Measurement of the superfluid fraction of a supersolid by Josephson effect.

A new class of superfluids and superconductors with spatially periodic modulation of the superfluid density is arising 1-12 . It might be related to the supersolid phase of matter, in which the spontaneous breaking of gauge and translational symmetries leads to a spatially modulated macroscopic wavefunction 13-16 . This relation was recognized only in some cases 1,2,5-9 and there is the need for a universal property quantifying the differences between supersolids and ordinary matter, such as the superfluid fraction, which measures the reduction in superfluid stiffness resulting from the spatial modulation 16-18 . The superfluid fraction was introduced long ago 16 , but it has not yet been assessed experimentally. Here we demonstrate an innovative method to measure the superfluid fraction based on the Josephson effect, a ubiquitous phenomenon associated with the presence of a physical barrier between two superfluids or superconductors 19 , which might also be expected for supersolids 20 , owing to the spatial modulation. We demonstrate that individual cells of a supersolid can sustain Josephson oscillations and we show that, from the current-phase dynamics, we can derive directly the superfluid fraction. Our study of a cold-atom dipolar supersolid 7 reveals a relatively large sub-unity superfluid fraction that makes realistic the study of previously unknown phenomena such as partially quantized vortices and supercurrents 16-18 . Our results open a new direction of research that may unify the description of all supersolid-like systems.