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Journal of Applied Physics

Bias current ramp rate dependence of the crossover temperature from Kramers to phase diffusion switching in moderately damped NbN/AlN/NbN Josephson junctions

Mikhail Lisitskiy, D. Massarotti, Luca Galletti, Luigi Longobardi, G. Rotoli, M. Russo, Francesco Tafuri, B. Ruggiero

Published Jul 24, 2014• 6 citations
Publisher

Abstract

We investigate the phase dynamics of moderately damped NbN/AlN/NbN Josephson junctions and we present experimental results on detailed aspects of phase diffusion processes. We measure both single escape and multiple escape and retrapping events obtaining a crossover temperature T* from Kramers to phase diffusion switching. We observe a clear dependence of the crossover temperature T* by the bias current ramp rate, while the damping factor Q remains the same. The measured effect is in strong agreement with theoretical predictions reported by Fenton and Warburton.

DOI
10.1063/1.4890317

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We investigate the phase dynamics of moderately damped NbN/AlN/NbN Josephson junctions and we present experimental results on detailed aspects of phase diffusion processes. We measure both single escape and multiple escape and retrapping events obtaining a crossover temperature T* from Kramers to phase diffusion switching. We observe a clear dependence of the crossover temperature T* by the bias current ramp rate, while the damping factor Q remains the same. The measured effect is in strong agreement with theoretical predictions reported by Fenton and Warburton.
We have measured and propose a model for switching rates in a hysteretic dc superconducting quantum interference device (SQUID) in the regime where phase-diffusion processes start to occur. We show that the switching rates in this regime are smaller than the rates given by Kramers' formula due to retrapping of the Josephson phase. The retrapping process, which is affected by the frequency dependent impedance of the environment of the dc SQUID, leads to a peaked second moment of the switching distribution as a function of temperature. The temperatures where the peaks occur are proportional to the critical current of the dc SQUID.
We report on measurements of the switching current probability both in the thermal and quantum regime on moderately damped NbN/MgO/NbN Josephson junctions with very low critical current density (’ 2A/cm2). We observed three distinct regimes: below 90 mK the width of the switching distributions is constant within the experimental error, while from 90 mK to 1.6 K the width increases with temperature, this change of behavior signaling the standard transition from macroscopic quantum tunneling (MQT) to thermal activation (TA) regime respectively. Above 1.6 K 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 parameters which completely characterize the dynamics of such moderately damped Josephson junctions have been also extracted.
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.
A two-step transition model describing phase diffusion and switching process in underdamped Josephson junctions is discussed. The model takes into account the phase particle's escape rate out of the potential well and transition rate from phase diffusion to the running state. Using as examples the experimental switching current distributions of two Nb/AlO x /Nb junctions of different sizes fabricated on the same chip, we extract the transition rate, which turns out to follow the predicted Arrhenius law in the thermal regime but is greatly enhanced when macroscopic quantum tunneling becomes the dominant escape mechanism. Our results show the validity of applying the model to obtain the transition rate out of the phase diffusion state into the running state from measured switching current distribution of underdamped Josephson junctions. The temperature and bias-current dependent data provide strong evidence for phase diffusion in both thermal and quantum regimes.
We report measurements of switching current distribution (SWCD) from a phase-diffusion branch (PDB) to a quasiparticle-tunneling branch (QTB) as a function of temperature in a cuprate-based intrinsic Josephson junction. Contrary to the thermal-activation model, the width of the SWCD increases and the corresponding switching rate shows a nonlinear behavior with a negative curvature in a semilogarithmic scale with decreasing temperature down to 1.5 K. Based on the multiple-retrapping model, we quantitatively demonstrate that the frequency-dependent junction quality factor, representing the energy dissipation in a phase-diffusion regime, determines the observed temperature dependence of the SWCD and the switching rate. We also show that a retrapping process from the QTB to the PDB is related to the low-frequency limit damping.
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.