Static and dynamic properties of annular Josephson junctions with injected current

We have investigated theoretically and experimentally a small annular Josephson junction with three leads, where the third lead is added to one of the ring-shaped electrodes to apply a control (injection) current and thereby create a local magnetic field. We study the static case, namely, we derive the general expression for the Josephson critical current in the presence of both an injection current and an external parallel magnetic field. Concerning the theoretical investigation of the dynamic case, we obtain an analytical expression for the Fiske steps amplitude as a function of the injection current intensity and the angle separating the two injection leads (θ1). The theoretical results show that a perfect analogy with the behavior of a rectangular junction in an external uniform magnetic field can be established for any orientation of the injector leads in the static case, while in the dynamic case the analogy holds only when the injector leads have a separation angle of θ1 =π. We present experimental dependences of the Josephson critical current and Fiske steps amplitudes on the injected current for two separation angles θ1 =π 2 and θ1 =π. The analysis and the comparison with the experiments confirm the theoretical predictions. The Fiske step measurements, presented for the case θ1 =π 2, have no straightforward analogous for the rectangular junction; however, we show a very good agreement between theory and experiments also in this case.