We present exact numerical calculations of supercurrent density, inductance, and impurity-induced flux noise of cylindrical superconducting wires in the nonlocal Pippard regime, which occurs when the Pippard coherence length is larger than the London penetration depth. In this regime the supercurrent density displays a peak away from the surface, and changes sign inside the superconductor, signalling a breakdown of the usual approximation of local London electrodynamics with a renormalized penetration depth. Our calculations show that the internal inductance and the bulk flux noise power is enhanced in nonlocal superconductors. In contrast, the kinetic inductance is reduced and the surface flux noise remains the same. As a result, impurity spins in the bulk may dominate the flux noise in superconducting qubits in the Pippard regime, such as the ones using aluminum superconductors with large electron mean free path.
Terahertz Electrodynamics and Kinetic Inductance of Disordered Titanium-Vanadium Alloy Thin Films
Free Electron Laser Utilization Laboratory, Raja Ramanna Center for Advanced Technology（自由电子激光利用实验室，拉贾·拉曼纳先进技术中心）；Homi Bhabha National Institute（霍米·巴哈国家研究所）
We demonstrate single-photon counting at 1550 nm with titanium-nitride (TiN) microwave kinetic inductance detectors. Energy resolution of 0.4 eV and arrival-time resolution of 1.2 microseconds are achieved. 0-, 1-, 2-photon events are resolved and shown to follow Poisson statistics. We find that the temperature-dependent frequency shift deviates from the Mattis-Bardeen theory, and the dissipation response shows a shorter decay time than the frequency response at low temperatures. We suggest that the observed anomalous electrodynamics may be related to quasiparticle traps or subgap states in th…
We investigate thin films of conducting aluminium-oxide, also known as granular aluminium, as a material for superconducting high quality, high kinetic inductance circuits. The films are deposited by an optimised reactive DC magnetron sputter process and characterised using microwave measurement techniques at milli-Kelvin temperatures. We show that, by precise control of the reactive sputter conditions, a high room temperature sheet resistance and therefore high kinetic inductance at low temperatures can be obtained. For a coplanar waveguide resonator with 1.5\,k$Ω$ sheet resistance and a kine…
The introduction of crystalline defects or dopants can give rise to so-called "dirty superconductors", characterized by reduced coherence length and quasiparticle mean free path. In particular, granular superconductors such as Granular Aluminum (GrAl), consisting of remarkably uniform grains connected by Josephson contacts have attracted interest since the sixties thanks to their rich phase diagram and practical advantages, like increased critical temperature, critical field, and kinetic inductance. Here we report the measurement and modeling of circuit quantum electrodynamics properties of Gr…
We have investigated the electrodynamic properties of High-Tc strip-lines made by ion irradiation, in order to evaluate the potentialities of such a technology for RSFQ superconductor digital electronic. SQUID loops of different length and width have been fabricated by ion bombardment of 70 nm thick films through e-beam lithographied shadow masks, and measured at different temperatures. The voltage modulations have been recorded by direct injection of a control current in the SQUIDs arms. The corresponding line inductances have been measured and compared with 3D simulations. A quantitative agr…
Power-Law Suppression of Superfluid Stiffness in High-Kinetic-Inductance NbN Films
Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体与超导研究所）；Leibniz Institute for Solid State and Materials Research Dresden (IFW Dresden)（德累斯顿莱布尼茨固体与材料研究所）；Technische Universität Dresden（德累斯顿工业大学）；CSIR - National Physical Laboratory（印度科学工业研究理事会-国家物理实验室）
Recently transport measurements have been carried out in resistively shunted long superconducting nanowires [M. W. Brenner {\it et. al.}, Phys. Rev. B {\bf{85}}, 224507 (2012)]. The measured voltage-current ($V$-$I$) characteristics was explained by the appearance of the phase slip centers in the shunted wire, and the whole wire was modeled as a single Josephson junction. The kinetic inductance of the long nanowires used in experiments is generally large. Here we argue that the shunted superconducting nanowire acts as a Josephson junction in series with an inductor. The inductance depends on t…
We study the distribution of transport current across superconducting Bi$_2$Sr$_2$CaCu$_2$O$_8$ crystals and the vortex flow through the sample edges. We show that the $T_x$ transition is of electrodynamic rather than thermodynamic nature, below which vortex dynamics is governed by the edge inductance instead of the resistance. This allows measurement of the resistance down to two orders of magnitude below the transport noise. By irradiating the current contacts the resistive step at vortex melting is shown to be due to loss of c-axis correlations rather than breakdown of quasi-long-range orde…
High kinetic inductance materials constitute a valuable resource for superconducting quantum circuits and hybrid architectures. Superconducting granular aluminum (grAl) reaches kinetic sheet inductances in the nH/$\square$ range, with proven applicability in superconducting quantum bits and microwave detectors. Here we show that the single photon internal quality factor $Q_{\mathrm{i}}$ of grAl microwave resonators exceeds $10^5$ in magnetic fields up to 1T, aligned in-plane to the grAl films. Small perpendicular magnetic fields, in the range of 0.5mT, enhance $Q_{\mathrm{i}}$ by approximately…
Kinetic Inductance of Few-Layer NbSe$_2$ in the Two-Dimensional Limit
Research Laboratory of Electronics, Massachusetts Institute of Technology（麻省理工学院电子研究实验室）；Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology（麻省理工学院电气工程和计算机科学系）；John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）；Department of Physics, Massachusetts Institute of Technology（麻省理工学院物理系）；Lincoln Laboratory, Massachusetts Institute of Technology（麻省理工学院林肯实验室）
