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

Quasicharge models of Josephson junction arrays

Samuel A. Wilkinson

Published May 16, 2019• 0 citations
Publisher

Abstract

Josephson junction arrays (JJAs) are engineered many-body quantum systems consisting of several superconducting islands connected by thin tunnel barriers - Josephson junctions (JJs). They are of interest both from a fundamental point of view (e.g. addressing questions of macroscopic quantum physics, providing model systems in which to study complex many-body phenomena) and from the prospect of technological applications (e.g. quantum computing, metrology, metamaterials). In this thesis we present various tools and techniques for the theoretical study of JJAs, and then put these tools to use in the modelling of two particular experiments on JJAs. In our presentation of the physics of JJAs, we emphasise phenomena unique to arrays (i.e. not seen in single junction devices such as qubits). We investigate charge transport through the the bilinear array, consisting of two linear chains of JJs, and show that it exhibits both Coulomb drag and depinning. We predict new phenomena arising from the interplay between Coulomb drag and depinning at voltages higher than have so far been experimentally reported. We then turn our attention to recent experiments in which planar JJAs were placed in 3-D microwave cavities, with vortices being injected via an externally applied magnetic eld. We calculate the impedance spectrum using linear response theory, which enables us to see when new vortices enter the system in the form of sharp changes in the resonance frequency.

DOI
10.25439/rmt.27582768

Related papers

Linear response theory of Josephson junction arrays in a microwave cavity

Samuel A. Wilkinson, Jared H. Cole

Recent experiments on Josephson junction arrays (JJAs) in microwave cavities have opened up a new avenue for investigating the properties of these devices while minimizing the amount of external noise coming from the measurement apparatus itself. These experiments have already shown promise for probing many-body quantum effects in JJAs. In this work, we develop a general theoretical description of such experiments by deriving a quantum phase model for planar JJAs containing quantized vortices. The dynamical susceptibility of this model is calculated for some simple circuits, and signatures of the injection of additional vortices are identified. The effects of decoherence are considered via a Lindblad master equation.

arXiv:1811.01737•Physical review. B./Physical review. B•Apr 2, 2019•2 citations

Josephson junctions in charge and phase picture Theory and applications

Juha Hassel

Properties of weak links between two superconductors, or Josephson junctions, make them interesting for fundamental physics research. Since their discovery over four decades ago, they have provided a unique way to study the behavior of the superconducting quantum phase. More recently, ultra small, or mesoscopic, Josephson junctions with substantial single Cooper pair charging energy have gained interest due to their behavior as macroscopic quantum objects. In addition to the theoretical interest, Josephson junctions can be used as active elements in circuit applications. Particularly, in this Thesis we study two different devices. We develop the required theoretical treatments, derive device properties, and compare the results with experimental data. The first application is a Josephson voltage standard based on externally damped Superconductor - Insulator - Superconductor junctions. It consists of an array of large Josephson junctions connected in series and irradiated with a 70 GHz microwave signal. Phase locking the Josephson dynamics into the signal leads to the quantization of the voltage. This is utilized in metrology. We introduce a new circuit solution based on frequency dependent damping of the junctions. Optimization and some designs for practical arrays are presented. The purpose is to find such a design that the array is fast, has low power consumption and is as stable as possible. Arrays able to generate DC voltages of order 1 volt with metrological accuracy are demonstrated experimentally and their applicability in AC voltage calibrations is analyzed. The second application is the Bloch Oscillating Transistor (BOT). The BOT is based on controlling the Cooper pair current in an ultra small Josephson junction by means of quasiparticles tunneling through a normal junction. As part of the thesis work, the principle of operation is first demonstrated computationally. The model is then refined to yield quantitative predictions of the characteristics. Finally, an analytic theory for the device is developed and the properties as an amplifier are derived.

•Nov 9, 2004•0 citations

回路量子電磁力学の手法を用いたジョセフソン接合列の研究

R. Cosmic

Superconducting Josephson junction arrays (JJAs) are prototypical systems consisting of an array of superconducting islands connected by small Josephson junctions which provide an explicit realization of the canonical XY model of condensed matter physics.In this study we show how circuit quantumelectrodynamics (QED) techniques, perfected for implementing high-quality quantum bits, enable the exploration of new high-frequency regimes of JJAs.By making use of extremely low excitation power and heating of the array, we can probe physics of these systems using one single photon on average.

