UC Davis

The Josephson effect is one of the macroscopic quantum phenomena and it was predicted by B.D Josephson in 1962. For a typical S-I-S Josephson junction, there exists a continuous supercurrent across the junction without any external voltage applied due to the Cooper pair tunneling. The Cooper pair is a bound state of a pair of electrons caused by a small attraction due to the electron-phonon interaction in a metal at low temperatures. When the temperature is increased or external bias voltage is imposed, the Cooper pairs could be broken due to the thermal motion or the voltage overcoming the binding energy of the paired electrons. The term “activation” or “switching” of Josephson junction from superconducting state to normal or resistive state refers to such a process, that the normal electrons formed from the broken Cooper pairs result in a normal current, which is higher than a threshold, namely, critical current, so that a voltage drop across the junction can be measured and the current-voltage relation satisfies the Ohm’s law.

According to the Josephson relations, the current flowing through the junction is characterizes by the phase difference between the two superconductors of the junction, and the resistively and capacitively shunted junction (RCSJ) model was proposed in 1968 for the description of phase dynamics. The governing equation of the phase difference is a Langevin equation analogously describing a Brownian particle moving in a periodic potential well. Accordingly, the escape ofBrownian particles from the well was used to study the switching of the junction. The RCSJ model in the past five decades has been accepted as a good model for successfully providing a switching mechanism called “thermal activation (TA)” at high temperatures relative to the “crossover temperature”. As a series of Josephson experiments were reported during 1980s, the RCSJ model was considered failing to explain some phenomena, such as the saturation of the switching current distribution (SCD) as the temperature is down to zero. Meanwhile, the theory of macroscopic quantum tunneling (MQT) was built; the phase was quantized and the saturation of SCD was attributed to the tunneling of the phase particle through the potential barrier. As a test for the secondary quantum effect, MQT has been accepted as a main theory for the interpretation of saturation of SCD in Josephson switching experiments.

In this dissertation, we try to explore a classical switching mechanism as an alternative and simpler description for the phase difference of the Josephson junction at low temperatures besides MQT. The content of this thesis is structured as follows: in Chapter 1, we review the background of Josephson effect and present some of the key concepts that will be used in thefollowing chapters. In Chapter 2, by solving the Langevin equation of the RCSJ model using the GJ thermostat method, we will investigate the effects of the parameters in the equation, such as damping, temperature, sweep rate and initial conditions. Non-equilibrium phenomena are observed and discussed. In Chapter 3, the effects of initial conditions, especially the saturation phenomena in non-equilibrium state will be discussed. In Chapter 4, with the understandings on the classical switching mechanism of the junction, we will compare the results generated by our model to the published experimental data. Up to Chapter 4, our discussion is based on a single Josephson junction, while in Chapter 5, the simulation will be generalized to a one-dimension long Josephson junction, which will be a more complex system in which additional phenomena, such as kink-soliton, can be studied. In Chapter 6, we summarize the discussion in this dissertation.