Josephson Transmission Line Research Articles

FLUX CLONING ANOMALITIES IN JOSEPHSON NANO-JUNCTIONS

The propagation of single flux quanta in T -shaped Josephson junctions gives rise to the flux cloning phenomenon. We have studied numerically the dynamics of flux cloning in cases of extended Josephson junctions. The changing thicknesses of T -junctions lead to new and interesting effects in terms of their dynamics. We have found out that when an additional Josephson transmission line is larger than the main Josephson transmission line, numerical simulations do not show the cloning phenomenon and soliton is reflected when it approaches the T junction. This strange result may be happened because the soliton losses more energy in the sharp edge. Although the vortex is moving very highly and it has huge energy but it still does not give birth to a new vortex. We have investigated conditions at which flux cloning occurs when both widths, W and W0, are changing.

Analysis of Series-Connected Discrete Josephson Transmission Line

Employing a generalized resistive-capacitive shunted junction model for Josephson junctions (JJs), the nonlinear wave propagation in the series-connected discrete Josephson transmission line (DJTL) is investigated. A DJTL consists of a finite number of unit cells, each including a segment of superconducting transmission line with a single array stack, or generally a block including an N identical lumped JJ element. As the governing nonlinear wave propagation is a system of nonlinear partial differential equations with mixed boundary conditions, the method of the finite difference time domain is used to solve the equations. By this numerical technique, the behavior of wave propagation along the DJTL can be monitored in time and space domains. Cutoff propagation, dispersive behavior, and shock-wave formation through the DJTL is addressed in this paper.

MODIFIED JOSEPHSON EQUATION AND MEASUREMENT DYNAMICS FOR THE JOSEPHSON TRANSMISSION LINE DETECTOR

By introducing the entangled state representation and following Feynman's assumption that "electron pairs are bosons … A bound pair acts as a Bose particle", we construct a Hamiltonian operator for the Josephson transmission line (JTL) detector, then we use the Heisenberg equation of motion to derive the modified Josephson equation. Based on the modified Josephson equation, the measurement dynamics of JTL detector is investigated, which will be helpful for us to analyze the quantum measurement of JTL detector.

Shock Wave Generation and Cut Off Condition in Nonlinear Series Connected Discrete Josephson Transmission Line

In this paper, we investigate the nonlinear wave propagation in a series-connected discrete Josephson junction transmission line (DJTL). This structure consists of a superconductive coplanar waveguide (CPW), which is assisted by Al Josephson junctions (JJ) in a periodic fashion. Each junction is represented by the basic circuit model which leads to a nonlinear inductor element. Having a significant number of junctions per wavelength, the discrete transmission line (TL) can be considered as a uniform nonlinear transmission line. The nonlinear wave equations are solved numerically by finite difference time domain (FDTD) method. Features and characteristics such as cut-off propagation, dispersive behavior and shock wave formation, which are expected from wave propagation through the nonlinear DJTL, are discussed in this paper.

The Effects of a DC Power Layer in a 10-Nb-Layer Device for SFQ LSIs

We have evaluated the effects of a DC power (DCP) layer in a 10-Nb-layer device using SQUIDs and large-scale Josephson transmission lines (LS-JTLs). The 10-Nb-layer device has recently been developed for SFQ LSIs, with an active layer including Josephson junctions (JJs) at the top, two passive transmission line layers in the middle, and the DCP layer for bias current feeds at the bottom. The evaluation with SQUIDs revealed that the 10-Nb-layer device structure drastically reduced the magnetic flux induced by DC currents flowing through the DCP line, in comparison with the previous advanced process device structure. A major factor for this reduction was an increase in the number of ground layers between the DCP layer and the active layer. In the test of the LS-JTLs containing about 12000 JJs, we obtained the operating margins as wide as numerically simulated ones. We also observed no difference in the margins between a method for extracting ground return currents through ground layers and that through the dedicated layer. These results demonstrated that the 10-Nb-layer device structure is suitable for SFQ-LSIs.

