Spectroscopy of the Fractional Vortex Eigenfrequency in a Long Josephson $0\mathrm{\text{−}}\kappa$ Junction

Fractional Josephson vortices carry a magnetic flux $\Phi$, which is a fraction of the magnetic flux quantum ${\Phi }_0\approx 2.07\times {10}^{-15}\mathrm{Wb}$. Their properties are very different from the properties of the usual integer fluxons. In particular, fractional vortices in $0\mathrm{\text{−}}\kappa$ Josephson junctions are pinned and have an oscillation eigenfrequency which is expected to be within the Josephson plasma gap. Using microwave spectroscopy, we investigate the dependence of the eigenfrequency of a fractional Josephson vortex on its magnetic flux $\Phi$ and on the bias current. The experimental results are in good agreement with the theory.

Figure 1

Optical image (top view) of the investigated sample: ALJJ with two pairs of injectors. The phase discontinuity $-\kappa$, created by injectors induces a $\kappa$ vortex. The microwaves induce ac current $I_{\mathrm{ac}}$ in the bias leads which adds up with the dc bias current $I$ supplied by the current source.

Figure 2

The dependence $I_c(I_{\mathrm{inj}})$ measured at $T\approx 4.2\mathrm{K}$ (symbols) and corresponding theoretical curve (continuous line).

Figure 3

Principle of the measurements. The escape histogram measured at ${\omega }_{\mathrm{ex}}/2\pi =29\mathrm{GHz}$ (a) for $\kappa =0$, i.e., ${\omega }_p(\gamma )={\omega }_0(0,\gamma )$ and (b) for fractional vortex $\kappa =0.82\pi$. The histograms show two peaks corresponding to resonant escape and thermal activation. (c) shows the numerically simulated dependences ${\omega }_0(0.82\pi ,\gamma )$ (2) and ${\omega }_p(\gamma )$ (4). Applied frequency ${\omega }_{\mathrm{ex}}$ is shown by the horizontal line.

Figure 4

Comparison between the theoretical curves with measurements of the eigenfrequency.