We report the realization of quantum microwave circuits using hybrid superconductor-semiconductor Josephson elements comprised of InAs nanowires contacted by NbTiN. Capacitively shunted single elements behave as transmon circuits with electrically tunable transition frequencies. Two-element circuits also exhibit transmonlike behavior near zero applied flux but behave as flux qubits at half the flux quantum, where nonsinusoidal current-phase relations in the elements produce a double-well Josephson potential. These hybrid Josephson elements are promising for applications requiring microwave superconducting circuits operating in a magnetic field. DOI: 10.1103/PhysRevLett.115.127002 PACS numbers: 85.25.Hv, 62.23.Hj, 74.45.+c, 84.40.Dc In superconducting circuits, macroscopic degrees of freedom like currents and voltages can exhibit quantum mechanical behavior. These circuits can behave as artificial atoms with discrete, anharmonic levels whose transitions can be driven coherently [1]. In the field of circuit quantum electrodynamics (cQED), these artificial atoms are coupled to resonators to perform microwave quantum optics in the solid state [2,3]. Over the past decade, cQED has also grown into a promising platform for quantum information processing, wherein the ground and first-excited levels of each atom serve as an effective qubit [4]. To date, implementations of superconducting quantum circuits have relied almost exclusively on aluminum-aluminum-oxidealuminum (Al=AlOx=Al) tunnel junctions as the source of nonlinearity without dissipation. However, many exciting applications require magnetic fields (∼0.5 T) at which superconductivity in aluminum is destroyed, calling for an alternative approach to realizing microwave artificial atoms.Recent advances in materials development and nanowire (NW) growth have enabled the development of superconductor-semiconductor structures supporting coherent charge transport without dissipation [5] and providing signatures of Majorana bound states [6]. To date, superconductor-semiconductor-superconductor Josephson elements (JEs) have been studied exclusively in quasi-dc [7][8][9][10] and radio-frequency [11] transport. Building microwave circuits operating in the quantum regime, in which transition energies between levels exceed the thermal energy, offers new ways to investigate the physics of hybrid superconductor-semiconductor structures using spectroscopy [12][13][14][15].In this Letter, we report the realization of microwavefrequency cQED circuits made from hybrid JEs based on InAs NWs contacted by NbTiN. Capacitively shunted single JEs behave as weakly anharmonic oscillators, or transmons [16], with transition frequencies tunable by the field effect, i.e., voltage on a proximal side gate. Doubleelement devices show similar transmonlike behavior at zero applied flux but behave as flux qubits [17] near full frustration owing to a double-well Josephson potential arising from nonsinusoidal current-phase relations (CPR s). We observe microwave-driven transitions between states ...

We use magnetoconductance measurements in dual-gated InSb nanowire devices, together with a theoretical analysis of weak antilocalization, to accurately extract spin-orbit strength. In particular, we show that magnetoconductance in our three-dimensional wires is very different compared to wires in two-dimensional electron gases. We obtain a large Rashba spin-orbit strength of 0.5-1 eVÅ corresponding to a spin-orbit energy of 0.25-1 meV. These values underline the potential of InSb nanowires in the study of Majorana fermions in hybrid semiconductor-superconductor devices. Hybrid semiconductor nanowire-superconductor devices are a promising platform for the study of topological superconductivity [1]. Such devices can host Majorana fermions [2,3], bound states with non-Abelian exchange statistics. The realization of a stable topological state requires an energy gap that exceeds the temperature at which experiments are performed (∼50 mK). The strength of the spin-orbit interaction (SOI) is the main parameter that determines the size of this topological gap [4] and thus the potential of these devices for the study of Majorana fermions. The identification of nanowire devices with a strong SOI is therefore essential. This entails both performing measurements on a suitable material and device geometry as well as establishing theory to extract the SOI strength.InSb nanowires are a natural candidate to create devices with a strong SOI, since bulk InSb has a strong SOI [5,6]. Nanowires have been used in several experiments that showed the first signatures of Majorana fermions [7][8][9][10]. Nanowires are either fabricated by etching out wires in planar heterostructures or are grown bottom up. The strong confinement in the growth direction makes etched wires two dimensional (2D) even at high density. SOI has been studied in 2D InSb wires [11] and in planar InSb heterostructures [12], from which a SOI due to structural inversion asymmetry [13], a Rashba SOI α R of 0.03 eVÅ has been obtained [12]. Bottom-up grown nanowires are three dimensional (3D) when the Fermi wavelength is smaller than the wire diameter. In InSb wires of this type, SOI has been studied by performing spectroscopy on quantum dots [14,15] [19,20]. Our approach is to use a high-k dielectric in combination with a top gate that covers the InSb nanowire. The standard method to extract SOI strength in extended regions is through low-field magnetoconductance (MC) measurements [21,22]. Quantum interference (see Fig. 1) in the presence of a strong SOI results in an increased conductance, called weak antilocalization (WAL) [23], that reduces to its classical value when a magnetic field is applied [24]. From fits of MC data to theory a spin relaxation length is extracted. If spin relaxation results from inversion asymmetry, a spin precession length and SOI strength can be defined. To extract SOI strength in nanowires the theory should contain (1) the length over which the electron dephases in the presence of a magnetic field, the magnetic dephasing length [25], and (...

Growth of GaAs/GaAsSb heterostructure nanowires on silicon without the need for gold seed particles is presented. A high vertical yield of GaAs nanowires is first obtained, and then GaAsxSb1-x segments are successfully grown axially in these nanowires. GaAsSb can also be integrated as a shell around the GaAs core. Finally, two GaAsSb segments are grown inside a GaAs nanowire and passivated using an AlxGa1-xAs shell. It is found that no stacking faults or twin planes occur in the GaAsSb segments.