Measurements of a Quantum Dot with an Impedance-Matching On-Chip LC Resonator at GHz Frequencies

We report the realization of a bonded-bridge on-chip superconducting coil and its use in impedance-matching a highly ohmic quantum dot (QD) to a $\rm{3~GHz}$ measurement setup. The coil, modeled as a lumped-element $LC$ resonator, is more compact and has a wider bandwidth than resonators based on coplanar transmission lines (e.g. $\lambda/4$ impedance transformers and stub tuners) at potentially better signal-to-noise ratios. In particular for measurements of radiation emitted by the device, such as shot noise, the 50$\times$ larger bandwidth reduces the time to acquire the spectral density. The resonance frequency, close to 3.25 GHz, is three times higher than that of the one previously reported wire-bonded coil. As a proof of principle, we fabricated an $LC$ circuit that achieves impedance-matching to a $\rm{\sim 15~k\Omega}$ load and validate it with a load defined by a carbon nanotube QD of which we measure the shot noise in the Coulomb blockade regime.Comment: 7 pages, 6 figure

Absolutely continuous spectrum for a random potential on a tree with strong transverse correlations and large weighted loops

We consider random Schr\"odinger operators on tree graphs and prove absolutely continuous spectrum at small disorder for two models. The first model is the usual binary tree with certain strongly correlated random potentials. These potentials are of interest since for complete correlation they exhibit localization at all disorders. In the second model we change the tree graph by adding all possible edges to the graph inside each sphere, with weights proportional to the number of points in the sphere.Comment: 25 pages, 4 figure

Shot noise of a quantum dot measured with GHz stub impedance matching

The demand for a fast high-frequency read-out of high impedance devices, such as quantum dots, necessitates impedance matching. Here we use a resonant impedance matching circuit (a stub tuner) realized by on-chip superconducting transmission lines to measure the electronic shot noise of a carbon nanotube quantum dot at a frequency close to 3 GHz in an efficient way. As compared to wide-band detection without impedance matching, the signal to noise ratio can be enhanced by as much as a factor of 800 for a device with an impedance of 100 k$\Omega$. The advantage of the stub resonator concept is the ease with which the response of the circuit can be predicted, designed and fabricated. We further demonstrate that all relevant matching circuit parameters can reliably be deduced from power reflectance measurements and then used to predict the power transmission function from the device through the circuit. The shot noise of the carbon nanotube quantum dot in the Coulomb blockade regime shows an oscillating suppression below the Schottky value of $2eI$, as well an enhancement in specific regions.Comment: 6 pages, 4 figures, supplementar

Partielle Quadrizepssehnenruptur bei einem sechsjährigen Jungen

Zusammenfassung: Bei Kindern werden Ausrissfrakturen der Patella häufiger beobachtet als Rupturen der Quadrizepssehne. Bei verdächtigen Verletzungen der Quadrizepssehne ist differenzialdiagnostisch ein Vergleich zwischen beiden Patellae mit Hilfe von konventionellem Röntgen und Ultraschall sinnvoll. Eine Arthroskopie empfiehlt sich für die Diagnose von begleitenden intraartikulären Knieläsionen und ermöglicht die Kniegelenkspülung mit Evakuierung des Hämarthro

Partielle Quadrizepssehnenruptur bei einem sechsjährigen Jungen

Zusammenfassung: Bei Kindern werden Ausrissfrakturen der Patella häufiger beobachtet als Rupturen der Quadrizepssehne. Bei verdächtigen Verletzungen der Quadrizepssehne ist differenzialdiagnostisch ein Vergleich zwischen beiden Patellae mit Hilfe von konventionellem Röntgen und Ultraschall sinnvoll. Eine Arthroskopie empfiehlt sich für die Diagnose von begleitenden intraartikulären Knieläsionen und ermöglicht die Kniegelenkspülung mit Evakuierung des Hämarthro

Locating the Source of Diffusion in Large-Scale Networks

How can we localize the source of diffusion in a complex network? Due to the tremendous size of many real networks--such as the Internet or the human social graph--it is usually infeasible to observe the state of all nodes in a network. We show that it is fundamentally possible to estimate the location of the source from measurements collected by sparsely-placed observers. We present a strategy that is optimal for arbitrary trees, achieving maximum probability of correct localization. We describe efficient implementations with complexity O(N^{\alpha}), where \alpha=1 for arbitrary trees, and \alpha=3 for arbitrary graphs. In the context of several case studies, we determine how localization accuracy is affected by various system parameters, including the structure of the network, the density of observers, and the number of observed cascades.Comment: To appear in Physical Review Letters. Includes pre-print of main paper, and supplementary materia

Ground States in the Spin Boson Model

We prove that the Hamiltonian of the model describing a spin which is linearly coupled to a field of relativistic and massless bosons, also known as the spin-boson model, admits a ground state for small values of the coupling constant lambda. We show that the ground state energy is an analytic function of lambda and that the corresponding ground state can also be chosen to be an analytic function of lambda. No infrared regularization is imposed. Our proof is based on a modified version of the BFS operator theoretic renormalization analysis. Moreover, using a positivity argument we prove that the ground state of the spin-boson model is unique. We show that the expansion coefficients of the ground state and the ground state energy can be calculated using regular analytic perturbation theory

Electrolyte gate dependent high-frequency measurement of graphene field-effect transistor for sensing applications

We performed radiofrequency (RF) reflectometry measurements at 2.4 GHz on electrolyte-gated graphene field-effect transistors (GFETs) utilizing a tunable stub-matching circuit for impedance matching. We demonstrate that the gate voltage dependent RF resistivity of graphene can be deduced even in the presence of the electrolyte which is in direct contact with the graphene layer. The RF resistivity is found to be consistent with its DC counterpart in the full gate voltage range. Furthermore, in order to access the potential of high-frequency sensing for applications, we demonstrate time-dependent gating in solution with nanosecond time resolution.Comment: 14 pages, 4 figure

Convexity of Resistive Circuit Characteristics

We give topological criteria for the convexity and the concavity of a current or a voltage in a resistive circuit, as a function of a source voltage or current, when the nonlinear resistor characteristics are all either convex or concave. When the criteria are satisfied, all circuits with the same structure will have a convex, or all will have a concave transfer characteristic. The application of the criterion to ladder circuits leads to explicit and easily verifyable conditions

A discrete model for studying existence and uniqueness of solutions in nonlinear resistive circuits

AbstractTwo combinatorial problems raised by the fundamental question of the existence and uniqueness of solutions in nonlinear electric circuits are presented. The first problem, namely the existence of a pair of conjugate trees, has been solved in polynomial time using an original model based on matroïd intersection. For the second problem, which is the search of a particular orientation in a multigraph with labeled edges, an elaborate branch and bound procedure is proposed