Superconducting Nanowires as Nonlinear Inductive Elements for Qubits

We report microwave transmission measurements of superconducting Fabry-Perot resonators (SFPR), having a superconducting nanowire placed at a supercurrent antinode. As the plasma oscillation is excited, the supercurrent is forced to flow through the nanowire. The microwave transmission of the resonator-nanowire device shows a nonlinear resonance behavior, significantly dependent on the amplitude of the supercurrent oscillation. We show that such amplitude-dependent response is due to the nonlinearity of the current-phase relationship (CPR) of the nanowire. The results are explained within a nonlinear oscillator model of the Duffing oscillator, in which the nanowire acts as a purely inductive element, in the limit of low temperatures and low amplitudes. The low quality factor sample exhibits a "crater" at the resonance peak at higher driving power, which is due to dissipation. We observe a hysteretic bifurcation behavior of the transmission response to frequency sweep in a sample with a higher quality factor. The Duffing model is used to explain the Duffing bistability diagram. We also propose a concept of a nanowire-based qubit that relies on the current dependence of the kinetic inductance of a superconducting nanowire.Comment: 28 pages, 7 figure

Nucleation of Superconductivity in a Mesoscopic Loop of Finite Width

The normal/superconducting phase boundary Tc has been calculated for mesoscopic loops, as a function of an applied perpendicular magnetic field H. While for thin-wire loops and filled disks the Tc(H) curves are well known, the intermediate case, namely mesoscopic loops of finite wire width, have been studied much less. The linearized first Ginzburg-Landau equation is solved with the proper normal/vacuum boundary conditions both at the internal and at the external loop radius. For thin-wire loops the Tc(H) oscillations are perfectly periodic, and the Tc(H) background is parabolic (this is the usual Little-Parks effect). For loops of thicker wire width, there is a crossover magnetic field above which Tc(H) becomes quasi-linear, with the period identical to the Tc(H) of a filled disk (i.e. pseudoperiodic oscillations). This dimensional transition is similar to the 2D-3D transition for thin films in a parallel field, where vortices start penetrating the material as soon as the film thickness exceeds the temperature dependent coherence length by a factor 1.8. For the presently studied loops, the crossover point is controlled by a similar condition. In the high field '3D' regime, a giant vortex state establishes, where only a surface superconducting sheath near the sample's outer radius is present.Comment: 7 pages text, 2 EPS figures, uses LaTeX's elsart.sty, proceedings of the First Euroconference on "Vortex Matter in Superconductors", held in Crete (18-24 september 1999

Formation of Quantum Phase Slip Pairs in Superconducting Nanowires

Macroscopic quantum tunneling (MQT) is a fundamental phenomenon of quantum mechanics related to the actively debated topic of quantum-to-classical transition. The ability to realize MQT affects implementation of qubit-based quantum computing schemes and their protection against decoherence. Decoherence in qubits can be reduced by means of topological protection, e.g. by exploiting various parity effects. In particular, paired phase slips can provide such protection for superconducting qubits. Here, we report on the direct observation of quantum paired phase slips in thin-wire superconducting loops. We show that in addition to conventional single phase slips that change superconducting order parameter phase by $2\pi$, there are quantum transitions changing the phase by $4\pi$. Quantum paired phase slips represent a synchronized occurrence of two macroscopic quantum tunneling events, i.e. cotunneling. We demonstrate the existence of a remarkable regime in which paired phase slips are exponentially more probable than single ones

Quantitative analysis of quantum phase slips in superconducting MoGe nanowires revealed by switching-current statistics

We measure quantum and thermal phase-slip rates using the standard deviation of the switching current in superconducting nanowires at high bias current. Our rigorous quantitative analysis provides firm evidence for the presence of quantum phase slips (QPS) in homogeneous nanowires. We observe that as temperature is lowered, thermal fluctuations freeze at a characteristic crossover temperature Tq, below which the dispersion of the switching current saturates to a constant value, indicating the presence of QPS. The scaling of the crossover temperature Tq with the critical temperature Tc is linear, which is consistent with the theory of macroscopic quantum tunneling. We can convert the wires from the initial amorphous phase to a single crystal phase, in situ, by applying calibrated voltage pulses. This technique allows us to probe directly the effects of the wire resistance, critical temperature and morphology on thermal and quantum phase slips.Comment: 7 pages, 7 figures, 1 tabl

Superconducting properties of polycrystalline Nb nanowires templated by carbon nanotubes

Journal ArticleContinuous Nb wires, 7-15 nm in diameter, have been fabricated by sputter-coating single fluorinated carbon nanotubes. Transmission electron microscopy revealed that the wires are polycrystalline, having grain sizes of about 5 nm. The critical current of wires thicker than ~12 nm is very high (107 A/cm2) and comparable to the expected depairing current. The resistance versus temperature curves measured down to 0.3 K are well described by the Langer-Ambegaokar-McCumber-Halperin theory of thermally activated phase slips. Quantum phase slips are suppressed

Vortex matter in mesoscopic superconductors

Superconducting mesoscopic devices in magnetic fields present novel properties which can only be accounted for by both the quantum confinement of the Cooper pairs and by the interaction between the magnetic-field-induced vortices. Sub-micrometer disks, much the same as their semiconductor counterparts known as quantum dots, are being subject to experimental investigation by measuring their conducting properties and, more recently, their magnetization by using state-of-the-art ballistic Hall magnetometry. In this work I review the main results obtained in these two types of experiments as well as the current theoretical developments which are contributing to our understanding of the superconducting condensate in these systems.Comment: 16 pages, 4 figures. Invited presentation at the 13th International Conference on High Magnetic Fields in Semiconductor Physics to appear in Physica