Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Transactions on Applied Superconductivity

Modeling of a long Josephson junction coupled to SFQ elements

Yongming Zhang

Published Jun 1, 1999• 2 citations
Publisher

Abstract

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.

DOI
10.1109/77.783917

Related papers

Superconductor digital circuits with π junctions alone

Feng Li, Yuto Takeshita, Masamitsu Tanaka +1 more

We adopt superconductor/ferromagnet/insulator/superconductor (SFIS) Josephson junctions (JJs) as both switching JJs and intrinsic π phase shifters in superconductor digital circuits. The critical current density (Jc) and characteristic voltage (Vc) of the SFIS junctions are about 22 A/cm2 and 22 μV, respectively. The intrinsic π phase shift is confirmed by measuring the suppressed nominal critical current Icn and half-period-shifted modulation pattern of a π–π–π superconducting quantum interference device (SQUID) that contains three π-JJs in a superconducting loop. A single-flux-quantum (SFQ) circuit composed of a DC/SFQ, Josephson transmission line (JTL), and SFQ/DC converter based on SFIS JJs alone is demonstrated at 4.2 K. The energy dissipation of the SFQ/DC converter decreases by 80% because some JJs are self-biased by the π phase shifter. The intrinsic circulating currents induced by the π phase shifters lead to a narrow bias margin (±5%) and even error function, which can be solved by parameters optimization or circuit initialization in the future. The half-modulation period (Φ0/2) of a half-flux-quantum (HFQ) SQUID (a partial HFQ JTL) exhibits propagation of HFQ between π–π–π SQUIDs, indicating that more complex HFQ circuits can be developed with π-JJs alone in the future.

Applied Physics Letters•Apr 17, 2023•10 citations

Demonstration of Interface Circuits Between Half- and Single- Flux- Quantum Circuits

Daiki Hasegawa, Yuto Takeshita, Feng Li +4 more

We demonstrated interface circuits between a half-flux-quantum (HFQ) circuit and a rapid single-flux-quantum (RSFQ) circuit to obtain SFQ/HFQ and HFQ/SFQ converters. These converters were created by simply inserting a resistor between an RSFQ circuit and the adjacent HFQ circuit, where both circuits are based on pulse logic. These converters enable us to create combinatory circuits that make the best use of the features of the two circuits. Using a DC/SFQ, SFQ/HFQ, HFQ/SFQ, and SFQ/DC converter, we measure an HFQ Josephson transmission line (JTL) composed of eight 0-0-π superconducting quantum interference devices (SQUIDs), which are the essential elements of an HFQ circuit. The 0-0-π SQUIDs are composed of two conventional Josephson junctions and a π-shifted ferromagnetic junction. The HFQ JTL demonstrated in this study is driven by a bias current 11-fold lower than that of a similar RSFQ JTL. These experimental results indicate that the HFQ circuit requires power that is two or more orders of magnitude lower than that of an RSFQ circuit.

IEEE Transactions on Applied Superconductivity•Apr 14, 2021•18 citations

Josephson transmission lines with multilayer Josephson junctions

Susanne Lomatch, E. D. Rippert

We present a new type of Josephson transmission line (JTL) in which discrete multilayer Josephson junctions are employed instead of the standard single tri-layer junction technology. It is shown via numerical simulation that such a structure supports the propagation of multiple flux quantum solitons, which are represented in this system by a 2πn kink in the phase difference across a multilayer junction of n superconductor-insulator-superconductor layers. As a practical aspect, parallel and series connected multilayer junctions in a JTL can significantly reduce the need for microstrip line inductance, thereby providing the optimal conditions for large scale integration of JTL-based logic and memory circuitry. In this article we investigate in detail through numerical simulation the properties of JTL designs with multilayer junctions, incorporating expected variations in junction characteristics. A brief description of the current fabrication of multilayer junctions for flux quantum circuitry will be provided.

Journal of Applied Physics•Aug 1, 1994•13 citations

Fluxon interaction in an overdamped Josephson transmission line

V. K. Kaplunenko

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.

