Self-induced Josephson oscillations and self-trapping in a supersolid dipolar quantum gas

The Josephson effect characterizes superfluids and superconductors separated by a weak link, the so-called Josephson junction. A recent experiment has shown that Josephson oscillations can be observed also in a supersolid, where the weak link is not due to an external barrier, but is self-induced by interparticle interactions. Here we show theoretically that supersolids -- despite their self-induced character -- feature all the standard properties of bosonic Josephson junction arrays, including macroscopic quantum self-trapping. We focus on the harmonically trapped dipolar supersolids of interest for current experiments, and show that they can be described with a generalized Josephson model that takes into account spatial inhomogeneities. Our work shades new light on the dynamics of supersolids and opens the way to the study of a novel class of Josephson junctions.