Quantum metamaterials: Electromagnetic waves in Josephson qubit lines

AbstractWe consider the propagation of a classical electromagnetic wave through a transmission line, formed by identical superconducting charge qubits inside a superconducting resonator. Since the qubits can be in a coherent superposition of quantum states, we show that such a system demonstrates interesting new effects, such as a “breathing” photonic crystal with an oscillating bandgap. Similar behaviour is expected from a transmission line formed by flux qubits. The key ingredient of these effects is that the optical properties of the Josephson transmission line are controlled by the quantum coherent state of the qubits (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Fluxon dynamics in boundary driven Josephson transmission line

Analysis of the different stationary states of a boundary driven Frenkel-Kontorova Model and the associated sine-Gordon equation shows the existence a new regime that can be represented by a kink (fluxon) motion back and forth in the restricted geometry. This dynamics is produced by driving the system at one end at a given frequency. As a consequence our result suggests the conception of a device which could switch to the conducting regime not according to intensity range but rather to given (quantized) frequency range. Moreover our findings indicate also a frequency converting scenario by choosing appropriately the system length and injected fluxon number.

Quantum metamaterials: Electromagnetic waves in a Josephson qubit line

We consider the propagation of a classical electromagnetic wave through a transmission line, formed by identical superconducting charge qubits inside a superconducting resonator. Since the qubits can be in a coherent superposition of quantum states, we show that such a system demonstrates interesting effects, such as a ``breathing'' photonic crystal with an oscillating band gap and a ``quantum Archimedean screw'' that transports, at an arbitrary controlled velocity, Josephson plasma waves through a transmission line. The key ingredient of these effects is that the optical properties of the Josephson transmission line are controlled by the quantum coherent state of the qubits.

Superconducting NbN nanowire photo switches for generating single flux quantum pulses

We investigated superconducting NbN nanowire as a photo switch for generating single flux quantum (SFQ) pulses. Epitaxially grown NbN thin films were prepared on MgO(100) substrates by a dc magnetron sputtering method using gas mixture of Ar+N2, without substrate heating. NbN thin films showed Tc of 13.6 K for 8 nm, and 10 K for 4 nm. NbN nanowires were patterned using a electron beam lithography with 200 nm thick electron beam resist. To increasing photo-sensitive regions, we fabricated 50 × 50 μm2 meander patterns with NbN nanowires. Line width of nanowires was varied from 150 nm to 500 nm. Critical current density of NbN nanowires was about 3×106A/cm2 at 4.2 K. We irradiated 850-nm laser pulses via 50-μm multi-mode optical fibers. Repetition frequency and pulse width could be controlled by a pulse pattern generator. The maximum laser pulse power was about 1 mW. Using 150-nm-wide NbN nanowires, half of critical current was suppressed by 1 mW CW laser irradiations. High speed responses were observed for laser pulses with repetition frequency of 1 MHz and pulse width of 2 ns. Besides the NbN nanowire photo switches, we designed an SFQ interface circuit based on Josephson transmission lines. The designed circuit could generate SFQ pulses by input current of 10 μA, 25 GHz current pulses. Dc bias margin of the circuit was ±15% for 60 μA current pulses.

High-speed single flux-quantum up/down counter for neural computation using stochastic logic

We propose the high-speed single flux-quantum(SFQ) up/down counter for the neural computation using stochastic logic. Up and down signals are counted by two independent counters, respectively. The proposed counter circuit can count SFQ signals of 50GHz with large operation margins. To realize the up/down counter, we fabricated a 2-bit up counter circuit and a 2-bit down counter circuit as basic blocks by Nb integrated circuits. The low-speed test results of these circuits show correct operations. We also measured dc voltages of Josephson transmission lines to investigate the responses of carry operations for SFQ pulse trains. The results show that the counter circuits have potential to count 144GHz SFQ pulses.

Resonances between fluxons and plasma waves in underdamped Josephson transmission lines of stripline geometry

We present experiments and theoretical studies on the propagation of Josephson fluxons and electromagnetic waves in parallel arrays of Josephson junctions in the limit of small discreteness. Locking between the fluxon rotation frequency and the frequency of the radiated electromagnetic waves leads to a series of resonances, which we observe on the dc-current-voltage characteristics of the arrays. The arrays consist of small Josephson junctions embedded in an annular superconducting stripline. The experimental data are analyzed using the discrete sine-Gordon model and an extension by including a capacitive interaction between neighboring Josephson junctions. We compare experimental data with both analysis and numerical simulations and find an excellent quantitative agreement.

