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The dynamics of fluxon in a long Josephson transmission line containing a spatial inhomogeneity of variable polarity are investigated, taking into account the discreteness of the medium. This type of impurity models a qubit inductively coupled to a Josephson transmission line. The effect of discreteness on qubit-state readout, based on measuring the fluxon transit time through the dipole impurity, is analyzed. The results are compared with a long continuous Josephson junction containing a finite-size dipole inhomogeneity [1]. By accounting for the effects of an external bias current and dissipation, we analytically derive the fluxon equation of motion and the effective potential governing its dynamics. The critical current for fluxon pinning at the impurity is calculated, and its dependence on the discreteness parameter, impurity amplitude, and dissipation is investigated. The difference in fluxon transit times for the two qubit states, referred to as the delay time, is determined. Its dependence on the bias current, discreteness parameter, and dissipation is also analyzed, along with the influence of the Josephson transmission line length. The results show that discreteness reduces the separation between the critical currents for fluxon pinning when the qubit occupies different states, thereby potentially reducing the sensitivity of qubit-state readout. Conversely, discreteness increases the fluxon delay time at the qubit, which can improve readout sensitivity [2].
[1] Ivan O. Starodub, Yaroslav Zolotaryuk, Physics Letters A 383, 1419 (2019). https://doi.org/10.1016/j.physleta.2019.01.051.
[2] Ivan O. Starodub, Yaroslav Zolotaryuk, Physics Letters A 503, 129414 (2024). https://doi.org/10.1016/j.physleta.2024.129414.
