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

Macroscopic quantum phenomena in superconductors: study of phase dynamics and dissipation in moderately damped Josephson junctions

D. Massarotti

Published Apr 2, 2013• 0 citations
OpenAlex

Abstract

The topic of the PhD project is a comparative study of phase dynamics and macroscopic quantum phenomena in moderately damped NbN, YBaCuO grain boundary (GB) Josephson junctions (JJs) and hybrid devices. This type of research activity responds to the needs of better identifying phase dynamics in JJs in the moderately damped regime, which is going to be more and more common in hybrid nanostructures. Issues on a more detailed understanding of coherence, dissipation and noise in the various devices have a relevant role in the progress of quantum circuits. In the last few years, studies of phase dynamics and macroscopic quantum phenomena have been extended to junctions composed of materials other than the traditional low critical temperature superconductors (LTS) and to novel types of structures with unconventional barriers composed for instance of graphene sheets or of grain boundaries. Progress in engineering new materials into junctions and in understanding and controlling the physics of interfaces may offer novel solutions for junctions of superior quality and complementary functionalities, and therefore may lead in the long run to improve also specific qubit performances. For LTS JJs, once the barrier thickness and the critical current density (Jc) have been fixed, a reduction in its size unavoidably leads to a lowering of the critical current and determines a quite different phase dynamics re-normalized to the new scaling energy. Lower critical currents Ic result in lower Josephson energies EJ, and higher levels of dissipation are expected. The range of the energy dynamical parameters is significantly enlarged, and it is technologically easier to reproducibly realize nontrivial configurations. These devices are characterized by intermediate levels of dissipation (moderately damped regime) and by phase diffusion phenomena. The low Jc limit seems to be characteristic also of all futuristic nanohybrids devices incorporating nanowires, and the moderately damped regime (MDR) is intrinsically more common than it could be expected. Measurements of switching current distribution (SCD) in these last years have turned to be standard tools to investigate phase dynamics in unconventional and hybrid systems and nanostructures. High critical temperature superconductors (HTS) are an example of unconventional systems, because of the d-wave order parameter symmetry and of the presence of low-energy quasiparticles, which are expected to induce high level of dissipation and as a consequence to spoil macroscopic quantum coherence. A comparative study in systems so different and complementary is of great interest. During the PhD program, we have performed measurements of SCD, both in the thermal and quantum regime down to 20 mK, on moderately damped NbN/MgO/NbN JJs and on YBCO biepitaxial GB JJs. The NbN JJs exhibit a crossover from thermal activation (TA) to macroscopic quantum tunneling (MQT) regime at about 90 mK. After the MQT saturation, the width of the SCD follows the expected dependence in the TA regime. Deviations are evident in proximity and above the crossover temperature T* (about 1.6K) where we find effects of anti-correlation between the bath temperature and thermal fluctuations since the width of the histograms starts to collapse, and indications of a transition to a third regime called phase diffusion (PD) are evident, such as the change of the switching distributions symmetry. Experimental data have been analyzed through numerical fitting of the switching probability and Monte Carlo simulations, and we found a good agreement with theoretical expectations based on multiple re-trapping processes, which strongly depend on the junction damping. The combined analysis of these three regimes allowed us to extract the fundamental parameters, which completely characterize the dynamics of such moderately damped NbN JJs. In addition, clear signatures of the PD regime have been detected and numerical methods have been developed to estimate the dissipation level in the MDR. As a term of comparison, the studies on moderately damped systems have been also carried out on HTS junctions, which have different levels of intrinsic dissipation induced by low energy quasi-particles, and are for this reason of great impact as a reference. In such JJs we have clearly observed a direct transition from the MQT to the PD regime. The width of the SCDs is constant below 100mK, which is a clearly indication of a quantum activation regime. Above 100mK the negative temperature derivative of the width is consistent with a diffusive motion due to multiple escape and re-trapping in the potential wells. Thermal behavior of the width has been fitted through numerical simulations, thus providing the estimate of the damping factor. These conclusions of a PD regime also in YBaCuO JJs are supported by data in presence of an externally applied magnetic field, and are consistent with the numerical outcomes. Numerical simulations of the thermal behavior of the SCD width for different values of the quality factor ranging from 1 to 10 have been carried out. Such numerical simulations allow us to reconstruct a (Q, kBT/EJ) phase diagram summarizing the various activation regimes. The transition curve between the PD regime and the running state following thermal or quantum activation has been determined numerically by varying the damping factor Q as function of the ratio between the thermal energy and the Josephson energy. The result of the calculation is a universal curve. A phase diagram valid in a large range of dissipation conditions emerges as a functional guide to classify the switching behavior and to settle the fundamental junction parameters and energies in the MDR. It is therefore a reference for phase dynamics of novel types of junction and system for which the nature of the current induced transition from the superconducting to the normal state has not been completely clarified.

