Abstract:
We investigate rf SQUIDs (Superconducting QUantum Interference Devices), coupled to a resonant input circuit, a readout tank circuit and a preamplifier, by numerically solving the corresponding Langevin equations and optimizing model parameters with respect to noise temperature. We also give approximate analytic solutions for the noise temperature, which we reduce to parameters of the SQUID and the tank circuit in the absence of the input circuit. The analytic solutions agree with numerical simulations of the full circuit to within 10%, and are similar to expressions used to calculate the noise temperature of dc SQUIDs. The best device performance is obtained when \beta_L'\equiv 2\pi L I_0\Phi_0 is 0.6 - 0.8; L is the SQUID inductance, I_0 the junction critical current and \Phi_0 the flux quantum. For a tuned input circuit we find an optimal noise temperature T_{N,opt}\approx 3Tf/f_c, where T, f and f_c denote temperature, signal frequency and junction characteristic frequency, respectively. This value is only a factor of 2 larger than the optimal noise temperatures obtained by approximate analytic theories carried out previously in the limit \beta_L'<<1. We study the dependence of the noise temperature on various model parameters, and give examples using realistic device parameters of the extent to which the intrinsic noise temperature can be realized experimentally.

Abstract:
We investigate the characteristics and noise performance of rf Superconducting Quantum Interference Devices (SQUIDs) by solving the corresponding Langevin equations numerically and optimizing the model parameters with respect to noise energy. After introducing the basic concepts of the numerical simulations, we give a detailed discussion of the performance of the SQUID as a function of all relevant parameters. The best performance is obtained in the crossover region between the dispersive and dissipative regimes, characterized by an inductance parameter \beta_L'\equiv 2\pi L I_0/\Phi_0\approx 1; L is the loop inductance, I_0 the critical current of the Josephson junction, and \Phi_0 the flux quantum. In this regime, which is not well explored by previous analytical approaches, the lowest (intrinsic) values of noise energy are a factor of about 2 above previous estimates based on analytical approaches. However, several other analytical predictions, such as the inverse proportionality of the noise energy on the tank circuit quality factor and the square of the coupling coefficient between the tank circuit and the SQUID loop, could not be well reproduced. The optimized intrinsic noise energy of the rf SQUID is superior to that of the dc SQUID at all temperatures. Although for technologically achievable parameters this advantage shrinks, particularly at low thermal fluctuation levels, we give an example for realistic parameters that leads to a noise energy comparable to that of the dc SQUID even in this regime.

Abstract:
Josephson junctions with a phase drop pi in the ground state allow to create vortices of supercurrent carrying only half of the magnetic flux quantum Phi_0~2.07*10^-15 Wb. Such semifluxons have two-fold degenerate ground states denoted up (with flux +Phi_0/2 and supercurrent circulating clockwise) and down (with flux -Phi_0/2 and supercurrent circulating counterclockwise). We investigate a molecule consisting of two coupled semifluxons in a 0-pi-0 long Josephson junction. The fluxes (polarities) of semifluxons are measured by two on-chip SQUIDs. By varying the dc bias current applied to the 0-pi-0 junction, we demonstrate controllable manipulation and switching between two states, up-down and down-up, of a semifluxon molecule. These results provide a major step towards employing semifluxons as bits or qubits for classical and quantum digital electronics.

Abstract:
Grain boundary bicrystal Josephson junctions of the electron-doped infinite-layer superconductor Sr$_{1-x}$La$_x$CuO$_2$ ($x = 0.15$) were grown by pulsed laser deposition. BaTiO$_3$-buffered $24\,^\circ$ [001]-tilt symmetric SrTiO$_3$ bicrystals were used as substrates. We examined both Cooper pair (CP) and quasiparticle (QP) tunneling by electric transport measurements at temperatures down to 4.2\,K. CP tunneling revealed an extraordinary high critical current density for electron-doped cuprates of $j_c > 10^3\,$A/cm$^2$ at 4.2\,K. Thermally activated phase slippage was observed as dissipative mechanism close to the transition temperature. Out-of-plane magnetic fields $H$ revealed a remarkably regular Fraunhofer-like $j_c(H)$ pattern as well as Fiske and flux flow resonances, both yielding a Swihart velocity of $3.1\cdot10^6\,$m/s. Furthermore, we examined the superconducting gap by means of QP tunneling spectroscopy. The gap was found to be V-shaped with an extrapolated zero temperature energy gap $\Delta_0 \approx 2.4\,$meV. No zero bias conductance peak was observed.

Abstract:
The operation of superconducting coplanar waveguide cavities, as used for circuit quantum electrodynamics and kinetic inductance detectors, in perpendicular magnetic fields normally leads to a reduction of the device performance due to energy dissipating Abrikosov vortices. We experimentally investigate the vortex induced energy losses in such Nb resonators with different spatial distributions of micropatterned pinning sites (antidots) by transmission spectroscopy measurements at 4.2 K. In comparison to resonators without antidots we find a significant reduction of vortex induced losses and thus increased quality factors over a broad range of frequencies and applied powers in moderate fields.

