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Applied Physics Letters

Fluxon interaction in an overdamped Josephson transmission line

V. K. Kaplunenko

Published Jun 12, 1995• 48 citations
Publisher

Abstract

We have simulated fluxon propagation within a Josephson transmission line that is one of the elements of a rapid single flux quantum (RSFQ) circuit. This line is a parallel connection of damped Josephson junctions coupled by superconducting inductances. Geometries with and without mutual inductances between neighboring cells are considered. If the time interval between two fluxons is less than 0.3 φ0Vc−1 (Vc characteristic voltage) a repulsion between them was observed. The repulsion sets a specific time delay between the fluxons that impose a rigid limitation for high frequency performance of RSFQ logic. The delay depends on the shunting parameter, bias current, and values of interconnecting inductances.

DOI
10.1063/1.113759

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We have simulated fluxon propagation within a Josephson transmission line that is one of the elements of a rapid single flux quantum (RSFQ) circuit. This line is a parallel connection of damped Josephson junctions coupled by superconducting inductances. Geometries with and without mutual inductances between neighboring cells are considered. If the time interval between two fluxons is less than 0.3 φ0Vc−1 (Vc characteristic voltage) a repulsion between them was observed. The repulsion sets a specific time delay between the fluxons that impose a rigid limitation for high frequency performance of RSFQ logic. The delay depends on the shunting parameter, bias current, and values of interconnecting inductances.
We propose and demonstrate the functioning of a special Rapid Single Flux Quantum (RSFQ) circuit with frequency-dependent damping. This damping is achieved by shunting individual Josephson junctions by pieces of open-ended RC transmission lines. Our circuit includes a toggle flip-flop cell, Josephson transmission lines transferring single flux quantum pulses to and from this cell, as well as DC/SFQ and SFQ/DC converters. Due to the desired frequency-dispersion in the RC line shunts which ensures sufficiently low noise at low frequencies, such circuits are well-suited for integrating with the flux/phase Josephson qubit and enable its efficient control.
By combining a long Josephson junction (LJJ) with single-flux-quantum (SFQ) circuits, new digital applications for long junctions can be explored. To fully investigate the dynamics of the hybrid LJJ/SFQ circuits, a numerical model was developed for an unshunted long junction coupled to shunted SFQ Josephson transmission line (JTL) through superconducting strips. The model is based on a one-dimensional array of Josephson junctions that is described by a set of discrete sine-Gordon equations. Simulations support our experimental observation that the first zero-field step can exist when the LJJ is terminated by SFQ elements. The influences on the first zero-field step by the self-inductance, the critical current, and the shunt resistance of JTL cells are studied in detail. Simulation also confirms that each 4/spl pi/ phase leap at the end of the long junction creates two separated SFQ pulses after several overdamped JTL cells.
The Rapid Single Flux Quantum (RSFQ) technique is regarded as one of the most promising electronics due to its extremely high operating speed and low power consumption. Middle-scale RSFQ applications operating at multigigahertz frequency have recently been reported on. At such high operating frequencies, the on-chip interconnects start to play a limiting role for the performance of the densely packaged digital circuits. Our previous studies have theoretically investigated the parasitic coupling effects between superconductive microstrip transmission lines and conclusions have been drawn about the critical coupling levels of several typical microstrip geometries. Here, basic RSFQ structures are investigated experimentally, which contain a Josephson transmission line stage with large inductance and can either trap or pass SFQ pulses. These structures are incorporated in critical microstrip layouts, thus being subjected to parasitic coupling. The bias levels are monitored at which the structures start to pass the SFQ pulses with and without coupling influences. Thus, the conclusions of our previous theoretical investigations are verified experimentally.
A transmission line consisting of a parallel connection of shunted Josephson junctions is one of the base elements in the new Rapid Single Flux Quantum (RSFQ) logic. When an additional bias current is applied to the edge junction of the transmission line it generates and injects series of flux quanta on the line. This kind of pulse generators have important applications for testing RSFQ devices at high frequencies. In such experiments unwanted steps always show up in the I-V curve of the generator junction. This problem has been experimentally and numerically investigated for parallel arrays of identical junctions. Steps with extremely low differential resistance are found to be due to the self-induced magnetic field produced by the edge current. The underlying mechanism is that the non-uniform field divides the array into domains consisting of several (unit) cells each containing the same number of flux quanta. The influence of an applied homogeneous external magnetic field and a uniformly distributed bias current is also considered.
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 to the 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 flux quantum (RSFQ) interface circuitry to launch and receive the delayed flux solitons. The parameters of this driver and receiver have been optimized to produce low fluxon speed at launch and impedance matching at the receiver. The delayed solitons are compared to a reference line using a detector with time resolution of better than 16 ps. Both the JTL and RSFQ interface were designed for the Nb 30 A cm −2 process developed at VTT, Finland, with postdeposition of the Al qubit at IPHT, Germany.
We theoretically investigate a readout scheme of the quantum state of a superconducting qubit based on time delay of a single flux quantum (SFQ), also known as a fluxon, propagating in a Josephson transmission line (JTL). We concretely study the time-delay readout based on capacitive coupling between a transmon qubit and a JTL, and we evaluate the time delay depending on the qubit state. We also reveal a feature of the absence of fluxon pinning and exponential suppression of nonadiabatic transitions caused by the propagating fluxon, which is advantageous for the time-delay readout. We extend the analysis to a multi-level transmon as well. Owing to the spectral gap in the JTL, the radiative decay of the qubit mediated by the JTL is exponentially suppressed, and thus the transmission line itself also serves as a filter protecting the qubit. The readout scheme requires neither complicated wiring to low-temperature stages nor bulky microwave components, which are bottlenecks for integration of a large-scale superconducting quantum computer.