Dynamics Mechanism Of Josephson Vortex Based On Path Integral Periodic Instantin Method

The Josephson junction consists of two superconducting layers and a thin insulating interlayer,has attracted much attention due to the rich physical properties.Since Wallraff and M.V.Fistul first observed the quantum tunneling phenomenon of a single vortex in the annular Josephson junction in 2003,Josephson vortex has become one of the important candidates for qubits in the research and development of quantum computers.The successful fabrication of superconducting Josephson junctions with different shapes and the research and observation of Josephson vortex in the junctions provide a good platform for us to theoretically explore the quantum characteristics of Josephson vortex.Compared with the experimental research,the theoretical research on vortex mechanism in Josephson junction is relatively lagging behind.In this paper,the dynamic principle of Josephson vortex is mainly discussed theoretically.Firstly,a model based on the superconducting Josephson bias current master equation(?) is established,and the vortex in the Josephson junction with the motion of particles in the washboard potential well(?) is compared.The instanton method based on path integral has obvious advantages in studying the tunneling properties of particles.The dynamic problems such as vortex tunneling rate,energy level splitting degree,and the influence of temperature on tunneling rate in Josephson junction are theoretically calculated by this method.The conclusions are as follows:(1)The bound state energy level is approximately obtained for a single well.Due to the existence of tunneling phenomenon,the energy state in the well is unstable,and the energy level obtains an imaginary part related to tunneling.(2)One-sided tunneling approximation.The tunneling rate suitable for the whole temperature range is given.(3)Double well approximation.The energy level splitting degree caused by tunneling,and the influence of temperature and energy level splitting degree on tunneling rate is noticed,thus correcting the tunneling rate suitable for the whole temperature range.The results show that higher temperature and splitting of energy levels increase the activity of particles,which in turn leads to an increase in tunneling rate.(4)The tunneling in the whole temperature range is divided into three regions,namely,quantum tunneling in the ground state,thermal tunneling in the excited state,and thermally assisted tunneling from the ground state to the excited state.The analysis shows that the tunneling transition temperature of single well is higher than that of double well,and the transition process from quantum tunneling to thermal tunneling is a second-order phase transition process.Our theoretical results provide basis and guidance for exploring the dynamic mechanism and experimental observation of Josephson vortex.