High-Q cavity-induced fluxon bunching in inductively coupled Josephson junctions

We consider fluxon dynamics in a stack of inductively coupled long Josephson junctions connected capacitively to a common resonant cavity at one of the boundaries. We study, through theoretical and numerical analyses, the possibility for the cavity to induce a transition from the energetically favored state of spatially separated shuttling fluxons in the different junctions to a high-velocity high-energy state of identical fluxon modes.

Figure 1

The identical long Josephson junctions coupled to a cavity at $x=l$.

Figure 2

$\phi$ from Eqs. (13a, 13b), $F_b$ from Eq. (33), and $F_I$ from Eq. (30). $N=2$, $l=8$, $\alpha =0.1$, $Q=100$, $c=0.02$, $\Omega =0.3$, $S=-0.05$, and $r=4$

Figure 3

Amplitude of $\dot{q}$ (top), current-voltage (middle), and $r/u$ (bottom). $N=2$, $l=8$, $\alpha =0.1$, $Q=100$, $c=0.02$, $\Omega =0.3$, and $S=-0.05$. $\omega$ is the fluxon-shuttling frequency controlled by the bias current $\left(\eta \right)$ in experiments.

Figure 4

Amplitude of $\dot{q}$ (top), current-voltage (middle), and $r/u$ (bottom). $N=2$, $l=4$, $\alpha =0.1$, $Q=100$, $c=0.02$, $\Omega =0.6$, and $S=-0.05$. $\omega$ is the fluxon-shuttling frequency controlled by the bias current $\left(\eta \right)$ in experiments.

Figure 5

Amplitude of $\dot{q}$ (top) and $r/u$ (bottom) as a function of the cavity current frequency. $N=2$, $l=8$, $\alpha =0.1$, $Q=100$, $c=0.02$, $\Omega =0.3$, and $S=-0.45$. $\omega$ is the fluxon-shuttling frequency controlled by the bias current $\left(\eta \right)$ in experiments. The simulation was started at high bias current resulting in high cavity frequency, and then the bias current was lowered resulting in a lowering of the cavity current frequency. At line $a$ the system switches from a high cavity current frequency to a low cavity current frequency state. At point $b$ the system switches from a low cavity current frequency to a high cavity current frequency state.