Abstract:
We performed transmission spectroscopy experiments on coplanar half wavelength niobium resonators at a temperature T=4.2 K. We observe not only a strong dependence of the quality factor Q and the resonance frequency f_res on an externally applied magnetic field but also on the magnetic history of our resonators, i.e. on the spatial distribution of trapped Abrikosov vortices in the device. We find these results to be valid for a broad range of frequencies and angles between the resonator plane and the magnetic field direction as well as for resonators with and without antidots near the edges of the center conductor and the ground planes. In a detailed analysis we show, that characteristic features of the experimental data can only be reproduced in calculations, if a highly inhomogeneous rf-current density and a flux density gradient with maxima at the edges of the superconductor is assumed. We furthermore demonstrate, that the hysteretic behaviour of the resonator properties can be used to considerably reduce the vortex induced losses and to fine-tune the resonance frequency by the proper way of cycling to a desired magnetic field.

Abstract:
We present an optimization study of the spin sensitivity of nanoSQUIDs based on resistively shunted grain boundary Josephson junctions. In addition the dc SQUIDs contain a narrow constriction onto which a small magnetic particle can be placed (with its magnetic moment in the plane of the SQUID loop and perpendicular to the grain boundary) for efficient coupling of its stray magnetic field to the SQUID loop. The separation of the location of optimum coupling from the junctions allows for an independent optimization of the coupling factor $\phi_\mu$ and junction properties. We present different methods for calculating $\phi_\mu$ (for a magnetic nanoparticle placed 10\,nm above the constriction) as a function of device geometry and show that those yield consistent results. Furthermore, by numerical simulations we obtain a general expression for the dependence of the SQUID inductance on geometrical parameters of our devices, which allows to estimate their impact on the spectral density of flux noise $S_\Phi$ of the SQUIDs in the thermal white noise regime. Our analysis of the dependence of $S_\Phi$ and $\phi_\mu$ on the geometric parameters of the SQUID layout yields a spin sensitivity $S_\mu^{1/2}=S_\Phi^{1/2}/\phi_\mu$ of a few $\mu_{\rm{B}}/\rm{Hz^{1/2}}$ ($\mu_B$ is the Bohr magneton) for optimized parameters, respecting technological constraints. However, by comparison with experimentally realized devices we find significantly larger values for the measured white flux noise, as compared to our theoretical predictions. Still, a spin sensitivity on the order of $10\,\mu_{\rm B}/\rm{Hz^{1/2}}$ for optimized devices seems to be realistic.

Abstract:
Microwave spectroscopy is a powerful experimental tool to reveal information on the intrinsic properties of superconductors. Superconducting stripline resonators, where the material under study constitutes one of the ground planes, offer a high sensitivity to investigate superconducting bulk samples. In order to improve this measurement technique, we have studied stripline resonators made of niobium, and we compare the results to lead stripline resonators. With this technique we are able to determine the temperature dependence of the complex conductivity of niobium and the energy gap $\Delta(0)=2.1$ meV. Finally we show measurements at the superconducting transition of a tantalum bulk sample using niobium stripline resonators.

Abstract:
We present an optimization study of the spin sensitivity of nanoSQUIDs based on resistively shunted grain boundary Josephson junctions. In addition the dc SQUIDs contain a narrow constriction onto which a small magnetic particle can be placed (with its magnetic moment in the plane of the SQUID loop and perpendicular to the grain boundary) for efficient coupling of its stray magnetic field to the SQUID loop. The separation of the location of optimum coupling from the junctions allows for an independent optimization of the coupling factor $\phi_\mu$ and junction properties. We present different methods for calculating $\phi_\mu$ (for a magnetic nanoparticle placed 10\,nm above the constriction) as a function of device geometry and show that those yield consistent results. Furthermore, by numerical simulations we obtain a general expression for the dependence of the SQUID inductance on geometrical parameters of our devices, which allows to estimate their impact on the spectral density of flux noise $S_\Phi$ of the SQUIDs in the thermal white noise regime. Our analysis of the dependence of $S_\Phi$ and $\phi_\mu$ on the geometric parameters of the SQUID layout yields a spin sensitivity $S_\mu^{1/2}=S_\Phi^{1/2}/\phi_\mu$ of a few $\mu_{\rm{B}}/\rm{Hz^{1/2}}$ ($\mu_B$ is the Bohr magneton) for optimized parameters, respecting technological constraints. However, by comparison with experimentally realized devices we find significantly larger values for the measured white flux noise, as compared to our theoretical predictions. Still, a spin sensitivity on the order of $10\,\mu_{\rm B}/\rm{Hz^{1/2}}$ for optimized devices seems to be realistic.

Abstract:
Presently, cerium-doped LaMnO$_3$ is vividly discussed as an electron-doped counterpart prototype to the well-established hole-doped mixed-valence manganites. Here, La$_{0.7}$Ce$_{0.3}$MnO$_3$ thin films of different thicknesses, degrees of CeO$_2$ phase segregation, and oxygen deficiency, grown on SrTiO$_3$ single crystal substrates, are compared with respect to their resistance-vs.-temperature (R vs. T) behavior from 300~K down to 90~K. While the variation of the film thickness (and thus the degree of epitaxial strain) in the range between 10~nm and 100~nm has only a weak impact on the electrical transport, the degree of oxygen deficiency as well as the existence of CeO$_2$ clusters can completely change the type of hopping mechanism. This is shown by fitting the respective \textit{R-T} curves with three different transport models (adiabatic polaron hopping, Mott variable-range hopping, Efros-Shklovskii variable-range hopping), which are commonly used for the mixed-valence manganites. Several characteristic transport parameters, such as the hopping energies, the carrier localization lengths, as well as the Mn valences are derived from the fitting procedures.