Related papers

Macroscopic quantum tunneling and retrapping processes in moderately damped YBaCuO Josephson junctions

D. Massarotti, Luigi Longobardi, Luca Galletti +3 more

The moderately damped regime in Josephson junctions (JJ) is quite common in devices characterized by low critical currents and, therefore, by low Josephson energies. Measurements of the switching current distribution (SCD) are a direct way of determining the phase dynamics in the nontrivial case of moderate damping, which is becoming more common with advances in nanopatterning superconductors and in materials science for fabricating hybrid systems. We report measurements of SCDs, in both the thermal and quantum regimes for moderately damped YBaCuO grain boundary biepitaxial JJs. A direct transition from a phase diffusion regime to macroscopic quantum tunnelling occurs at about 130 mK. The crossover to the quantum regime is determined by the magnetic field and the phase dynamics can be described by a fully consistent set of junction parameters obtained by numerical simulation.

Low Temperature Physics•Mar 1, 2013•9 citations

Study of the phase dynamics in moderately damped Josephson junctions and its applications

Suman Dhamala

The observation of macroscopic quantum tunneling (MQT) manifests the quantumness of macroscopic variables, such as the phase difference across a Josephson junction (JJ). Since then, MQT has become a hallmark experiment to show the quantum nature of JJ-based devices. It has also paved a way to test other macroscopic quantum effects and has led to engineering a variety of artificial atoms, i.e., qubits. However, in the progress of quantum circuits for different applications, it is crucial to understand the influence of thermal and quantum fluctuations, dissipation, and noise to various quantum devices. Thus, the role of the factors mentioned above and the junction parameters $E_{J}$ (Josephson coupling energy) and $E_{C}$ (charging energy) can be scrutinized by understanding the dynamics of the fictitious phase particle. Similarly, in the application perspective, Szilard engine based on SET device are too slow to convert heat into work and are not efficient in-terms of power performance. To overcome the drawbacks, we proposed a high-efficiency fast Szilard engine based on a flux logic device (FLD) and investigated its property numerically and optimize its performance. \\\\ In the first part of the dissertation, we studied the phase dynamics of moderately damped Josephson junctions. The time of flight technique is used to measure the switching current distributions (SCDs). Different dynamical states, thermal activation (TA), MQT, and phase diffusion (PD) are identified from SCDs through well-defined criteria. We observed unambiguous evidence of MQT when temperature is below $\sim0.5\text{-}0.8$ K. The importance of the tilt in the phase dynamics of the junctions, which has been overlooked in previous studies, is clarified. We found that the junction with larger $E_{J}$ but the same $\omega_{p0}$ requires greater tilt and lower temperature to enter MQT regime. \\ \\ In the second part of the dissertation, to overcome the limitation of the SET based Szilard engine, we used superconducting quantum interference device (SQUID) as a one-bit flux logic cell to realize a fast Szilard engine for optimal power. In the past decade, due to technological advancement, the study of energy fluctuations in nano-scale systems such as optical or electrical traps and single-electron tunneling (SET) devices has transformed Szilard's engine to experimental realizations. However, the heat engine realized are slow to convert heat into work limiting their performance in speed and power. The SQUID-based flux logic device (FLD) has a high characteristic frequency, $\omega_\text{p}$/2$\pi \sim$10$^{10}$ Hz, making it an excellent candidate for realizing a high-efficiency Szilard engine with unprecedented performance. We showed that, on average, the proposed heat engine can extract k$_\text{B}T$ln2 of heat per cycle from the thermal reservoir in the quasi-static (QS) limit. In addition, we showed that the FLD-based Szilard engine delivers maximum power when operated about 200 times faster than the threshold speed of quasi-static operation. Our result demonstrates that Szilard's engine's performance based on FLD exceeds other nano-device implementations by orders of magnitude. \\

