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.
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.
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.
We have studied the temperature dependence of escape phenomena in various underdamped Josephson junctions (JJs). The junctions had different Josephson coupling energies E J which were relatively small, but larger than the charging energy E C . Upon increasing the temperature T , we first observe the usual cross-over between macroscopic quantum tunnelling and thermally activated (TA) behaviour at temperatures k B T ∼ ℏω p , where ω p is the plasma frequency of the junction. Increasing T further, the width of the switching current distribution has, counterintuitively, a non-monotonic temperature dependence. This can be explained by the novel cross-over from TA behaviour to underdamped phase diffusion. We show that this cross-over is expected to occur at temperatures such that k B T ∼ E J (1 − 4/π Q ) 3 /2, where Q is the quality factor of the junction at the plasma frequency, in agreement with experiment. Our findings can be compared with detailed model calculations which take into account dissipation and level quantization in a metastable well. Particular attention is paid to the sample with the smallest E J , which shows extensive phase diffusion even at the lowest temperatures. This sample consists of a dc-SQUID and a single JJ close to each other, such that the SQUID acts as a tunable inductive protection for the single junction from fluctuations of a dissipative environment. By varying the flux through the dc-SQUID, we present, for the first time, experimental evidence of the escape of a JJ from the phase diffusion regime to the free running state in a tunable environment. We also show that in the zero voltage state the losses mainly occur at frequencies near the plasma resonance.
We have investigated the dynamics of underdamped Josephson junctions with a relatively small Josephson coupling EJ. In addition to the usual crossover between macroscopic quantum tunneling and thermally activated (TA) behavior we observe, for the first time, the transition from TA behavior to underdamped phase diffusion. Above the crossover temperature, the threshold for switching into the finite-voltage state becomes extremely sharp. We propose a (T, EJ) phase diagram with various regimes and show that for a proper description of it, dissipation and level quantization in a metastable well are crucial.
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.
Here we present the direct observation of macroscopic quantum properties in an all high-critical-temperature superconductor d-wave Josephson junction. Although dissipation caused by low-energy excitations is expected to strongly suppress macroscopic quantum effects, we demonstrate energy level quantization in our d-wave Josephson junction. The result indicates that the role of dissipation mechanisms in high-temperature superconductors has to be revised, and it may also have consequences for the class of solid-state "quiet" quantum bits with superior coherence time.
Experiments to investigate the quantum behavior of a macroscopic degree of freedom, namely the phase difference across a Josephson tunnel junction, are described. The experiments involve measurements of the escape rate of the junction from its zero voltage state. Low temperature measurements of the escape rate for junctions that are either nearly undamped or moderately damped agree very closely with predictions for macroscopic quantum tunneling, with no adjustable parameters. Microwave spectroscopy reveals quantized energy levels in the potential well of the junction in excellent agreement with quantum-mechanical calculations. The system can be regarded as a "macroscopic nucleus with wires."