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Josephson junctions in charge and phase picture Theory and applications

Juha Hassel

Published Nov 9, 2004• 0 citations
OpenAlex

Abstract

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.

Related papers

Josephson Junctions: Oscillators and Broadband Spectrometers at Frequencies up to 1 THz

J. Edstam

This thesis is devoted to some selected applications of the Josephson junction oscillator. The initial work was performed using low-Tc Nb/PbBi tunnel junctions, while the later parts were done using the recently developed high-Tc YBa2Cu3O7 (YBCO) Josephson junctions. The latter junctions have raised the hope for Josephson oscillator applications with substantially increased operation frequencies and temperatures. In the first part of this thesis the use of inductor-resistor (LR) shunted tunnel junctions in arrays of phase locked Josephson junction oscillators was investigated. The LR shunt is designed to resonate out the intrinsic tunnel junction capacitance at the operation frequency. We show that LR shunted tunnel junctions have important advantages compared to the commonly used resistively shunted tunnel junctions; i.e. narrower linewidths, higher impedance of the junctions and that they can be optimized also at frequencies higher than about 100 GHz. Design rules for stable, non-chaotic oscillations with optimized output power were developed. Measurements on a non- optimized circuit show that oscillator arrays of LR shunted tunnel junctions can generate substantial power, ~10 nW to a 300 .OMEGA. load at 390 GHz from a 10 junction array. In the second part the phase locking of YBCO Josephson junctions was clearly demonstrated for the first time. Mutual phase locking of two junctions was observed at frequencies between 0.2 and 1 THz, and was only limited by the bandwidth of the coupling circuit. The locking was in good agreement with simulations based on the resistively shunted junction model. The interaction of a single Josephson junction with a 5 junction oscillator array was also measured at frequencies up to about 350 GHz, but was substantially reduced by the high losses of the coupling circuit. The YBCO Josephson junctions were found to be interesting candidates for microwave generation at frequencies approaching 1 THz and oscillator arrays to be mainly limited by the high losses of the coupling circuits at these frequencies. In the third part the interaction of YBCO Josephson junctions with integrated resonators were studied for the first time. Using a novel method, Josephson Broadband Spectroscopy (JOBS), the high frequency properties of the resonators were measured with a bandwidth of up to 1 THz and in the temperature range 4-77 K. The YBCO surface resistance (9 m.OMEGA. at 4 K and 100 GHz) was found to scale as f2 and had a temperature dependence in good agreement with the two-fluid model, modified with 18% non-pairing charge carriers. The YBCO London penetration depth was frequency independent (460 nm at 4 K) and had a temperature dependence in agreement with the two-fluid model.

•Jan 1, 1994•0 citations

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This thesis is a compilation of several works in the area of condensed matter physics, and with devices based on superconducting Josephson junctions (JJ) as the common denominator for the presented projects apart from the work on diffusive systems. Microwave measurements were conducted on a Superconducting Cooper pair transistor to explore its current-phase relationship. Measurements on a JJ-based qubit coupled to a LC resonator revealed the vibronic transitions obeying the Franck-Condon principle. The main body of the thesis is the work done on the Bloch Oscillating Transistor (BOT), an ultra low noise quantum amplifier. In the present work, we investigated the dynamics of the BOT near the bifurcation threshold as well as implemented differential BOTs to check its capability to reject common mode signals. To account for our studies of quantum features in mesoscopic systems other than JJs, we performed an experiment similar to the Hanbury-Brown and Twiss interferometry in optics. For this mesoscopic interference experiment we selected a multiterminal diffusive system. We developed a low temperature noise measurement scheme to study current-current correlations in the GHz frequency range. In our experiments we found a small positive HBT exchange correction factor in the non-interacting limit at low bias voltage in the presence of quantum interference. We found negative exchange correction factor in the hot electron case for similar structures, which agrees well with the theory. Altogether, our experiments demonstrated the theoretically predicted HBT exchange effects in non-interacting and interacting regime of electron transport in a diffusive mesoscopic system.

•Jan 1, 2015•1 citation

Quasicharge models of Josephson junction arrays

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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.