•Apr 1, 2021•0 citations

Escape dynamics in moderately damped Josephson junctions (Review Article)

D. Massarotti, Luigi Longobardi, Luca Galletti +6 more

The Josephson effect is a privileged access to the macroscopic quantum nature of superconductors. We review some ideas and experimental techniques on macroscopic quantum decay phenomena occurring in Josephson structures. The attention is mainly addressed to intermediate levels of dissipation which characterize a large majority of low critical current Josephson devices and are therefore an avoidable consequence of nanotechnology applied more and more to Josephson devices. Phase diffusion phenomena take over thermal activation in some temperature ranges also affecting the transition to macroscopic quantum tunneling, enriching the phase diagram mostly defined by the Josephson energy, the temperature and the level of dissipation.

Low Temperature Physics•Apr 1, 2012•27 citations

High critical temperature superconductor Josephson junctions for quantum circuit applications

Thilo Bauch, David Gustafsson, Karin Cedergren +5 more

Recent findings of macroscopic quantum properties in high critical temperature superconductor (HTS) Josephson junctions (JJs) point toward the need to revise the role of zero energy quasi-particles in this novel superconductor. We will discuss the possibility of designing superconducting artificial atoms in a transmon configuration to study the low energy excitation spectra of HTS. We have engineered high quality grain boundary JJs on low dielectric constant substrates. By fabricating submicron junctions, we extract values of capacitance and Josephson critical current densities that satisfy the main transmon design requirements. Moreover, the measured critical current noise power extrapolated at 1 Hz gives a dephasing time of 25 ns, which indicates that the observation of macroscopic quantum coherent effects in HTS JJ is a feasible task.

Physica Scripta•Dec 1, 2009•4 citations

Quantum dynamics of spin active and d-wave Josephson junctions

Jens Michelsen

Conventional tunnel Josephson junctions form the basic building blocks of superconducting electronics. Their operation is based on comparatively simple dynamics where the superconducting phases across the junctions is the only dynamical degree of freedom. The goal of the project on which this thesis is based, is to understand the physics and develop a consistent theoretical description of the quantum dynamics of unconventional Josephson structures: spin active junctions, junctions containing low energy quasiparticles, and junctions composed of $d$-wave superconductors. Spin active Josephson junctions involve the additional degree of freedom of quasiparticle spin. Here we theoretically investigate the spin-structure of the current carrying interface bound states - Andreev Bound States (ABS), and induced ground state spin polarization of a short (shorter than the superconducting coherence length) nanowire junction containing a localized magnetic moment. We show that temporal variation of the superconducting phase difference and magnetic moment induce rotations in spin polarized and unpolarized subspaces respectively, which is manifested by temporal oscillation of the Josephson current.The interlevel transitions obey a selection rule that forbids manipulations in a certain region ofexternal parameters and results from specific properties of Andreev bound states in magnetic contacts where, in a certain regime of phase bias and strength of magnetic scatterer, ABS belong to different eigenstates of the combined charge and parity inversion symmetry operator.A general framework is developed to include low energy quasiparticle states into the dynamics of Josephson junctions. Such states exist in e.g. constriction type junctions with high transparency channels or resonant states, as well as in junctions of unconventional superconductors. The existence of such states prevent the separation of energy scales which in conventional tunnel junctions freezes out the quasiparticle degrees of freedom. We show that the resonant interaction with such low energy states rather than the Josephson potential defines the nonlinear Josephson dynamics at small amplitudes.The framework is applied to high temperature Josephson junctions, whose unconventional order parameter admits ABS with energies in the middle of the superconducting gap - Mid Gap States (MGS). In addition to the non-linear dynamics induced by the MGS, we identify a reentrance effect in the transition between thermal activation and macroscopic quantum tunneling associated with the MGS, and connect this phenomenon to experimental observations.

