Control and manipulation of quantum states by measurements and bath engineering in open quantum systems, like in a quantum computer, have emerged as new paradigms in many-body physics. Taking a prototypical example of Josephson junction arrays (JJAs), we show how monitoring through continuous weak measurements and feedback can transform an insulating steady state in JJAs to a superconductor (SC) and vice versa. We show that the quantum feedback, when not too large, is crucial to realize such a superconducting steady state by maintaining an effective temperature in a semiclassical limit. However, we show that large feedback can destroy superconductivity by enhancing quantum phase fluctuations. Thus, dissipation and phase fluctuations in the presence of monitoring have fundamental differences from those in the well-studied case of JJAs in contact with an equilibrium Ohmic bath. In general, a description in terms of only an effective temperature is not adequate for the monitored JJAs. Using a variational approximation, and by considering various limiting cases, we demonstrate that these differences can give rise to reentrant SC-insulator phase transitions leading to an unusual inverse transition from a seemingly low-effective-temperature insulating normal state to a superconducting state at intermediate temperature.
Control and manipulation of quantum states by measurements and bath engineering in open quantum systems, like in a quantum computer, have emerged as new paradigms in many-body physics. Taking a prototypical example of Josephson junction arrays (JJAs), we show how monitoring through continuous weak measurements and feedback can transform an insulating steady state in JJAs to a superconductor (SC) and vice versa. We show that the quantum feedback, when not too large, is crucial to realize such a superconducting steady state by maintaining an effective temperature in a semiclassical limit. However, we show that large feedback can destroy superconductivity by enhancing quantum phase fluctuations. Thus, dissipation and phase fluctuations in the presence of monitoring have fundamental differences from those in the well-studied case of JJAs in contact with an equilibrium Ohmic bath. In general, a description in terms of only an effective temperature is not adequate for the monitored JJAs. Using a variational approximation, and by considering various limiting cases, we demonstrate that these differences can give rise to reentrant SC-insulator phase transitions leading to an unusual inverse transition from a seemingly low-effective-temperature insulating normal state to a superconducting state at intermediate temperature.
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).
Superconductor-insulator transitions, especially in thin films, can provide the simplest examples of the continuous quantum phase transition paradigm. Quantum phase transitions differ from thermal phase transitions in that they occur at zero temperature when the ground state of a system is changed in response to a variation of an external parameter of the Hamiltonian. In the example of the superconductor-insulator transition, this control parameter could be the parallel or perpendicular magnetic field, disorder, or charge density. Quantum phase transitions are studied through measurements at nonzero temperature of physical behaviors influenced by the quantum fluctuations associated with the transition. This review will focus on experimental aspects of superconductor-insulator transition in disordered films that are effectively two-dimensional. In particular, the evidence for quantum critical behavior in the various types of transitions will be presented. The various theoretical scenarios for the transitions will also be discussed along with the extent to which they are supported by experiment. Open questions relating to the nature of the very puzzling insulating regime and whether there are many different types of superconductor-insulator transitions will be presented. Although this research area is more than 20 years old, rather central issues are not resolved.
Quantum mechanics constrains conjugate observables from being simultaneously measurable with arbitrary precision. In a Josephson junction, these are the transferred electric charge and the quantum-mechanical phase difference between the superconducting domains. Which of them fluctuates determines the supercurrent: a dissipative trickle of single Cooper pairs in one limit, a coherent dissipationless flow in the other. Bridging both regimes in one device remained elusive because the Josephson and charging energies are fixed at fabrication. Here, we use the tunable tunnel junction of a scanning tunneling microscope at millikelvin temperature to vary their ratio continuously over many orders of magnitude. In this way, we monitor the smooth transition between incoherent and coherent Cooper pair flow in a single junction, revealing the quantum-to-classical transition in a controlled way.
Josephson elements are cornerstones of cryogenic classical and quantum superconducting technology, owing to their nonlinearity. Two important types of Josephson elements are often considered distinct: the tunnel junction (superconductor-insulator-superconductor, SIS) and the normal weak link (superconductor-normalsuperconductor, SNS) referring to any non-superconducting and non-insulating central region. SNS junctions and SIS junctions have appeared in related technological and basic science contexts over the last decade. In this perspective article, we review correspondences between SISIS junctions and SNS junctions in limiting regimes, in which a single, general energy-phase relationship describes the systems. We show how this insight helped to connect recent bodies of theoretical and experimental work in both systems. We conclude by describing a few important differences that also impact their use in applied contexts.
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.
Quantum phase transitions typically result in a broadened critical or crossover region at nonzero temperature. Josephson arrays are a model of this phenomenon, exhibiting a superconductor-insulator transition at a critical wave impedance, and a well-understood insulating phase. Yet high-impedance arrays used in quantum computing and metrology apparently evade this transition, displaying superconducting behavior deep into the nominally insulating regime. The absence of critical behavior in such devices is not well understood. Here we show that, unlike the typical quantum-critical broadening scenario, in Josephson arrays temperature dramatically shifts the critical region. This shift leads to a regime of superconductivity at high temperature, arising from the melted zero-temperature insulator. Our results quantitatively explain the low-temperature onset of superconductivity in nominally insulating regimes, and the transition to the strongly insulating phase. We further present, to our knowledge, the first understanding of the onset of anomalous-metallic resistance saturation. This work demonstrates a non-trivial interplay between thermal effects and quantum criticality. A practical consequence is that, counterintuitively, the coherence of high-impedance quantum circuits is expected to be stabilized by thermal fluctuations.