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This Thesis studies opportunities to create a quantum standard for the electric current with the help of tunnel junctions. We use two types of tunnel junctions: superconducting Josephson junctions, and NIS junctions where one of the electrodes is normal (N) and the other one superconducting (S). In both cases, tunnel junctions are employed in a single-electron transistor (SET) structure, which is used to transfer a controlled number k of electrons (e) with the repetition frequency f. The magnitude of the resulting current is thus I = kef. First, we study the Cooper pair sluice, where Josephson junctions are connected as two superconducting quantum interference devices (SQUID). A gate electrode is used to control the charge state of the superconducting island formed between the SQUIDs. The sluice is based on tuning the tunneling rates through the SQUIDs with local magnetic fluxes, which allows to control the direction of the charge transfer. Weak traces of current quantization can be observed up to above 1 nA, which is large enough current for many metrological purposes. However, the accuracy of the current is still far from what is required in metrology. We study also a new type of SQUID structure, the balanced SQUID, which could be used to improve the accuracy of the sluice or in, e.g., some quantum computing applications. Second, we employ NIS junctions in the hybrid (SINIS) single-electron transistor with superconducting leads and a normal-metal island. This structure can be used as the SINIS turnstile which lets electrons to flow one by one in the direction determined by the bias voltage. We report the first experimental results on the SINIS turnstile and two methods to improve the accuracy of the current: increasing the charging energy of the island or connecting the turnstile in a resistive environment. We also show that the SINIS turnstile can be used as an electronic radio-frequency refrigerator where tunneling processes cool the electron temperature of the normal-metal island.

•Jan 1, 2009•0 citations

Josephson transistors interacting with dissipative environment

Juha Leppäkangas

The quantum-mechanical effects typical for single atoms or molecules can be reproduced in micrometer-scale electric devices. In these systems the essential component is a small Josephson junction (JJ) consisting of two superconductors separated by a thin insulator. The quantum phenomena can be controlled in real time by external signals and have a great potential for novel applications. However, their fragility on uncontrolled disturbance caused by typical nearby environments is a drawback for quantum information science, but a virtue for detector technology. Motivated by this we have theoretically studied transistor kind of devices based on single-charge tunneling through small JJs. A common factor of the research is the analysis of the interplay between the coherent Cooperpair (charge carriers in the superconducting state) tunneling and incoherent environmental processes. In the first work we calculate the current due to incoherent Cooper-pair tunneling through a voltage-biased small JJ in series with large JJs and compare the results with recent experiments. We are able to reproduce the main experimental features and interpret these as traces of energy levels and energy bands of the mesoscopic device. In the second work we analyze a similar circuit (asymmetric single-Cooper-pair transistor) but under the assumption that the Cooper-pair tunneling is mainly coherent. This predicts new resonant transport voltages in the circuit due to higher-order processes. However, no clear traces of most of them are seen in the experiments, and similar discrepancy is present also in the case of the symmetric circuit. We continue to study this problem by modeling the interplay between the coherent and incoherent processes more accurately using a density-matrix approach. By this we are able to demonstrate that in typical conditions most of these resonances are indeed washed out by strong decoherence caused by the environment. We also analyze the contribution of three typical weakly interacting dissipative environments: electromagnetic environment, spurious charge fluctuators in the nearby insulating materials, and quasiparticles. In the last work we model the dynamics of a currentbiased JJ perturbed by a smaller JJ using a similar density-matrix approach. We demonstrate that the small JJ can be used also as a detector of the energy-band dynamics in a current biased JJ. The method is also used for modeling the charge transport in the Bloch-oscillating transistor.

•Jan 1, 2009•0 citations

The microwave phase locking in Bloch transistor

Ilya Antonov, Rais S. Shaikhaidarov, Kyung Ho Kim +5 more

Recent experimental demonstration of the quantum coherent phase slip and current quantization in the superconductors, the fundamental phenomena dual to the coherent Cooper pair tunneling and voltage quantization (Shapiro steps), enables the development of a new quantum device, the Bloch transistor (BT). BT has a unique functionality: it can deliver quantized non-dissipative current to the quantum circuit. BT consists of two coupled Josephson Junctions (JJ) in the regime of coherent quantum phase slip. At the heart of the BT operation is a new mechanism for phase-locking the Bloch oscillations in JJs to microwaves via induced charge. The charge phase locking allows not only quantization of current but also gate voltage control of this quantization through the Aharonov-Casher effect. We study the operation of the BT and analyze its parameters. BT technology is scalable and compatible with other superconducting quantum devices, making it part of an emerging cryogenic quantum technology platform.