We address, using concepts of the microscopic theory of superconductivity, parametric amplifiers and kinetic inductance detectors focusing on the interaction of microwave radiation with the superconducting condensate. This interaction was identified recently as the source of the apparent dissipation in microwave superconducting micro-resonators at low temperatures. Since the evaluation of the performance of practical devices based only on the microwave-response is not sufficiently informative about the underlying physical processes, we propose an experimental system to measure the microscopica…
Study of Magnetic Field Resilient High Impedance High-Kinetic Inductance Superconducting Resonators
Institute of Physics, Swiss Federal Institute of Technology (EPFL)（瑞士联邦理工学院物理研究所）；Center for Quantum Science and Engineering, EPFL（苏黎世联邦理工学院量子科学与工程中心）；Department of Physics, ETH Zurich（苏黎世联邦理工学院物理系）
Superconducting boron doped silicon is a promising material for integrated silicon quantum devices. In particular, its low electronic density and moderate disorder make it a suitable candidate for the fabrication of large inductances with low losses at microwave frequencies. Here, we study experimentally the electrodynamics of superconducting silicon thin layers patterned in coplanar waveguide resonators, targeting three key properties: kinetic inductance, internal losses, and the variation of these quantities with the read-out power. We report the first observation in a doped semiconductor of…
Data are presented on mutual and self-inductance of various inductors used in multilayered superconductor integrated circuits: microstrips and striplines with widths of signal traces from 250 nm to a few micrometers, located on the same circuit layer at various distances from each other (from 250 nm to a few micrometers) and/or on different layers spaced vertically; effect of long slits in the ground plane(s) along the inductors on their mutual inductance; inductance of right-angled bends; inductance of meanders. Simple analytical expressions for mutual and self-inductance of the basic inducto…
We reply to the recent Comment [cond-mat/9702231] by J.-M. Duan. Our point of view is markedly different on every issue raised. Much of the disagreement can be traced to a different preception of experimentally relevant length scales. i) We explain the difference between our formulation, which rests on a microscopic basis, and the phenomenological one of the author. ii) Our renormalization scheme is fundamentally right, as the "log(log)" interaction appears only in wires of astronomical lengths. iii) The tunneling barrier is profoundly reduced by the kinetic inductance. iv) We do make an appro…
We investigate the microwave electrodynamic properties of a single superconducting thin film split-ring resonator (SRR). The experiments were performed in an all-Nb waveguide, with Nb wires and Nb SRRs. Transmission data showed a high-Q stopband for a single Nb SRR ($Q \sim 4.5\times10^4$ at 4.2 K) below $T_c$, and no such feature for a Cu SRR, or closed Nb loops, of similar dimensions. Adding SRRs increased the bandwidth, but decreased the insertion loss of the features. Placing the Nb SRR into an array of wires produced a single, elementary negative-index passband ($Q \sim 2.26\times10^4$ at…
Localized quasiparticles in a fluxonium with quasi-two-dimensional amorphous kinetic inductors
University of Colorado Boulder（科罗拉多大学博尔德分校）；National Institute of Standards and Technology（美国国家标准与技术研究院）；Northwestern University（西北大学）；Budapest University of Technology and Economics（布达佩斯技术与经济大学）
Vacuum fluctuations fundamentally affect an atom by inducing a finite excited state lifetime along with a Lamb shift of its transition frequency. Here we report the reverse effect: modification of vacuum modes by a single atom in circuit quantum electrodynamics. Our one-dimensional vacuum is a long section of a high wave impedance (comparable to resistance quantum) superconducting transmission line. It is directly wired to a transmon qubit circuit. Owing to the combination of high impedance and galvanic connection, the transmon's spontaneous emission linewidth can greatly exceed the discrete t…
It is demonstrated that a thin-film Fabry-Perot superconducting resonator can be used to reveal the Little-Parks (LP) effect even at temperatures much lower than the critical temperature. A pair of parallel nanowires is incorporated into the resonator at the point of a supercurrent antinode. As magnetic field is ramped, the Meissner current develops, changing the kinetic inductance of the wires and, correspondingly, the resonance frequency of the resonator, which can be detected. The LP oscillation are revealed as a periodic set of distorted parabolas observed in the transmission of the resona…
Flux transformers are the necessary component of all superconductor digital integrated circuits utilizing ac power for logic cell excitation and clocking, and flux biasing, e.g., Adiabatic Quantum Flux Parametron (AQFP), Reciprocal Quantum Logic, superconducting sensor arrays, qubits, etc. We consider limitations to the integration scale (device number density) imposed by the critical current of the ac power transmission lines and cross coupling between the adjacent transformers. The former sets the minimum line width and the mutual coupling length in the transformer, whereas the latter sets t…
In the emerging field of quantum computation and quantum information, superconducting devices are promising candidates for the implementation of solid-state quantum bits or qubits. Single-qubit operations, direct coupling between two qubits, and the realization of a quantum gate have been reported. However, complex manipulation of entangled states - such as the coupling of a two-level system to a quantum harmonic oscillator, as demonstrated in ion/atom-trap experiments or cavity quantum electrodynamics - has yet to be achieved for superconducting devices. Here we demonstrate entanglement betwe…