•Sep 13, 2019•0 citations

Charging effects in small capacitance Josephson junction circuits

Peter Ågren

This thesis describes fabrication, measurements and analysisof two different Josephson junction circuits; the Cooper pairtransistor (CPT) and the one dimensional Josephson junctionarray (JJA). All experiments are conducted in a dilutionrefrigerator with a base temperature of 15{30 mK.In the experiments on CPTs the maximum supercurrent,called the switch- ing current, is measured versus the gatecharge. The importance of filtering of the measurement leads inorder to suppress quasi-particle excitations and to get2e-periodic switching currents is demonstrated. Normal metalgold leads close to the CPTs are introduced to further reducethe effect of quasi-particles. To prove that switching currentis 2e-periodic, magnetic fields and increased temperatures areused to induce a transition to e-periodicity. CPTs where eachJosephson junction is replaced by a Superconducting QuantumInterference de- vice (SQUID) have also been fabricated andmeasured. The SQUIDs make it possible to tune the effectiveJosephson energy with an external magnetic field. The measuredswitching current is tunable in magnitude and 2e-periodic. Theswitching currents are compared with theory. Good agreementbetween the- ory and experiments is found using a model of theCPT in an electrodynamic environment with a high effectivetemperature.The JJAs are also fabricated with a SQUID geometry toenable tuning of the effective Josephson energy. The currentvoltage characteristics (IVCs) of the measured JJAs exhibit aCoulomb blockade of Cooper pair tunneling which is tunable withmagnetic field and periodic with the ux quanta. The IVCs of theJJA show a region of negative differential resistance, alsocalled back- bending. This is interpreted as evidence of Blochoscillations in the JJAs. Two different models are discussed toexplain the measured IVC.The thesis ends by presenting a theoretical proposal ona Josephson junction charge qubit, called the array-qubit. Thearray-qubit consists of an array with N SQUIDs and N +1islands. The two basis states of the qubit corresponds to anexcess Cooper pair on either island 1 or N +1. These two statesare coupled through an Nth-order tunneling process which makesit possible to effectively suppress the Josephson coupling.This facilitate a long relaxation time so that the state of thequbit can be read with a slow detector.

•Jan 1, 2002•4 citations

Josephson Junction, the Quantum Engine: from S.QU.I.D. Sensors to Qubits for Quantum Computers

F.M.A. Moreira

In this review of our own work, we show the physics and applications of Josephson Junction (JJ) and 2D arrays (JJA) made with this powerful quantum engine.This study is based on more than twenty articles published in more than two decades.In actual days, applications of this device go from the most sensitive sensor to measure magnetic flux, called S.QU.I.D. (from Superconducting Quantum Interference Device) to quantum bits.A unit cell of a JJ, with a cost of about a few hundred dollars allows the availability of a magnetometer with a cost of about one million dollars to a quantum computer with cost of about ten million dollars.The Josephson junction is an old quantum engine for a rising new world with incredible disruptive technological possibilities.The article is organized as follows: in section 1 we give a short introduction to the subject; section 2 describes the physics of the Josephson effect and the engineering of the Josephson junction; in section 3 we show the magnetic, transport and thermal properties of 2D-JJA; and in section 4 we show the relation between JJA and superconducting granular systems, in particular those related to High-Temperature Superconductors (HTS).

Research & Development in Material Science•May 24, 2023•1 citation

Spatial and temporal distribution of phase slips in Josephson junction chains

Adem Ergül, Thomas Weißl, Jan Johansson +2 more

The Josephson effect, tunnelling of a supercurrent through a thin insulator layer between two superconducting islands, is a phenomena characterized by a spatially distributed phase of the superconducting condensate. In recent years, there has been a growing focus on Josephson junction devices particularly for the applications of quantum metrology and superconducting qubits. In this study, we report the development of Josephson junction circuit formed by serially connecting many Superconducting Quantum Interference Devices, SQUIDs. We present experimental measurements as well as numerical simulations of a phase-slip center, a SQUID with weaker junctions, embedded in a Josephson junction chain. The DC transport properties of the chain are the result of phase slips which we simulate using a classical model that includes linear external damping, terminating impedance, as well as internal nonlinear quasiparticle damping. We find good agreement between the simulated and the experimental current voltage characteristics. The simulations allow us to examine the spatial and temporal distribution of phase-slip events occurring across the chains and also the existence of travelling voltage pulses which reflect at the chain edges.

