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

Physical review. B, Condensed matter

Switching current of a Cooper pair transistor with tunable Josephson junctions

Peter Ågren, J. Walter, David B. Haviland

Published Jun 28, 2002• 6 citations
Publisher

Abstract

We investigate the switching current of a Cooper pair transistor with tunable Josephson energy. The junctions are fabricated in a superconducting quantum interference device (SQUID) geometry which allows for an in situ tunable effective Josephson energy by application of a magnetic field. We find a $2e$-periodic switching current versus gate charge. As the magnetic field is increased the switching current stays $2e$-periodic but the magnitude is suppressed. At a magnetic field of half a flux quantum through the SQUID's the switching current is minimum. We can theoretically model the experimental data by assuming a switching current which is proportional to the ideal critical current squarred. We show that such a dependence is expected in the limit where the effect of thermal fluctuations on the system is strong.

DOI
10.1103/physrevb.66.014510

Related papers

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

Measurements of Phase Dynamics in Planar Josephson Junctions and SQUIDs

D. Z. Haxell, Erik Cheah, Filip Křížek +8 more

We experimentally investigate the stochastic phase dynamics of planar Josephson junctions (JJs) and superconducting quantum interference devices (SQUIDs) defined in epitaxial InAs/Al heterostructures, and characterized by a large ratio of Josephson energy to charging energy. We observe a crossover from a regime of macroscopic quantum tunneling to one of phase diffusion as a function of temperature, where the transition temperature T^{*} is gate-tunable. The switching probability distributions are shown to be consistent with a small shunt capacitance and moderate damping, resulting in a switching current which is a small fraction of the critical current. Phase locking between two JJs leads to a difference in switching current between that of a JJ measured in isolation and that of the same JJ measured in an asymmetric SQUID loop. In the case of the loop, T^{*} is also tuned by a magnetic flux.

arXiv:2204.05619•Physical Review Letters•Feb 23, 2023•22 citations

Quantum effects in nanoscale Josephson junction circuits

S. Corlevi

This thesis presents the results of an experimental study on single-charge effects in nanoscale Josephson junctions and Cooper pair transistors (CPTs). In nanoscale Josephson junctions the charging energy EC becomes significant at sub-Kelvin temperatures and single-charge effects, such as the Coulomb blockade of Cooper pair tunneling, influence the transport properties. In order to observe charging effects in a single Josephson junction, the impedance of the electromagnetic environment surrounding the junction has to be larger than the quantum resistance (RQ=h/4e2≈6.45kΩ). In this work the high impedance environment is obtained by biasing the sample under test (single Josephson junction or CPT) with four one-dimensional Josephson junction arrays having SQUID geometry. The advantage of this configuration is the possibility of tuning in situ the effective impedance of the electromagnetic environment. By applying a magnetic field perpendicular to the SQUID loops, the Josephson energy EJ of the SQUIDs is suppressed, resulting in an increase of the measured zero bias resistance of the arrays of several orders of magnitude (104< R0 (Ω) <109). This bias method enables the measurement of the same sample in environments with different impedance. As the impedance of the environment is increased, the current-voltage characteristics (IVCs) of the single Josephson junction and of the CPT show a well defined Coulomb blockade feature with a region of negative differential resistance, signature of the coherent tunneling of single Cooper pairs. The measured IVCs of a single Josephson junction with SQUID geometry in the high impedance environment show a qualitative agreement with the Bloch band theory as the EJ/EC ratio of the junction is tuned with the magnetic field. We also studied a single nontunable Josephson junction with strong coupling (EJ/EC > 1), where the exact dual of the overdamped Josephson effect is realized, resulting in a dual shape of the IVC, where the roles of current and voltage are exchanged. Here, we make for the first time a detailed quantitative comparison with a theory which includes the effect of fluctuations due to the finite temperature of the environment. The measurements on CPTs in the high impedance environment showed that the Coulomb blockade voltage is modulated periodically by the gate-induced charge. The gate-voltage dependence of the CPT changes from e-periodic to 2e-periodic as the impedance of the environment is increased. The high impedance environment reduces quasiparticle tunneling rates, thereby restoring the even parity of the CPT island. This behavior suggests that high impedance leads can be used to effectively suppress quasiparticle poisoning.

