Creation of classical and quantum fluxons by a current dipole in a long Josephson junction

We study static and dynamical properties of fluxons in a long annular Josephson junction (JJ) with a current injected at one point and collected back at a close point. Uniformly distributed dc bias current with density γ is applied too. We demonstrate that, in the limit of the infinitely small size of the current dipole, the critical value of γ, above which static phase distributions do not exist, that was recently found (in the Fraunhofer’s analytical form) for the annular JJ with the length much smaller than the Josephson penetration length is valid irrespective of the junction’s length, including infinitely long JJ’s. In a long annular JJ, the dipole generates free fluxon(s) if γ exceeds the critical value. For long JJ’s, we also find another critical value (in an analytical form too), which is always slightly smaller than the Fraunhofer value, except for points where the dipole strength is 2πN with integer N, and both values vanish. The static phase configuration which yields the new critical value is based on an unstable fluxon-antifluxon bound state, therefore it will probably not manifest itself in the usual (classical) regime. However, it provides for a dominating instanton configuration for tunnel birth of a free fluxon, hence it is expected to determine a quantum-birth threshold for fluxons at ultralow temperatures. We also consider the interaction of a free fluxon with the complex consisting of the current dipole and antifluxon pinned by it. A condition for suppression of the net interaction force, which makes the long JJ nearly homogeneous for the free fluxon, is obtained in an analytical form. The analytical results are compared with numerical simulations. The analysis presented in the paper is relevant to the recently proposed new experimental technique of inserting fluxons into annular Josephson junctions.