•Jan 1, 2010•0 citations

Feasibility of a High Temperature Superconductor rf-SQUID Based on Biepitaxial Josephson Junction Technology

Luigi Longobardi, D. Stornaiuolo, Gian Paolo Papari +1 more

Recently, the observation of macroscopic quantum effects in high critical temperature superconductor (HTS) Josephson junctions (JJs) paved the way to the possible use of HTS in quantum hybrid circuits. Dissipation in HTS JJs has been proven to be below expectations, even in junction configurations designed to fully exploit the functionality of a d-wave order parameter symmetry, where low energy quasi-particles can be more harmful for coherence.

IEEE Transactions on Applied Superconductivity•Jan 3, 2011•1 citation
The topic of the PhD project is a comparative study of phase dynamics and macroscopic quantum phenomena in moderately damped NbN, YBaCuO grain boundary (GB) Josephson junctions (JJs) and hybrid devices. This type of research activity responds to the needs of better identifying phase dynamics in JJs in the moderately damped regime, which is going to be more and more common in hybrid nanostructures. Issues on a more detailed understanding of coherence, dissipation and noise in the various devices have a relevant role in the progress of quantum circuits.
In the last few years, studies of phase dynamics and macroscopic quantum phenomena have been extended to junctions composed of materials other than the traditional low critical temperature superconductors (LTS) and to novel types of structures with unconventional barriers composed for instance of graphene sheets or of grain boundaries. Progress in engineering new materials into junctions and in understanding and controlling the physics of interfaces may offer novel solutions for junctions of superior quality and complementary functionalities, and therefore may lead in the long run to improve also specific qubit performances.
For LTS JJs, once the barrier thickness and the critical current density (Jc) have been fixed, a reduction in its size unavoidably leads to a lowering of the critical current and determines a quite different phase dynamics re-normalized to the new scaling energy. Lower critical currents Ic result in lower Josephson energies EJ, and higher levels of dissipation are expected. The range of the energy dynamical parameters is significantly enlarged, and it is technologically easier to reproducibly realize nontrivial configurations. These devices are characterized by intermediate levels of dissipation (moderately damped regime) and by phase diffusion phenomena. The low Jc limit seems to be characteristic also of all futuristic nanohybrids devices incorporating nanowires, and the moderately damped regime (MDR) is intrinsically more common than it could be expected.
Measurements of switching current distribution (SCD) in these last years have turned to be standard tools to investigate phase dynamics in unconventional and hybrid systems and nanostructures. High critical temperature superconductors (HTS) are an example of unconventional systems, because of the d-wave order parameter symmetry and of the presence of low-energy quasiparticles, which are expected to induce high level of dissipation and as a consequence to spoil macroscopic quantum coherence. A comparative study in systems so different and complementary is of great interest.
During the PhD program, we have performed measurements of SCD, both in the thermal and quantum regime down to 20 mK, on moderately damped NbN/MgO/NbN JJs and on YBCO biepitaxial GB JJs. The NbN JJs exhibit a crossover from thermal activation (TA) to macroscopic quantum tunneling (MQT) regime at about 90 mK. After the MQT saturation, the width of the SCD follows the expected dependence in the TA regime. Deviations are evident in proximity and above the crossover temperature T* (about 1.6K) where we find effects of anti-correlation between the bath temperature and thermal fluctuations since the width of the histograms starts to collapse, and indications of a transition to a third regime called phase diffusion (PD) are evident, such as the change of the switching distributions symmetry.
Experimental data have been analyzed through numerical fitting of the switching probability and Monte Carlo simulations, and we found a good agreement with theoretical expectations based on multiple re-trapping processes, which strongly depend on the junction damping. The combined analysis of these three regimes allowed us to extract the fundamental parameters, which completely characterize the dynamics of such moderately damped NbN JJs. In addition, clear signatures of the PD regime have been detected and numerical methods have been developed to estimate the dissipation level in the MDR.
As a term of comparison, the studies on moderately damped systems have been also carried out on HTS junctions, which have different levels of intrinsic dissipation induced by low energy quasi-particles, and are for this reason of great impact as a reference.