arXiv:2504.08692•Nature Communications•Feb 2, 2026•4 citations
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.
This thesis is devoted to some selected applications of the Josephson junction oscillator. The initial work was performed using low-Tc Nb/PbBi tunnel junctions, while the later parts were done using the recently developed high-Tc YBa2Cu3O7 (YBCO) Josephson junctions. The latter junctions have raised the hope for Josephson oscillator applications with substantially increased operation frequencies and temperatures. In the first part of this thesis the use of inductor-resistor (LR) shunted tunnel junctions in arrays of phase locked Josephson junction oscillators was investigated. The LR shunt is designed to resonate out the intrinsic tunnel junction capacitance at the operation frequency. We show that LR shunted tunnel junctions have important advantages compared to the commonly used resistively shunted tunnel junctions; i.e. narrower linewidths, higher impedance of the junctions and that they can be optimized also at frequencies higher than about 100 GHz. Design rules for stable, non-chaotic oscillations with optimized output power were developed. Measurements on a non- optimized circuit show that oscillator arrays of LR shunted tunnel junctions can generate substantial power, ~10 nW to a 300 .OMEGA. load at 390 GHz from a 10 junction array. In the second part the phase locking of YBCO Josephson junctions was clearly demonstrated for the first time. Mutual phase locking of two junctions was observed at frequencies between 0.2 and 1 THz, and was only limited by the bandwidth of the coupling circuit. The locking was in good agreement with simulations based on the resistively shunted junction model. The interaction of a single Josephson junction with a 5 junction oscillator array was also measured at frequencies up to about 350 GHz, but was substantially reduced by the high losses of the coupling circuit. The YBCO Josephson junctions were found to be interesting candidates for microwave generation at frequencies approaching 1 THz and oscillator arrays to be mainly limited by the high losses of the coupling circuits at these frequencies. In the third part the interaction of YBCO Josephson junctions with integrated resonators were studied for the first time. Using a novel method, Josephson Broadband Spectroscopy (JOBS), the high frequency properties of the resonators were measured with a bandwidth of up to 1 THz and in the temperature range 4-77 K. The YBCO surface resistance (9 m.OMEGA. at 4 K and 100 GHz) was found to scale as f2 and had a temperature dependence in good agreement with the two-fluid model, modified with 18% non-pairing charge carriers. The YBCO London penetration depth was frequency independent (460 nm at 4 K) and had a temperature dependence in agreement with the two-fluid model.
This thesis is a compilation of several works in the area of condensed matter physics, and with devices based on superconducting Josephson junctions (JJ) as the common denominator for the presented projects apart from the work on diffusive systems. Microwave measurements were conducted on a Superconducting Cooper pair transistor to explore its current-phase relationship. Measurements on a JJ-based qubit coupled to a LC resonator revealed the vibronic transitions obeying the Franck-Condon principle. The main body of the thesis is the work done on the Bloch Oscillating Transistor (BOT), an ultra low noise quantum amplifier. In the present work, we investigated the dynamics of the BOT near the bifurcation threshold as well as implemented differential BOTs to check its capability to reject common mode signals. To account for our studies of quantum features in mesoscopic systems other than JJs, we performed an experiment similar to the Hanbury-Brown and Twiss interferometry in optics. For this mesoscopic interference experiment we selected a multiterminal diffusive system. We developed a low temperature noise measurement scheme to study current-current correlations in the GHz frequency range. In our experiments we found a small positive HBT exchange correction factor in the non-interacting limit at low bias voltage in the presence of quantum interference. We found negative exchange correction factor in the hot electron case for similar structures, which agrees well with the theory. Altogether, our experiments demonstrated the theoretically predicted HBT exchange effects in non-interacting and interacting regime of electron transport in a diffusive mesoscopic system.
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.