Scientific Reports•Sep 7, 2017•9 citations
Josephson junction arrays (JJAs) are engineered many-body quantum systems consisting of several superconducting islands connected by thin tunnel barriers - Josephson junctions (JJs). They are of interest both from a fundamental point of view (e.g. addressing questions of macroscopic quantum physics, providing model systems in which to study complex many-body phenomena) and from the prospect of technological applications (e.g. quantum computing, metrology, metamaterials). In this thesis we present various tools and techniques for the theoretical study of JJAs, and then put these tools to use in the modelling of two particular experiments on JJAs. In our presentation of the physics of JJAs, we emphasise phenomena unique to arrays (i.e. not seen in single junction devices such as qubits). We investigate charge transport through the the bilinear array, consisting of two linear chains of JJs, and show that it exhibits both Coulomb drag and depinning. We predict new phenomena arising from the interplay between Coulomb drag and depinning at voltages higher than have so far been experimentally reported. We then turn our attention to recent experiments in which planar JJAs were placed in 3-D microwave cavities, with vortices being injected via an externally applied magnetic eld. We calculate the impedance spectrum using linear response theory, which enables us to see when new vortices enter the system in the form of sharp changes in the resonance frequency.
Recent experiments on Josephson junction arrays (JJAs) in microwave cavities have opened up a new avenue for investigating the properties of these devices while minimizing the amount of external noise coming from the measurement apparatus itself. These experiments have already shown promise for probing many-body quantum effects in JJAs. In this work, we develop a general theoretical description of such experiments by deriving a quantum phase model for planar JJAs containing quantized vortices. The dynamical susceptibility of this model is calculated for some simple circuits, and signatures of the injection of additional vortices are identified. The effects of decoherence are considered via a Lindblad master equation.
Properties of weak links between two superconductors, or Josephson junctions, make them interesting for fundamental physics research. Since their discovery over four decades ago, they have provided a unique way to study the behavior of the superconducting quantum phase. More recently, ultra small, or mesoscopic, Josephson junctions with substantial single Cooper pair charging energy have gained interest due to their behavior as macroscopic quantum objects. In addition to the theoretical interest, Josephson junctions can be used as active elements in circuit applications. Particularly, in this Thesis we study two different devices. We develop the required theoretical treatments, derive device properties, and compare the results with experimental data. The first application is a Josephson voltage standard based on externally damped Superconductor - Insulator - Superconductor junctions. It consists of an array of large Josephson junctions connected in series and irradiated with a 70 GHz microwave signal. Phase locking the Josephson dynamics into the signal leads to the quantization of the voltage. This is utilized in metrology. We introduce a new circuit solution based on frequency dependent damping of the junctions. Optimization and some designs for practical arrays are presented. The purpose is to find such a design that the array is fast, has low power consumption and is as stable as possible. Arrays able to generate DC voltages of order 1 volt with metrological accuracy are demonstrated experimentally and their applicability in AC voltage calibrations is analyzed. The second application is the Bloch Oscillating Transistor (BOT). The BOT is based on controlling the Cooper pair current in an ultra small Josephson junction by means of quasiparticles tunneling through a normal junction. As part of the thesis work, the principle of operation is first demonstrated computationally. The model is then refined to yield quantitative predictions of the characteristics. Finally, an analytic theory for the device is developed and the properties as an amplifier are derived.
Superconducting Josephson junction arrays (JJAs) are prototypical systems consisting of an array of superconducting islands connected by small Josephson junctions which provide an explicit realization of the canonical XY model of condensed matter physics.In this study we show how circuit quantumelectrodynamics (QED) techniques, perfected for implementing high-quality quantum bits, enable the exploration of new high-frequency regimes of JJAs.By making use of extremely low excitation power and heating of the array, we can probe physics of these systems using one single photon on average.