In such JJs we have clearly observed a direct transition from the MQT to the PD regime. The width of the SCDs is constant below 100mK, which is a clearly indication of a quantum activation regime. Above 100mK the negative temperature derivative of the width is consistent with a diffusive motion due to multiple escape and re-trapping in the potential wells. Thermal behavior of the width has been fitted through numerical simulations, thus providing the estimate of the damping factor. These conclusions of a PD regime also in YBaCuO JJs are supported by data in presence of an externally applied magnetic field, and are consistent with the numerical outcomes.
Numerical simulations of the thermal behavior of the SCD width for different values of the quality factor ranging from 1 to 10 have been carried out. Such numerical simulations allow us to reconstruct a (Q, kBT/EJ) phase diagram summarizing the various activation regimes. The transition curve between the PD regime and the running state following thermal or quantum activation has been determined numerically by varying the damping factor Q as function of the ratio between the thermal energy and the Josephson energy. The result of the calculation is a universal curve. A phase diagram valid in a large range of dissipation conditions emerges as a functional guide to classify the switching behavior and to settle the fundamental junction parameters and energies in the MDR. It is therefore a reference for phase dynamics of novel types of junction and system for which the nature of the current induced transition from the superconducting to the normal state has not been completely clarified.
The moderately damped regime in Josephson junctions (JJ) is quite common in devices characterized by low critical currents and, therefore, by low Josephson energies. Measurements of the switching current distribution (SCD) are a direct way of determining the phase dynamics in the nontrivial case of moderate damping, which is becoming more common with advances in nanopatterning superconductors and in materials science for fabricating hybrid systems. We report measurements of SCDs, in both the thermal and quantum regimes for moderately damped YBaCuO grain boundary biepitaxial JJs. A direct transition from a phase diffusion regime to macroscopic quantum tunnelling occurs at about 130 mK. The crossover to the quantum regime is determined by the magnetic field and the phase dynamics can be described by a fully consistent set of junction parameters obtained by numerical simulation.
The observation of macroscopic quantum tunneling (MQT) manifests the quantumness of macroscopic variables, such as the phase difference across a Josephson junction (JJ). Since then, MQT has become a hallmark experiment to show the quantum nature of JJ-based devices. It has also paved a way to test other macroscopic quantum effects and has led to engineering a variety of artificial atoms, i.e., qubits. However, in the progress of quantum circuits for different applications, it is crucial to understand the influence of thermal and quantum fluctuations, dissipation, and noise to various quantum devices. Thus, the role of the factors mentioned above and the junction parameters EJE_{J}EJ​ (Josephson coupling energy) and ECE_{C}EC​ (charging energy) can be scrutinized by understanding the dynamics of the fictitious phase particle. Similarly, in the application perspective, Szilard engine based on SET device are too slow to convert heat into work and are not efficient in-terms of power performance. To overcome the drawbacks, we proposed a high-efficiency fast Szilard engine based on a flux logic device (FLD) and investigated its property numerically and optimize its performance. \\\\ In the first part of the dissertation, we studied the phase dynamics of moderately damped Josephson junctions. The time of flight technique is used to measure the switching current distributions (SCDs). Different dynamical states, thermal activation (TA), MQT, and phase diffusion (PD) are identified from SCDs through well-defined criteria. We observed unambiguous evidence of MQT when temperature is below ∼0.5-0.8\sim0.5\text{-}0.8∼0.5-0.8 K. The importance of the tilt in the phase dynamics of the junctions, which has been overlooked in previous studies, is clarified. We found that the junction with larger EJE_{J}EJ​ but the same ωp0\omega_{p0}ωp0​ requires greater tilt and lower temperature to enter MQT regime. \\ \\ In the second part of the dissertation, to overcome the limitation of the SET based Szilard engine, we used superconducting quantum interference device (SQUID) as a one-bit flux logic cell to realize a fast Szilard engine for optimal power. In the past decade, due to technological advancement, the study of energy fluctuations in nano-scale systems such as optical or electrical traps and single-electron tunneling (SET) devices has transformed Szilard's engine to experimental realizations. However, the heat engine realized