Applied Physics Letters•Jun 12, 1995•48 citations

Detection of Low-Energy Fluxons From Discrete Long Josephson Junctions for Ballistic Computing

Han Cai, Liuqi Yu, Waltraut Wustmann +2 more

Single-flux quantum (SFQ) digital logic is typically energy efficient and fast, and logic that uses ballistic and reversible principles will provide a new platform for efficient computing. We are studying long Josephson junctions (LJJs), SFQs within them, and an SFQ detector, all intended for future ballistic logic gate experiments. Specifically, we launch low-energy SFQ into discrete LJJs, made from an array of 80 Josephson junctions (JJs) and connecting inductors. The component JJs have critical currents ($I_{c}$) of only 7.5$\mu \text{A}$. Measurements of the discrete inductors from our LJJs indicate that the LJJ operates in the continuous regime of the Josephson transmission line, giving dynamics similar to continuous LJJs. The Josephson penetration depth is approximately 2.4 unit cells, and the rest energy of the SFQ in the LJJ is$\approx$47 zJ. While the SFQ launcher is fairly standard, the SFQ detector uses JJ critical currents of only$\approx$16$\mu \text{A}$. To understand the effects of noise in the circuit, we measured it in two systems: 1) at 4.2 K using a helium dunk probe; and 2) at 3.5 K in a cryogen-free refrigerator. Data show that SFQ detection events are synchronous with SFQ launch events in both systems. The additional jitter in one system over the other is predominantly attributed to noise in the detector. The traversal of the SFQ is consistent with ballistic propagation. This study shows the creation of low-energy SFQs in LJJs composed of discrete components and a method to detect these SFQs, as a step toward achieving ballistic reversible gates.

arXiv:2406.15671•IEEE Transactions on Applied Superconductivity•Sep 9, 2025•0 citations

Zero-Static-Power RSFQ Interconnects via Inductively Biased Unshunted JTLs in a Planarized Double-JJ-Layer Nb Process

Mingfan Chen, Xue Zhang, Junrong Zhao +4 more

To improve circuit density and minimize static power dissipation in Single Flux Quantum (SFQ) circuits, this work investigates the application of inductively biased, unshunted Josephson transmission lines (JTLs) which achieve zero static power, compared with regular resistively biased JTLs. Both simulation and experiment results confirm that unshunted JTLs can reliably propagate SFQ pulses with a bias current margin larger than 50%. Based on this, a new fabrication process has been developed featuring eight niobium (Nb) layers, including two Nb/Al-AlOx/Nb junction layers, a dedicated bias-inductor layer, and dual DC-power layers. The vertical functional separation allows 2 active layers. The 1stactive layer uses conventional shunted JJs for logic gates, while the 2nduses unshunted JTLs with inductive bias. This configuration eliminates static power in the interconnect network and simplifies thermal management in stacked Rapid SFQ (RSFQ) architectures. A ten-stage unshunted JTL chain and a hybrid half-adder were designed and demonstrated. Measurements show a 66.7% reduction in static power and a 64.7% reduction in area compared with the Chinese Academy of Scienceconventional single-JJ-layer process. These results verify, for the first time, that inductively biased unshunted interconnects can be monolithically integrated with standard RSFQ logic, offering a scalable path toward ultra-dense, lower-power multilayer superconducting circuits.