•Jan 1, 2006•5 citations

Tunable ±φ,φ0 , and φ0±φ Josephson junction

E. Goldobin, D. Koelle, R. Kleiner

We study a 0-$\ensuremath{\pi}$ dc superconducting quantum interference device (SQUID) with asymmetric inductances and critical currents of the two Josephson junctions (JJs). By considering such a dc SQUID as a black box with two terminals, we calculate its effective current-phase relation ${I}_{s}(\ensuremath{\psi})$ and the Josephson energy $U(\ensuremath{\psi})$, where $\ensuremath{\psi}$ is the Josephson phase across the terminals. We show that there is a domain of parameters where the black box has the properties of a $\ensuremath{\varphi}$ JJ with degenerate ground state phases $\ensuremath{\psi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$. The $\ensuremath{\varphi}$ domain is rather large, so one can easily construct a $\ensuremath{\varphi}$ JJ experimentally. We derive the current phase relation and show that it can be tuned in situ by applying an external magnetic flux resulting in a continuous transition between the systems with static solutions $\ensuremath{\psi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi},\phantom{\rule{0.16em}{0ex}}\ensuremath{\psi}={\ensuremath{\varphi}}_{0} ({\ensuremath{\varphi}}_{0}\ensuremath{\ne}0,\ensuremath{\pi})$ and even $\ensuremath{\psi}={\ensuremath{\varphi}}_{0}\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$. The dependence of ${\ensuremath{\varphi}}_{0}$ on applied magnetic flux is not $2\ensuremath{\pi}$ (one flux quantum) periodic.

arXiv:1504.05858•Physical Review B•Jun 17, 2015•31 citations

Coulomb blockade of Cooper pair tunneling and parity effects in the Cooper pair transistor

S. Corlevi, Wiebke Guichard, F. W. J. Hekking +1 more

We have measured the Cooper pair transistor (CPT) in a tunable electromagnetic environment consisting of four one-dimensional superconducting quantum interference device arrays. The transport properties of the CPT in the high impedance limit, ${Z}_{\mathrm{env}}⪢{R}_{Q}\ensuremath{\simeq}6.45\phantom{\rule{0.3em}{0ex}}\mathrm{k}\ensuremath{\Omega}$, are studied for different ratios of the Josephson coupling energy to the charging energy. As the impedance of the environment is increased, the current-voltage characteristic (IVC) of the CPT develops a Coulomb blockade of Cooper pair tunneling and the measured IVCs agree qualitatively with a theory based on quasicharge dynamics for a CPT. Increasing the impedance of the environment induces a transition in the modulation of the IVC with the gate charge from $e$-periodic to $2e$-periodic.

arXiv:cond-mat/0606407•Physical Review B•Dec 13, 2006•21 citations

Measuring the switching current of a superconducting single electron transistor in a tunable dissipative environment

S Meng, L. R. Yaraskavitch, Andy S. Sachrajda +1 more

We experimentally investigated the switching current I sw of a superconducting single electron transistor (sSET), with competitive Josephson coupling energy E J and charging energy E c , in an in situ tunable dissipative environment. At low temperature, averaged I sw shows a clear 1e periodic function of gate induced charge on the island. The relative contrast of this oscillation increases when E J /Ec is lowered. Increasing dissipation reduce the quantum fluctuations of the phase across the sSET, leading to an increased I sw .

