Hannes Toepfer

Demonstration of digital readout circuit for superconducting nanowire single photon detector.

We demonstrate the transfer of single photon triggered electrical pulses from a superconducting nanowire single photon detector (SNSPD) to a single flux quantum (SFQ) pulse. We describe design and test of a digital SFQ based SNSPD readout circuit and demonstrate its correct operation. Both circuits (SNSPD and SFQ) operate under the same cryogenic conditions and are directly connected by wire bonds. A future integration of the present multi-chip configuration seems feasible because both fabrication process and materials are very similar. In contrast to commonly used semiconductor amplifiers, SFQ circuits combine very low power dissipation (a few microwatts) with very high operation speed, thus enabling count-rates of several gigahertz. The SFQ interface circuit simplifies the SNSPD readout and enables large numbers of detectors for future compact multi-pixel systems with single photon counting resolution. The demonstrated circuit has great potential for scaling the present interface solution to 1,000 detectors by using a single SFQ chip.

Design centering methods for yield optimization of cryoelectronic circuits

We present the results of comparison of different design centering methods, e.g. simplicial approximation method and centers-of-gravity method. The effectiveness of the proposed yield optimization strategies is demonstrated by application to various RSFQ circuits and analytical test functions. A SPICE-type program which includes the possibilities of analog behavior modeling and transient noise simulation was used for circuit simulation. Based on these methods, an interactive yield optimization framework for cryo-electronic circuits was developed and tested.

Reduced Power Consumption in Superconducting Electronics

Rapid single flux quantum (RSFQ) electronics is based on the Josephson junction as an active switching element. In standard RSFQ circuits its switching energy is much lower than the static power consumption caused by the resistive current distribution network. Due to this thermal heating of the chip, the maximum number of junctions on a single chip is limited to about 1 million. The frequency-dependent contribution to power dissipation from junction switchings is only about 2 percent of the static one. This fact limits the direct construction of VLSI systems for high-performance computing as well as small-scale circuit applications in the vicinity of ultra-sensitive detectors or even quantum circuits. We present an assessment of different approaches for reducing the static power consumption by investigating the potential of inductive bias distribution networks as well as reduced critical currents. We analyse the operation stability of simple digital circuits with 5 times smaller critical currents at 4.2 K. The combination of the reduced critical currents and inductive biasing can provide digital superconductive circuits with significantly reduced static power consumption.

Orthogonal sequencing multiplexer for superconducting nanowire single-photon detectors with RSFQ electronics readout circuit

We propose an efficient multiplexing technique for superconducting nanowire single-photon detectors based on an orthogonal detector bias switching method enabling the extraction of the average count rate of a set of detectors by one readout line. We implemented a system prototype where the SNSPDs are connected to an integrated cryogenic readout and a pulse merger system based on rapid single flux quantum (RSFQ) electronics. We discuss the general scalability of this concept, analyze the environmental requirements which define the resolvability and the accuracy and demonstrate the feasibility of this approach with experimental results for a SNSPD array with four pixels.

Formal description of the functional behavior of RSFQ logic circuits for design and optimization purposes

For being used in the design of Rapid Single Flux Quantum (RSFQ) circuits in a multipurpose manner, we developed a systematic and consistent approach for modeling the nominal circuit behavior using hardware description languages. We are presenting a method for establishing evaluation criteria for the circuits behavior which can directly be used in the input for circuit simulation and serve as a behavioral reference in yield-driven optimization cycles. Furthermore, this behavioral modeling technique allows for mixed-mode simulation with its advantages of both analysis speed-up and error localization. Finally, we demonstrate the application in high-level circuit synthesis which will be necessary to manage complex design problems.