IEEE Transactions on Applied Superconductivity•Mar 23, 2026•2 citations
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.
We adopt superconductor/ferromagnet/insulator/superconductor (SFIS) Josephson junctions (JJs) as both switching JJs and intrinsic π phase shifters in superconductor digital circuits. The critical current density (Jc) and characteristic voltage (Vc) of the SFIS junctions are about 22 A/cm2 and 22 μV, respectively. The intrinsic π phase shift is confirmed by measuring the suppressed nominal critical current Icn and half-period-shifted modulation pattern of a π–π–π superconducting quantum interference device (SQUID) that contains three π-JJs in a superconducting loop. A single-flux-quantum (SFQ) circuit composed of a DC/SFQ, Josephson transmission line (JTL), and SFQ/DC converter based on SFIS JJs alone is demonstrated at 4.2 K. The energy dissipation of the SFQ/DC converter decreases by 80% because some JJs are self-biased by the π phase shifter. The intrinsic circulating currents induced by the π phase shifters lead to a narrow bias margin (±5%) and even error function, which can be solved by parameters optimization or circuit initialization in the future. The half-modulation period (Φ0/2) of a half-flux-quantum (HFQ) SQUID (a partial HFQ JTL) exhibits propagation of HFQ between π–π–π SQUIDs, indicating that more complex HFQ circuits can be developed with π-JJs alone in the future.
We demonstrated interface circuits between a half-flux-quantum (HFQ) circuit and a rapid single-flux-quantum (RSFQ) circuit to obtain SFQ/HFQ and HFQ/SFQ converters. These converters were created by simply inserting a resistor between an RSFQ circuit and the adjacent HFQ circuit, where both circuits are based on pulse logic. These converters enable us to create combinatory circuits that make the best use of the features of the two circuits. Using a DC/SFQ, SFQ/HFQ, HFQ/SFQ, and SFQ/DC converter, we measure an HFQ Josephson transmission line (JTL) composed of eight 0-0-π superconducting quantum interference devices (SQUIDs), which are the essential elements of an HFQ circuit. The 0-0-π SQUIDs are composed of two conventional Josephson junctions and a π-shifted ferromagnetic junction. The HFQ JTL demonstrated in this study is driven by a bias current 11-fold lower than that of a similar RSFQ JTL. These experimental results indicate that the HFQ circuit requires power that is two or more orders of magnitude lower than that of an RSFQ circuit.
We present a new type of Josephson transmission line (JTL) in which discrete multilayer Josephson junctions are employed instead of the standard single tri-layer junction technology. It is shown via numerical simulation that such a structure supports the propagation of multiple flux quantum solitons, which are represented in this system by a 2πn kink in the phase difference across a multilayer junction of n superconductor-insulator-superconductor layers. As a practical aspect, parallel and series connected multilayer junctions in a JTL can significantly reduce the need for microstrip line inductance, thereby providing the optimal conditions for large scale integration of JTL-based logic and memory circuitry. In this article we investigate in detail through numerical simulation the properties of JTL designs with multilayer junctions, incorporating expected variations in junction characteristics. A brief description of the current fabrication of multilayer junctions for flux quantum circuitry will be provided.
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.
Single-flux quantum (SFQ) digital logic is typically energy efficient and fast, and logic that uses ballistic and reversible principles will provide a new platform for efficient computing. We are studying long Josephson junctions (LJJs), SFQs within them, and an SFQ detector, all intended for future ballistic logic gate experiments. Specifically, we launch low-energy SFQ into discrete LJJs, made from an array of 80 Josephson junctions (JJs) and connecting inductors. The component JJs have critical currents (IcI_{c}Ic​) of only 7.5μA\mu \text{A}μA. Measurements of the discrete inductors from our LJJs indicate that the LJJ operates in the continuous regime of the Josephson transmission line, giving dynamics similar to continuous LJJs. The Josephson penetration depth is approximately 2.4 unit cells, and the rest energy of the SFQ in the LJJ is$\approx47zJ.WhiletheSFQlauncherisfairlystandard,theSFQdetectorusesJJcriticalcurrentsofonly47 zJ. While the SFQ launcher is fairly standard, the SFQ detector uses JJ critical currents of only47zJ.WhiletheSFQlauncherisfairlystandard,theSFQdetectorusesJJcriticalcurrentsofonly\approx161616\mu \text{A}$. To understand the effects of noise in the circuit, we measured it in two systems: 1) at 4.2 K using a helium dunk probe; and 2) at 3.5 K in a cryogen-free refrigerator. Data show that SFQ detection events are synchronous with SFQ launch events in both systems. The additional jitter in one system over the other is predominantly attributed to noise in the detector. The traversal of the SFQ is consistent with ballistic propagation. This study shows the creation of low-energy SFQs in LJJs composed of discrete components and a method to detect these SFQs, as a step toward achieving ballistic reversible gates.
To improve circuit density and minimize static power dissipation in Single Flux Quantum (SFQ) circuits, this work investigates the application of inductively biased, unshunted Josephson transmission lines (JTLs) which achieve zero static power, compared with regular resistively biased JTLs. Both simulation and experiment results confirm that unshunted JTLs can reliably propagate SFQ pulses with a bias current margin larger than 50%. Based on this, a new fabrication process has been developed featuring eight niobium (Nb) layers, including two Nb/Al-AlOx/Nb junction layers, a dedicated bias-inductor layer, and dual DC-power layers. The vertical functional separation allows 2 active layers. The 1stactive layer uses conventional shunted JJs for logic gates, while the 2nduses unshunted JTLs with inductive bias. This configuration eliminates static power in the interconnect network and simplifies thermal management in stacked Rapid SFQ (RSFQ) architectures. A ten-stage unshunted JTL chain and a hybrid half-adder were designed and demonstrated. Measurements show a 66.7% reduction in static power and a 64.7% reduction in area compared with the Chinese Academy of Scienceconventional single-JJ-layer process. These results verify, for the first time, that inductively biased unshunted interconnects can be monolithically integrated with standard RSFQ logic, offering a scalable path toward ultra-dense, lower-power multilayer superconducting circuits.