Journal of Physics Conference Series•Dec 17, 2012•0 citations
We investigate the switching current of a Cooper pair transistor with tunable Josephson energy. The junctions are fabricated in a superconducting quantum interference device (SQUID) geometry which allows for an in situ tunable effective Josephson energy by application of a magnetic field. We find a 2e2e2e-periodic switching current versus gate charge. As the magnetic field is increased the switching current stays 2e2e2e-periodic but the magnitude is suppressed. At a magnetic field of half a flux quantum through the SQUID's the switching current is minimum. We can theoretically model the experimental data by assuming a switching current which is proportional to the ideal critical current squarred. We show that such a dependence is expected in the limit where the effect of thermal fluctuations on the system is strong.
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.
We experimentally investigate the stochastic phase dynamics of planar Josephson junctions (JJs) and superconducting quantum interference devices (SQUIDs) defined in epitaxial InAs/Al heterostructures, and characterized by a large ratio of Josephson energy to charging energy. We observe a crossover from a regime of macroscopic quantum tunneling to one of phase diffusion as a function of temperature, where the transition temperature T^{*} is gate-tunable. The switching probability distributions are shown to be consistent with a small shunt capacitance and moderate damping, resulting in a switching current which is a small fraction of the critical current. Phase locking between two JJs leads to a difference in switching current between that of a JJ measured in isolation and that of the same JJ measured in an asymmetric SQUID loop. In the case of the loop, T^{*} is also tuned by a magnetic flux.
This thesis presents the results of an experimental study on single-charge effects in nanoscale Josephson junctions and Cooper pair transistors (CPTs). In nanoscale Josephson junctions the charging energy EC becomes significant at sub-Kelvin temperatures and single-charge effects, such as the Coulomb blockade of Cooper pair tunneling, influence the transport properties. In order to observe charging effects in a single Josephson junction, the impedance of the electromagnetic environment surrounding the junction has to be larger than the quantum resistance (RQ=h/4e2≈6.45kΩ). In this work the high impedance environment is obtained by biasing the sample under test (single Josephson junction or CPT) with four one-dimensional Josephson junction arrays having SQUID geometry. The advantage of this configuration is the possibility of tuning in situ the effective impedance of the electromagnetic environment. By applying a magnetic field perpendicular to the SQUID loops, the Josephson energy EJ of the SQUIDs is suppressed, resulting in an increase of the measured zero bias resistance of the arrays of several orders of magnitude (104< R0 (Ω) <109). This bias method enables the measurement of the same sample in environments with different impedance. As the impedance of the environment is increased, the current-voltage characteristics (IVCs) of the single Josephson junction and of the CPT show a well defined Coulomb blockade feature with a region of negative differential resistance, signature of the coherent tunneling of single Cooper pairs. The measured IVCs of a single Josephson junction with SQUID geometry in the high impedance environment show a qualitative agreement with the Bloch band theory as the EJ/EC ratio of the junction is tuned with the magnetic field. We also studied a single nontunable Josephson junction with strong coupling (EJ/EC > 1), where the exact dual of the overdamped Josephson effect is realized, resulting in a dual shape of the IVC, where the roles of current and voltage are exchanged. Here, we make for the first time a detailed quantitative comparison with a theory which includes the effect of fluctuations due to the finite temperature of the environment. The measurements on CPTs in the high impedance environment showed that the Coulomb blockade voltage is modulated periodically by the gate-induced charge. The gate-voltage dependence of the CPT changes from e-periodic to 2e-periodic as the impedance of the environment is increased. The high impedance environment reduces quasiparticle tunneling rates, thereby restoring the even parity of the CPT island. This behavior suggests that high impedance leads can be used to effectively suppress quasiparticle poisoning.
We study a 0-$\ensuremath{\pi}$ dc superconducting quantum interference device (SQUID) with asymmetric inductances and critical currents of the two Josephson junctions (JJs). By considering such a dc SQUID as a black box with two terminals, we calculate its effective current-phase relation ${I}_{s}(\ensuremath{\psi})$ and the Josephson energy $U(\ensuremath{\psi})$, where $\ensuremath{\psi}$ is the Josephson phase across the terminals. We show that there is a domain of parameters where the black box has the properties of a $\ensuremath{\varphi}$ JJ with degenerate ground state phases $\ensuremath{\psi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$. The $\ensuremath{\varphi}$ domain is rather large, so one can easily construct a $\ensuremath{\varphi}$ JJ experimentally. We derive the current phase relation and show that it can be tuned in situ by applying an external magnetic flux resulting in a continuous transition between the systems with static solutions $\ensuremath{\psi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi},\phantom{\rule{0.16em}{0ex}}\ensuremath{\psi}={\ensuremath{\varphi}}_{0} ({\ensuremath{\varphi}}_{0}\ensuremath{\ne}0,\ensuremath{\pi})$ and even $\ensuremath{\psi}={\ensuremath{\varphi}}_{0}\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$. The dependence of ${\ensuremath{\varphi}}_{0}$ on applied magnetic flux is not $2\ensuremath{\pi}$ (one flux quantum) periodic.
We have measured the Cooper pair transistor (CPT) in a tunable electromagnetic environment consisting of four one-dimensional superconducting quantum interference device arrays. The transport properties of the CPT in the high impedance limit, ${Z}_{\mathrm{env}}⪢{R}_{Q}\ensuremath{\simeq}6.45\phantom{\rule{0.3em}{0ex}}\mathrm{k}\ensuremath{\Omega}$, are studied for different ratios of the Josephson coupling energy to the charging energy. As the impedance of the environment is increased, the current-voltage characteristic (IVC) of the CPT develops a Coulomb blockade of Cooper pair tunneling and the measured IVCs agree qualitatively with a theory based on quasicharge dynamics for a CPT. Increasing the impedance of the environment induces a transition in the modulation of the IVC with the gate charge from eee-periodic to 2e2e2e-periodic.
We experimentally investigated the switching current I sw of a superconducting single electron transistor (sSET), with competitive Josephson coupling energy E J and charging energy E c , in an in situ tunable dissipative environment. At low temperature, averaged I sw shows a clear 1e periodic function of gate induced charge on the island. The relative contrast of this oscillation increases when E J /Ec is lowered. Increasing dissipation reduce the quantum fluctuations of the phase across the sSET, leading to an increased I sw .