are slow to convert heat into work limiting their performance in speed and power. The SQUID-based flux logic device (FLD) has a high characteristic frequency, ωp\omega_\text{p}ωp​/2$\pi \sim101010^{10}$ Hz, making it an excellent candidate for realizing a high-efficiency Szilard engine with unprecedented performance. We showed that, on average, the proposed heat engine can extract kBT_\text{B}TB​Tln2 of heat per cycle from the thermal reservoir in the quasi-static (QS) limit. In addition, we showed that the FLD-based Szilard engine delivers maximum power when operated about 200 times faster than the threshold speed of quasi-static operation. Our result demonstrates that Szilard's engine's performance based on FLD exceeds other nano-device implementations by orders of magnitude. \\
The Josephson effect is a privileged access to the macroscopic quantum nature of superconductors. We review some ideas and experimental techniques on macroscopic quantum decay phenomena occurring in Josephson structures. The attention is mainly addressed to intermediate levels of dissipation which characterize a large majority of low critical current Josephson devices and are therefore an avoidable consequence of nanotechnology applied more and more to Josephson devices. Phase diffusion phenomena take over thermal activation in some temperature ranges also affecting the transition to macroscopic quantum tunneling, enriching the phase diagram mostly defined by the Josephson energy, the temperature and the level of dissipation.
Recent findings of macroscopic quantum properties in high critical temperature superconductor (HTS) Josephson junctions (JJs) point toward the need to revise the role of zero energy quasi-particles in this novel superconductor. We will discuss the possibility of designing superconducting artificial atoms in a transmon configuration to study the low energy excitation spectra of HTS. We have engineered high quality grain boundary JJs on low dielectric constant substrates. By fabricating submicron junctions, we extract values of capacitance and Josephson critical current densities that satisfy the main transmon design requirements. Moreover, the measured critical current noise power extrapolated at 1 Hz gives a dephasing time of 25 ns, which indicates that the observation of macroscopic quantum coherent effects in HTS JJ is a feasible task.
Conventional tunnel Josephson junctions form the basic building blocks of superconducting electronics. Their operation is based on comparatively simple dynamics where the superconducting phases across the junctions is the only dynamical degree of freedom. The goal of the project on which this thesis is based, is to understand the physics and develop a consistent theoretical description of the quantum dynamics of unconventional Josephson structures: spin active junctions, junctions containing low energy quasiparticles, and junctions composed of ddd-wave superconductors. Spin active Josephson junctions involve the additional degree of freedom of quasiparticle spin. Here we theoretically investigate the spin-structure of the current carrying interface bound states - Andreev Bound States (ABS), and induced ground state spin polarization of a short (shorter than the superconducting coherence length) nanowire junction containing a localized magnetic moment. We show that temporal variation of the superconducting phase difference and magnetic moment induce rotations in spin polarized and unpolarized subspaces respectively, which is manifested by temporal oscillation of the Josephson current.The interlevel transitions obey a selection rule that forbids manipulations in a certain region ofexternal parameters and results from specific properties of Andreev bound states in magnetic contacts where, in a certain regime of phase bias and strength of magnetic scatterer, ABS belong to different eigenstates of the combined charge and parity inversion symmetry operator.A general framework is developed to include low energy quasiparticle states into the dynamics of Josephson junctions. Such states exist in e.g. constriction type junctions with high transparency channels or resonant states, as well as in junctions of unconventional superconductors. The existence of such states prevent the separation of energy scales which in conventional tunnel junctions freezes out the quasiparticle degrees of freedom. We show that the resonant interaction with such low energy states rather than the Josephson potential defines the nonlinear Josephson dynamics at small amplitudes.The framework is applied to high temperature Josephson junctions, whose unconventional order parameter admits ABS with energies in the middle of the superconducting gap - Mid Gap States (MGS). In addition to the non-linear dynamics induced by the MGS, we identify a reentrance effect in the transition between thermal activation and macroscopic quantum tunneling associated with the MGS, and connect this phenomenon to experimental observations.