The fluxon interaction with the dipole impurity in the Josephson transmission line

Abstract

The fluxon dynamics in a long Josephson transmission line with the presence of a spatial inhomogeneity of variable polarity and taking into account the influence of the medium discreteness is studied. Such an impurity models a qubit inductively coupled to a Josephson transmission line. The influence of discreteness on the qubit state readout process, which is based on measuring the time of fluxon passage through the dipole impurity, is analyzed. The results are compared with the case of a long continuous Josephson junction with a dipole spatial inhomogeneity of finite size [1]. Taking into account the external current and dissipation, the equation of motion of the fluxon and the form of the potential in the field of which it is located are analytically obtained. The threshold current of the fluxon pinning on the impurity is calculated. The dependencies of the threshold current on the discreteness value, the impurity amplitude and dissipation in the system are built. The difference in the times of fluxon passage through the transmission line with the qubit in different states – the delay time – is found. The dependencies of the delay time on the external current, the discreteness coefficient and dissipation were obtained. The influence of the Josephson transmission line size on the delay time is analyzed. It was found that discreteness leads to a decrease of the interval between the threshold current of the fluxon on the qubit in different states, which worsens the sensitivity of the qubit state readout process. On the other hand, discreteness causes an increase in the fluxon delay time on the qubit, which is favorable for the sensitivity of the readout process [2].