Resonances between fluxons and plasma waves in underdamped Josephson transmission lines of stripline geometry

We present experiments and theoretical studies on the propagation of Josephson fluxons and electromagnetic waves in parallel arrays of Josephson junctions in the limit of small discreteness. Locking between the fluxon rotation frequency and the frequency of the radiated electromagnetic waves leads to a series of resonances, which we observe on the dc-current-voltage characteristics of the arrays. The arrays consist of small Josephson junctions embedded in an annular superconducting stripline. The experimental data are analyzed using the discrete sine-Gordon model and an extension by including a capacitive interaction between neighboring Josephson junctions. We compare experimental data with both analysis and numerical simulations and find an excellent quantitative agreement.

Figure 1

(Color online) Schematic drawing of a one-dimensional parallel array of Josephson junctions having the stripline geometry. The junctions are colored dark red (dark gray). A fluxon is indicated in blue (arrow).

Figure 2

(Color online) Experimental data of $IV\mathrm{C}$ measurements of the single-fluxon step in an array with $N=25$ junctions. The arrows denote the sweeping direction of the bias current. The return path is traced out separately and is shown in red (dark gray). The experimental data are obtained at a temperature of $T=6.17\mathrm{K}$.

Figure 3

(Color online) A single-fluxon step was measured in four arrays of Josephson junctions. All curves show plasma wave resonances. The respective resonance index $m$ is indicated at the left of every step. The temperatures of the measurements are estimated from the gap voltage according to its theoretically expected dependence (Ref. 16). The temperatures are given as $T=6.77\mathrm{K}$ for $N=12$, $T=6.53\mathrm{K}$ for $N=16$, $T=6.56\mathrm{K}$ for $N=20$, and $T=6.17\mathrm{K}$ for $N=25$. All arrays have the same diameter of $\oslash 355\mu \mathrm{m}$.

Figure 4

(Color online) Comparison between the SG model, the FCU model, and the experimental data.

Figure 5

A simulated $IV\mathrm{C}$ of a parallel array with $N=25$, $a=0.5$, and $\alpha =0.08$. The insets show the voltage versus time evolution for three resonance steps. The voltage evolution is measured at a single arbitrary chosen junction.

Figure 6

(Color online) Comparison between experimental data (black) and simulated current-voltage characteristics (red/gray) with $N=25$, $a=0.5$, and $\alpha =0.08$.