Design of a ballistic fluxon qubit readout

A detailed design is given for a flux qubit readout using ballistic fluxons. In this scheme,fluxons propagate through an underdamped Josephson transmission line (JTL) coupled tothe qubit, whose state affects the fluxon propagation time. For strong qubit–JTL coupling,and far from the symmetry point, a qubit can be measured with fidelity greater than 99%and measurement time of 4 ns. The readout circuit requires additional rapid single fluxquantum (RSFQ) interface circuitry to launch and receive the delayed flux solitons.The parameters of this driver and receiver have been optimized to produce lowfluxon speed at launch and impedance matching at the receiver. The delayedsolitons are compared to a reference line using a detector with time resolution ofbetter than 16 ps. Both the JTL and RSFQ interface were designed for the Nb30 A cm−2 process developed at VTT, Finland, with postdeposition of the Al qubit at IPHT,Germany.

Reading out the state of a flux qubit by Josephson transmission line solitons

We describe the readout process of the state of a Josephson flux qubit via solitons in Josephson transmission lines (JTLs) as they are in use in the standard rapid single flux quantum technology. We consider the situation where the information about the state of the qubit is stored in the time delay of the soliton. We analyze dissipative underdamped JTLs, take into account their jitter, and provide estimates of the measuring time and efficiency of the measurement for relevant experimental parameters.

Effects of a DC-Power Layer Under a Ground Plane in SFQ Circuits

Large-scale SFQ integrated circuits require a large amount of dc-bias current. The magnetic fields induced by the dc-bias currents and the return currents flowing in a ground plane have a great influence on the performance of SFQ circuits. As an approach to reduce the influence, the dc-power (DCP) layer placed under a ground plane is newly introduced in SRL advanced Nb process. We have experimentally evaluated the effects of the DCP layer using SQUIDs and large-scale Josephson transmission line (JTL) circuits with more than 10,000 junctions. The SQUIDs showed that there was small magnetic flux coupling between the DCP lines and themselves and that the coupled flux was enhanced by the return current. The coupled flux decreased with increasing line width of the DCP lines and with increasing distance from the centerlines of them. In the large-scale JTL tests, the cells with DCP patterns showed wider operating margins than the CONNECT OPEN cells with partial magnetic shielding of bias current lines. The test results also showed that a line shape along the periphery of a cell was more effective than a plane shape within a cell as a DCP layer pattern for bias current feeds.

Technology Related Timing Jitter in Superconducting Electronics

Digital superconducting systems based on Josephson junctions make generally use of the synchronous timing strategy. Today, one of its most promising applications is the high speed and high dynamic range signal sensing. A digital signal acquisition system should have a high resolution as well as a short sampling interval with a well known and constant time period. Short term clock fluctuations (clock jitter) induced by thermal noise can significantly disturb the system operation due to hazards of timing constraint violations. This uncertainty in the time period is currently a strong limitation for further improvements of fast signal sensing systems based on superconductive electronics. Recently, several theoretical and experimental studies describe the timing jitter in simple circuits, like Josephson transmission lines. In the presented work, we analyse different fabrication technologies for rapid single flux quantum (RSFQ) electronics and predict their timing jitter by the numerical solution of stochastic differential equations. We obtained a very good agreement between our simulation data and recent experimental results.

20 ${\hbox{kA/cm}}^{2}$ Process Development for Superconducting Integrated Circuits With 80 GHz Clock Frequency

Results of the development of an advanced fabrication process for superconductor integrated circuits (ICs) with 20 kA/cm2 Nb/AlOx/Nb Josephson junctions is presented. The process has 4 niobium superconducting layers, one MoNx resistor layer with 4.0 Ohm per square sheet resistance for the junction shunting and circuit biasing, and employs circular Josephson junctions with the minimum diameter of 1 mum; total 11 photolithography levels. The goal of this process development is the demonstration of the feasibility of 80 GHz clock speeds in superconducting ICs for digital signal processing (DSP) and high performance computing. Basic components of rapid single flux quantum (RSFQ) logic such as DC/SFQ, SFQ/DC converters, Josephson transmission lines (JTLs), and simple digital circuits such as T-flip-flops and 4-bit digital counters have been fabricated and tested. The T-flip-flops were shown to operate up to 400 GHz with the widest margin of operation of plusmn13% at 325 GHz. Digital testing results on the 4-bit counters as well as the junctions, resistors, and other process parameters are also presented. Prospects for yet higher speeds and very large scale integration are discussed.

