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Journal of Physics Conference Series

A two-step transition description of underdamped phase diffusion

Haifeng Yu, X. B. Zhu, Hui Deng, G. M. Xue, Ye Tian, Yanjun Ren, G H Chen, Dongning Zheng, X.N. Jing, Li Lü, S. P. Zhao, Siyuan Han

Published Dec 17, 2012• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1742-6596/400/4/042079

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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.
Quantum phase diffusion in a small underdamped Nb/AlO(x)/Nb junction (∼0.4 μm(2)) is demonstrated in a wide temperature range of 25-140 mK where macroscopic quantum tunneling (MQT) is the dominant escape mechanism. We propose a two-step transition model to describe the switching process in which the escape rate out of the potential well and the transition rate from phase diffusion to the running state are considered. The transition rate extracted from the experimental switching current distribution follows the predicted Arrhenius law in the thermal regime but is greatly enhanced when MQT becomes dominant.
We have investigated the dynamics of underdamped Josephson junctions with a relatively small Josephson coupling EJ{E}_{J}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 (TTT, EJ{E}_{J}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.
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.
Switching current distributions of an Nb/Al–AlO x /Nb Josephson junction are measured in a temperature range from 25 mK to 800 mK. We analyse the phase escape properties by using the theory of Larkin and Ovchinnikov (LO) which takes discrete energy levels into account. Our results show that the phase escape can be well described by the LO approach for temperatures near and below the crossover from thermal activation to macroscopic quantum tunneling. These results are helpful for further study of macroscopic quantum phenomena in Josephson junctions where discrete energy levels need to be considered.
We report on the switching current distributions in nano-hybrid Josephson junctions made of InAs semiconductor nanowires. The temperature dependence of the switching current distribution can be understood through the motion of Josephson phase particles escaping from a tilted washboard potential, and the data could be fitted well by using the macroscopic quantum tunneling, thermal activation or phase diffusion models, depending on temperature. Application of the gate voltage to tune the Josephson coupling strength enable us to adjust the effective temperature for the escape process, and holds promising for developing gate-tunable superconducting phase qubits.
We study $\mathrm{Nb}\ensuremath{-}{\mathrm{AlO}}_{x}$-Nb Josephson junctions (JJs) with a phase-discontinuity $\ensuremath{\kappa}$ created by a pair of current injectors attached to one of the Nb electrodes. For $\ensuremath{\kappa}\ensuremath{\approx}\ensuremath{\pi}$ the Josephson potential energy UUU as a function of the average phase $\ensuremath{\psi}$ across the JJ has the form of a $2\ensuremath{\pi}$-periodic double-well potential. Thus, the device behaves as a $\ensuremath{\varphi}$ JJ with degenerate ground state phases $\ensuremath{\psi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$ (the value of $\ensuremath{\varphi}$ depends on the system parameters). Experimentally, the existence of two wells of the potential is confirmed by the observation of two different critical currents ${I}_{\mathrm{c}\ifmmode\pm\else\textpm\fi{}}$, corresponding to the escape from different wells. We investigate the escape of the Josephson phase from both wells by collecting statistics of the switching currents. The histogram of switching current exhibits two peaks corresponding to ${I}_{\mathrm{c}\ifmmode\pm\else\textpm\fi{}}$. The dependence of the width ${\ensuremath{\sigma}}_{+}$ and ${\ensuremath{\sigma}}_{\ensuremath{-}}$ of each peak on the bath temperature TTT indicates the transition from thermal activation to macroscopic quantum tunneling (MQT) at ${T}^{★}\ensuremath{\approx}260\phantom{\rule{0.28em}{0ex}}\mathrm{mK}$ as TTT decreases. We argue that the observed saturation value of ${\ensuremath{\sigma}}_{+}$ and ${\ensuremath{\sigma}}_{\ensuremath{-}}$ below T★{T}^{★}T★ is indeed related to quantum tunneling rather than to parasitic noise in the system, as the histogram width can be reduced by tuning the value of $\ensuremath{\kappa}$ away from $\ensuremath{\pi}$. The comparison of the experimental escape rate $\mathrm{\ensuremath{\Gamma}}$ with theoretical predictions further confirms MQT of the phase $\ensuremath{\psi}$ from both wells.