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arXiv:cond-mat/0503729 · Physical Review B

Crossover from Kramers to phase-diffusion switching in moderately damped Josephson junctions

Jaan Männik, Shaoxiong Li, Wei Qiu, W. Chen, Vijay Patel, Siyuan Han, James E. Lukens

Published Jun 24, 2005• 72 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.71.220509

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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 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.
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.
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.
We measured the retrapping current of a small-capacitance underdamped dc superconducting quantum interference device (SQUID) at low temperatures as a function of magnetic field. We found that the relative phase relation between the magnetic-field dependence of the retrapping current and that of the switching current jumped from 0 to $\ensuremath{\pi}$ at ${E}_{\mathrm{J}}\ensuremath{\sim}{E}_{\mathrm{C}},$ where EJ{E}_{\mathrm{J}}EJ​ and EC{E}_{\mathrm{C}}EC​ are the Josephson energy and the charging energy of a Cooper pair. This phenomenon cannot be reproduced by a model that approximates the SQUID as a single junction with a controllable switching current. It can be explained phenomenologically by taking into account two kinds of dissipation that arise from ac currents flowing through the lead and along the SQUID's loop.
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.
Abstract This work investigates the distribution of flux states of hysteretic dc superconducting quantum interference devices (SQUIDs) obtained from standard current ramp measurement at 2.50 and 0.35 K. Each flux state corresponds to a specific number of flux quanta trapped in the superconducting loop, associated with a metastable state in the two-dimensional potential energy of the hysteretic SQUID. The flux states can be distinguished by the multiple switching currents. The observed distribution is different from the distribution caused only by thermal excitation at a specific temperature. There are notable systematic deviations between the measurement results of three samples and the standard Boltzmann distribution, which can be clearly identified from the ratios between the proportions of different flux states. A formula resembling the Boltzmann distribution, involving multiple effective temperatures, is proposed to provide a better fit to the measured results. The finding suggests that the observed distribution of flux states is established during the SQUID’s transition from the dissipative state to the zero-voltage state, and multiple equivalent temperatures may be involved in the process.