A New Design Methodology for Single-Flux-Quantum (SFQ) Logic Circuits Using Passive-Transmission-Line (PTL) Wiring

The introduction of passive-transmission-line (PTL) wiring to large-scale SFQ logic circuits offers several advantages over traditional Josephson-transmission-line (JTL) wiring, such as smaller wiring area, less delay, lower power consumption, and more freedom in routing. PTL wiring can drastically change the style of designing SFQ logic circuits. We propose a new methodology for designing large-scale SFQ circuits using PTL wiring. Aiming at generalizing SFQ circuit design, we chose synchronous clocking. We developed a placer that was suitable for SFQ circuit design to assist us with the new design methodology. The placer first synthesizes an H-tree clock distribution network, placing SFQ pulse splitter cells at each branch. It then places logic cells to minimize the maximum length of data PTL wires, aiming at higher operating speeds. Finally, a router completes the PTL wiring. To evaluate the design methodology we designed an 8-bit general purpose RISC processor. Within twelve hours, we obtained a 15-mm-square SFQ circuit that could operate up to 27.6 GHz. We adopted an advanced Nb process, which was characterized by a critical current density of 10 kA/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , two 5-mum-wide PTL wiring layers, and a minimum cell size of 30 mum times 30 mum. The circuit consisted of about 20,000 logic cells, which approximated more than 400,000 Josephson junctions including splitters to distribute the clock signal.

Decimation Filter With Improved DC Biasing and Data Transfer

Decimation filters are still the most complex and valuable superconductor digital circuits, so it is natural to use them to compare different design techniques. In the paper we discuss two new techniques. The first deals with the DC biasing scheme. For debugging purposes it is convenient to use separate power lines for different functional blocks. However, the lines occupy extra space, which could be unacceptable for a final design, when the decimation filters become part of larger circuits, for example, low-pass or band-pass ADCs. We will discuss an efficient rewiring technique that saves space during the connection of separate power lines after the circuit is debugged. The second technique is a selective use of micro-strip lines. Our solution contrasts with extreme recommendations for micro-strip lines as a universal tool for inter cell connections. More specifically for each connection we select either Josephson transmission or micro-strip line connection to keep the occupied area as small as possible. This highly custom design is possible due to parametric cell technique that dramatically accelerates the design procedure. In particular, we easily converted the circuit initially developed for 1 kA/cm2 standard HYPRES technology to the advanced technology with higher (4.5 kA/cm2 ) critical current density. The filter has 20 GHz and 40 GHz target sampling frequencies for 1 kA/cm2 and 4.5 kA/cm2 fabrication processes respectively. The circuits are fully operational at low frequency.

Flying Superconducting Qubits

A flying qubit is proposed that uses an elementary excitation in superconducting nanocircuits including Josephson transmission lines. Our proposed qubit can resolve an existing qubit-manipulation problem that is unavoidable in solid-state based quantum computers, and has the potential for integrating computation and communication using its flying nature. A concrete example is provided of quantum logic gates using our proposed qubit.

Timing Jitter Measurement in Single-Flux-Quantum Circuits Based on Time-to-Digital Converters With High Time-Resolution

We evaluated timing jitter based on a time-to-digital converter (TDC) having sub-pico seconds time resolution. The measured jitter at liquid helium temperature was 65 fs for an optimally damped simple junction composing a conventional Josephson transmission line fabricated with the NEC standard process. The temperature dependence and shunt resistance dependence of jitter indicate that the jitter originates from thermal noise generated at the shunt resistor of the junction. We also found that the timing jitter of a balanced comparator is much larger than that of a JTL. The jitter of a balanced comparator is independent of temperature. This means that the jitter of a balanced comparator does not arise from thermal noise.