This thesis describes fabrication, measurements and analysisof two different Josephson junction circuits; the Cooper pairtransistor (CPT) and the one dimensional Josephson junctionarray (JJA). All experiments are conducted in a dilutionrefrigerator with a base temperature of 15{30 mK.In the experiments on CPTs the maximum supercurrent,called the switch- ing current, is measured versus the gatecharge. The importance of filtering of the measurement leads inorder to suppress quasi-particle excitations and to get2e-periodic switching currents is demonstrated. Normal metalgold leads close to the CPTs are introduced to further reducethe effect of quasi-particles. To prove that switching currentis 2e-periodic, magnetic fields and increased temperatures areused to induce a transition to e-periodicity. CPTs where eachJosephson junction is replaced by a Superconducting QuantumInterference de- vice (SQUID) have also been fabricated andmeasured. The SQUIDs make it possible to tune the effectiveJosephson energy with an external magnetic field. The measuredswitching current is tunable in magnitude and 2e-periodic. Theswitching currents are compared with theory. Good agreementbetween the- ory and experiments is found using a model of theCPT in an electrodynamic environment with a high effectivetemperature.The JJAs are also fabricated with a SQUID geometry toenable tuning of the effective Josephson energy. The currentvoltage characteristics (IVCs) of the measured JJAs exhibit aCoulomb blockade of Cooper pair tunneling which is tunable withmagnetic field and periodic with the ux quanta. The IVCs of theJJA show a region of negative differential resistance, alsocalled back- bending. This is interpreted as evidence of Blochoscillations in the JJAs. Two different models are discussed toexplain the measured IVC.The thesis ends by presenting a theoretical proposal ona Josephson junction charge qubit, called the array-qubit. Thearray-qubit consists of an array with N SQUIDs and N +1islands. The two basis states of the qubit corresponds to anexcess Cooper pair on either island 1 or N +1. These two statesare coupled through an Nth-order tunneling process which makesit possible to effectively suppress the Josephson coupling.This facilitate a long relaxation time so that the state of thequbit can be read with a slow detector.
In this review of our own work, we show the physics and applications of Josephson Junction (JJ) and 2D arrays (JJA) made with this powerful quantum engine.This study is based on more than twenty articles published in more than two decades.In actual days, applications of this device go from the most sensitive sensor to measure magnetic flux, called S.QU.I.D. (from Superconducting Quantum Interference Device) to quantum bits.A unit cell of a JJ, with a cost of about a few hundred dollars allows the availability of a magnetometer with a cost of about one million dollars to a quantum computer with cost of about ten million dollars.The Josephson junction is an old quantum engine for a rising new world with incredible disruptive technological possibilities.The article is organized as follows: in section 1 we give a short introduction to the subject; section 2 describes the physics of the Josephson effect and the engineering of the Josephson junction; in section 3 we show the magnetic, transport and thermal properties of 2D-JJA; and in section 4 we show the relation between JJA and superconducting granular systems, in particular those related to High-Temperature Superconductors (HTS).
The Josephson effect, tunnelling of a supercurrent through a thin insulator layer between two superconducting islands, is a phenomena characterized by a spatially distributed phase of the superconducting condensate. In recent years, there has been a growing focus on Josephson junction devices particularly for the applications of quantum metrology and superconducting qubits. In this study, we report the development of Josephson junction circuit formed by serially connecting many Superconducting Quantum Interference Devices, SQUIDs. We present experimental measurements as well as numerical simulations of a phase-slip center, a SQUID with weaker junctions, embedded in a Josephson junction chain. The DC transport properties of the chain are the result of phase slips which we simulate using a classical model that includes linear external damping, terminating impedance, as well as internal nonlinear quasiparticle damping. We find good agreement between the simulated and the experimental current voltage characteristics. The simulations allow us to examine the spatial and temporal distribution of phase-slip events occurring across the chains and also the existence of travelling voltage pulses which reflect at the chain edges.