Interference between magnetic field and cavity modes in an extended Josephson junction

An extended Josephson junction consists of two superconducting electrodes separated by an insulator and is therefore also a microwave cavity. The superconducting phase difference across the junction determines the amplitude as well as the spatial distribution of the supercurrent. Both external magnetic fields and resonant intracavity fields produce a spatial modification of the superconducting phase along the junction. The interplay between these two effects leads to interference in the critical current of the junction and allows us to continuously tune the coupling strength between the first cavity mode and the Josephson phase from 1 to $-0.68$. This enables static and dynamic control of the junction in the ultrastrong-coupling regime.

Figure 1

(a) Hysteretic current-voltage characteristic (red line) of extended Josephson junction, taken at 600 mK. The first Fiske resonance at $V=15\mu V$ (blue line) is taken at $\phi =0.7{\phi }_0$. (b) Sketch of extended Josephson junction. Electric-field distribution of the first resonant mode $k_1$ is indicated in red. (c) Fraunhofer pattern of $I_c$ (data: red line; theory: red dashed line), and first Fiske resonance $I_{c1}$ (blue line) as a function of applied (in plane) magnetic field with theoretical curve (blue dashed line) given in the text by Eq. (4).

Figure 2

(a) Josephson spectroscopy of first cavity mode: Resonance of normalized critical current as function of microwave frequency (red dots) at ${\nu }_1=7.18$ GHz with quality factor $Q_c=250$ from Lorentzian fit (blue line). (b) Suppression of critical current $I_c$ as function of injected microwave power. Blue line corresponds to theoretical fit. (c) Deviation of the critical current $\Delta I_c$ for resonant ($\nu =7.185$ GHz) and nonresonant ($\nu =6.950$ GHz) microwave excitation (red solid line). From this measurement the coupling constant $g_1$ can be extracted experimentally (dotted red line) using Eq. (3). The blue solid line and blue dotted line are the theoretical predictions for $\Delta I_c\left(\phi \right)$ and $g_1\left(\phi \right)$ from Eqs. (3) and (1), respectively.

Figure 3

(a) Color map showing normalized deviation of critical current $1-\Delta I_c/I_c$ as a function of microwave frequency and applied magnetic field. (b) Variation of the microwave resonant frequency for applied magnetic field, deduced from (a). The red line corresponds to the theoretically expected variation of ${\nu }_1$ as a function of an applied magnetic field.