Optimal Magnet Design for Lorentz Force Eddy-Current Testing

We propose a procedure to determine optimal magnet systems in the framework of the nondestructive evaluation technique Lorentz force eddy-current testing (LET). The underlying optimization problem is clearly defined considering the problem specificity of nondestructive testing scenarios. The quantities involved are classified as design variables, and system and scaling parameters to provide a high level of generality. The objective function is defined as the absolute defect response signal (ADS) of the Lorentz force resulting from an inclusion inside the object under test. Associated constraints are defined according to the applied force sensor technology. A numerical procedure based on the finite-element method is proposed to evaluate the nonlinear objective and constraint functions, and the method of sequential quadratic programming is applied to determine unconstrained and constrained optimal magnet designs. Consequently, we propose a new magnet design based on the Halbach principle in combination with high saturation magnetization iron-cobalt alloys. The proposed magnet system outperforms currently available cylindrical magnets in terms of weight and performance. The corresponding defect response signal is increased up to 180% in the case of small defects located close to the surface of the specimen. The combination of active and passive magnetic materials provides an increase of the ADS by 15% compared with the magnet designs that are built solely from permanent magnet material. The proposed procedure provides a highly adaptive optimization strategy in the framework of LET and proposes new magnet systems with inherently improved characteristics.

Comparison of RSFQ Logic Cells With and Without Phase Shifting Elements by Means of BER Measurements

Rapid single flux quantum (RSFQ) electronics is characterized by a very low switching energy. This advantage leads to a noise susceptibility, which becomes a challenge for large-scale circuits as well as for circuits using Josephson junctions with reduced critical current density. We demonstrate an improved operation range and advanced noise immunity of basic cells resulting from an implemented phase shifting element. One of those elements is the π-phase shifter. It consists of a single flux quantum trapped in a superconducting loop. The π-phase shifter can be easily produced in standard niobium technology without any process modifications. Utilizing a mature process brings advantages concerning the reliable fabrication of complex circuits.

Linearity of a Digital SQUID Magnetometer

A digital SQUID magnetometer measures the magnetic field amplitude by counting integer magnetic flux quanta within its superconducting input loop. Although resolution is limited in comparison to analog SQUID systems, the digital SQUID is able to outrange its analog counterpart with regard to parameters such as slew rate and dynamic range. In this work we evaluate the performance of a digital SQUID based on a three-level logic. Due to this basic principle, we face a combination of two comparator grayzones leading to hysteretic behavior of the sensor that produces a “dead zone” in the signal reversal point. The dependence of the comparator threshold on design parameters is investigated by simulation studies and reconfirmed by experimental results. We were able to reach a total dynamic range of more than 540,000 flux quanta (about 19 bit) with a linearity error of about 5 bit due to the mentioned hysteretic behavior. We discuss the results of our investigations and provide guidelines to extend dynamic range and linearity for future sensor designs.

Effects of a 20 K operation on the bit-error rates of a prospective MgB2 based digital circuit

The discovery of the superconductive properties of magnesium diboride enables us to attempt to produce a rapid single flux quantum (RSFQ) logic device with an operation temperature of about 20 K which can be easily reached with cryocoolers. As elevated temperatures significantly increase the probability of noise-induced errors, we examine the situation in this particular temperature range. We calculate bit-error rates (BER) due to thermal noise for a toggle flip-flop as a typical RSFQ circuit with a clock frequency of 100 GHz. For this, we consider parameter spread and noise separately and observe a very low noise-induced BER. The critical margin diminishes by a small amount only.

Uncertainty Analysis in Transcranial Magnetic Stimulation Using Nonintrusive Polynomial Chaos Expansion

We propose a framework of nonintrusive polynomial chaos methods for transcranial magnetic stimulation (TMS) to investigate the influence of the uncertainty in the electrical conductivity of biological tissues on the induced electric field. The conductivities of three different tissues, namely, cerebrospinal fluid, gray matter (GM), and white matter, are modeled as uniformly distributed random variables. The investigations are performed on a simplified model of a cortical gyrus/sulcus structure. The statistical moments are calculated by means of a generalized polynomial chaos expansion using a regression and cubature approach. Furthermore, the results are compared with the solutions obtained by stochastic collocation. The accuracy of the methods to predict random field distributions was compared by applying different grids and orders of expansion. An investigation on the convergence of the expansion showed that in the present framework, an order 4 expansion is sufficient to determine results with an error of <;1%. The results indicate a major influence of the uncertainty in electrical conductivity on the induced electric field. The standard deviation exceeds values of 20%-40% of the mean induced electric field in the GM. A sensitivity analysis revealed that the uncertainty in electrical conductivity of the GM affects the solution the most. This paper outlines the importance of exact knowledge of the electrical conductivities in TMS in order to provide reliable numerical predictions of the induced electric field. Furthermore, it outlines the performance and the applicability of spectral methods in the framework of TMS for future studies.