This Thesis studies opportunities to create a quantum standard for the electric current with the help of tunnel junctions. We use two types of tunnel junctions: superconducting Josephson junctions, and NIS junctions where one of the electrodes is normal (N) and the other one superconducting (S). In both cases, tunnel junctions are employed in a single-electron transistor (SET) structure, which is used to transfer a controlled number k of electrons (e) with the repetition frequency f. The magnitude of the resulting current is thus I = kef. First, we study the Cooper pair sluice, where Josephson junctions are connected as two superconducting quantum interference devices (SQUID). A gate electrode is used to control the charge state of the superconducting island formed between the SQUIDs. The sluice is based on tuning the tunneling rates through the SQUIDs with local magnetic fluxes, which allows to control the direction of the charge transfer. Weak traces of current quantization can be observed up to above 1 nA, which is large enough current for many metrological purposes. However, the accuracy of the current is still far from what is required in metrology. We study also a new type of SQUID structure, the balanced SQUID, which could be used to improve the accuracy of the sluice or in, e.g., some quantum computing applications. Second, we employ NIS junctions in the hybrid (SINIS) single-electron transistor with superconducting leads and a normal-metal island. This structure can be used as the SINIS turnstile which lets electrons to flow one by one in the direction determined by the bias voltage. We report the first experimental results on the SINIS turnstile and two methods to improve the accuracy of the current: increasing the charging energy of the island or connecting the turnstile in a resistive environment. We also show that the SINIS turnstile can be used as an electronic radio-frequency refrigerator where tunneling processes cool the electron temperature of the normal-metal island.
The quantum-mechanical effects typical for single atoms or molecules can be reproduced in micrometer-scale electric devices. In these systems the essential component is a small Josephson junction (JJ) consisting of two superconductors separated by a thin insulator. The quantum phenomena can be controlled in real time by external signals and have a great potential for novel applications. However, their fragility on uncontrolled disturbance caused by typical nearby environments is a drawback for quantum information science, but a virtue for detector technology. Motivated by this we have theoretically studied transistor kind of devices based on single-charge tunneling through small JJs. A common factor of the research is the analysis of the interplay between the coherent Cooperpair (charge carriers in the superconducting state) tunneling and incoherent environmental processes. In the first work we calculate the current due to incoherent Cooper-pair tunneling through a voltage-biased small JJ in series with large JJs and compare the results with recent experiments. We are able to reproduce the main experimental features and interpret these as traces of energy levels and energy bands of the mesoscopic device. In the second work we analyze a similar circuit (asymmetric single-Cooper-pair transistor) but under the assumption that the Cooper-pair tunneling is mainly coherent. This predicts new resonant transport voltages in the circuit due to higher-order processes. However, no clear traces of most of them are seen in the experiments, and similar discrepancy is present also in the case of the symmetric circuit. We continue to study this problem by modeling the interplay between the coherent and incoherent processes more accurately using a density-matrix approach. By this we are able to demonstrate that in typical conditions most of these resonances are indeed washed out by strong decoherence caused by the environment. We also analyze the contribution of three typical weakly interacting dissipative environments: electromagnetic environment, spurious charge fluctuators in the nearby insulating materials, and quasiparticles. In the last work we model the dynamics of a currentbiased JJ perturbed by a smaller JJ using a similar density-matrix approach. We demonstrate that the small JJ can be used also as a detector of the energy-band dynamics in a current biased JJ. The method is also used for modeling the charge transport in the Bloch-oscillating transistor.
Recent experimental demonstration of the quantum coherent phase slip and current quantization in the superconductors, the fundamental phenomena dual to the coherent Cooper pair tunneling and voltage quantization (Shapiro steps), enables the development of a new quantum device, the Bloch transistor (BT). BT has a unique functionality: it can deliver quantized non-dissipative current to the quantum circuit. BT consists of two coupled Josephson Junctions (JJ) in the regime of coherent quantum phase slip. At the heart of the BT operation is a new mechanism for phase-locking the Bloch oscillations in JJs to microwaves via induced charge. The charge phase locking allows not only quantization of current but also gate voltage control of this quantization through the Aharonov-Casher effect. We study the operation of the BT and analyze its parameters. BT technology is scalable and compatible with other superconducting quantum devices, making it part of an emerging cryogenic quantum technology platform.