Resonant plasmon scattering by discrete breathers in Josephson junction ladders

We study the resonant scattering of plasmons (linear waves) by discrete breather excitations in Josephson junction ladders. We predict the existence of Fano resonances, and find them by computing the resonant vanishing of the transmission coefficient. We propose an experimental setup of detecting these resonances, and conduct numerical simulations which demonstrate the possibility to observe Fano resonances in the plasmon scattering by discrete breathers in Josephson junction ladders.

Figure 1

Schematic of dynamically generated paths in the frequency domain by a time-periodic scattering potential with a period $2\pi ∕\Omega$. In general, there is an infinite number of paths which may lead to different interference phenomena.

Figure 2

Schematic of the Josephson junction ladder. Each cross represents a junction. Arrows denote the dc bias flow.

Figure 3

Schematic of $A$- and $B$-type breather resistive cores in JJLs with one vertical resistive junction. Black spots mark the junctions being in the resistive state while all others are in the superconducting one.

Figure 4

Transmission coefficient vs ${\omega }_3\left(q\right)$ with Fano resonances for waves scattered by $A$-type (dashed) and $B$-type (solid) DBs with one vertical resistive junction for ${\Omega }_b=3.1$, ${\beta }_L=0.5$, and $\eta =0.35$.

Figure 5

Direct numerical simulation of the linear wave propagation in a JJL with $N=100$ cells, $\alpha =0.05$, ${\beta }_L=0.5$, $\eta =0.35$ with a boundary ac bias ${\gamma }_1={\gamma }_{\mathrm{ac}}\cos \left(\omega t\right)$. (a) Oscillation power of vertical junction $n=101$ vs excitation frequency $\omega$ for an empty system (dotted line), for an $A$ DB at site $n=50$ with frequency ${\Omega }_b=2.777$ (solid line), and ${\Omega }_b=3.284$ (dashed line). (b) Transmission coefficient $\tau$ for an A DB of frequency ${\Omega }_b=2.777$ (solid line), ${\Omega }_b=3.284$ (dashed line), and frequency $\Omega =3.082$ (dotted line).

Figure 6

Dip frequency ${\omega }_{\mathrm{dip}}$ in the transmission from Fig. 5b vs DB frequency $\Omega$ for a type $A$ DB (two dips, marked by circles and squares) and a type $B$ DB (one dip, diamonds). Lines indicate linear fits of the dip frequency to Eq. (13).

Figure 7

(Color online.) Schematic experimental setup for measuring the plasmon scattering by a DB, showing source, scattering, and detector DB. The individual DBs are controlled using local bias currents ${\gamma }_1-{\gamma }_3$. Technical details are found in Ref. 24.