  An extended Josephson junction consists of two superconducting electrodes
that are separated by an insulator and it is therefore also a microwave cavity.
The superconducting phase difference across the junction determines the
supercurrent as well as its spatial distribution. Both, an external magnetic
field and a resonant cavity intrafield 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 -0.5. This enables static and dynamic
control over the junction in the ultra-strong coupling regime.
