomic qubits., Comment: 4 pages, 4 figures

Atomic cadmium ions are loaded into radiofrequency ion traps by photoionization of atoms in a cadmium vapor with ultrafast laser pulses. The photoionization is driven through an intermediate atomic resonance with a frequency-quadrupled mode-locked Ti:Sapphire laser that produces pulses of either 100 fsec or 1 psec duration at a central wavelength of 229 nm. The large bandwidth of the pulses photoionizes all velocity classes of the Cd vapor, resulting in high loading efficiencies compared to previous ion trap loading techniques. Measured loading rates are compared with a simple theoretical model, and we conclude that this technique can potentially ionize every atom traversing the laser beam within the trapping volume. This may allow the operation of ion traps with lower levels of background pressures and less trap electrode surface contamination. The technique and laser system reported here should be applicable to loading most laser-cooled ion species., Comment: 11 pages, 12 figures

We propose a scheme to perform probabilistic quantum gates on remote trapped atom qubits through interference of optical frequency qubits. The method does not require localization of the atoms to the Lamb-Dicke limit, and is not sensitive to interferometer phase instabilities. Such probabilistic gates can be used for scalable quantum computation.

We demonstrate ultrafast coherent coupling between an atomic qubit stored in a single trapped cadmium ion and a photonic qubit represented by two resolved frequencies of a photon. Such ultrafast coupling is crucial for entangling networks of remotely-located trapped ions through photon interference, and is also a key component for realizing ultrafast quantum gates between Coulomb-coupled ions., Comment: 4 pages, 4 figures

The electromagnetic manipulation of isolated atoms has led to many advances in physics, from laser cooling and Bose-Einstein condensation of cold gases to the precise quantum control of individual atomic ion. Work on miniaturizing electromagnetic traps to the micrometer scale promises even higher levels of control and reliability. Compared with 'chip traps' for confining neutral atoms, ion traps with similar dimensions and power dissipation offer much higher confinement forces and allow unparalleled control at the single-atom level. Moreover, ion microtraps are of great interest in the development of miniature mass spectrometer arrays, compact atomic clocks, and most notably, large scale quantum information processors. Here we report the operation of a micrometer-scale ion trap, fabricated on a monolithic chip using semiconductor micro-electromechanical systems (MEMS) technology. We confine, laser cool, and measure heating of a single 111Cd+ ion in an integrated radiofrequency trap etched from a doped gallium arsenide (GaAs) heterostructure., Comment: 4 pages, 4 figures

We demonstrate broadband laser cooling of atomic ions in an rf trap using ultrafast pulses from a modelocked laser. The temperature of a single ion is measured by observing the size of a time-averaged image of the ion in the known harmonic trap potential. While the lowest observed temperature was only about 1 K, this method efficiently cools very hot atoms and can sufficiently localize trapped atoms to produce near diffraction-limited atomic images.

We report precision measurements of the excited state lifetime of the $5p$ $^2P_{1/2}$ and $5p$ $^2P_{3/2}$ levels of a single trapped Cd$^+$ ion. The ion is excited with picosecond laser pulses from a mode-locked laser and the distribution of arrival times of spontaneously emitted photons is recorded. The resulting lifetimes are 3.148 $\pm$ 0.011 ns and 2.647 $\pm$ 0.010 ns for $^2P_{1/2}$ and $^2P_{3/2}$ respectively. With a total uncertainty of under 0.4%, these are among the most precise measurements of any atomic state lifetimes to date., Comment: 4 pages with 3 figures

We report the measurement of a Bell inequality violation with a single atom and a single photon prepared in a probabilistic entangled state. This is the first demonstration of such a violation with particles of different species. The entanglement characterization of this hybrid system may also be useful in quantum information applications., Comment: 4 pages, 2 figures

We report on ground state laser cooling of single 111Cd+ ions confined in radio-frequency (Paul) traps. Heating rates of trapped ion motion are measured for two different trapping geometries and electrode materials, where no effort was made to shield the electrodes from the atomic Cd source. The low measured heating rates suggest that trapped 111Cd+ ions may be well-suited for experiments involving quantum control of atomic motion, including applications in quantum information science., Comment: 4 pages, 6 figures, Submitted to PRA

We describe a novel high aspect ratio radiofrequency linear ion trap geometry that is amenable to modern microfabrication techniques. The ion trap electrode structure consists of a pair of stacked conducting cantilevers resulting in confining fields that take the form of fringe fields from parallel plate capacitors. The confining potentials are modeled both analytically and numerically. This ion trap geometry may form the basis for large scale quantum computers or parallel quadrupole mass spectrometers. PACS: 39.25.+k, 03.67.Lx, 07.75.+h, 07.10+Cm, Comment: 14 pages, 16 figures

We report new techniques for driving high-fidelity stimulated Raman transitions in trapped ion qubits. An electro-optic modulator induces sidebands on an optical source, and interference between the sidebands allows coherent Rabi transitions to be efficiently driven between hyperfine ground states separated by 14.53 GHz in a single trapped 111Cd+ ion.

Inelastic neutron scattering profiles of spin waves in the dilute quasi-one-dimensional Ising-like antiferromagnet CsCo_{0.83}Mg_{0.17}Br_3 have been investigated. Calculations of S^{xx}(Q,omega), based on an effective spin Hamiltonian, accurately describe the experimental spin wave spectrum of the 2J mode. The Q dependence of the energy of this spin wave mode follows the analytical prediction omega_{xx}(Q)=(2J)(1-5epsilon^{2}cos^{2}Qa+2epsilon^{2})^{1/2}, calculated by Ishimura and Shiba using perturbation theory., Comment: 13 pages, 4 figures