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 ago¹⁶, 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 superconductors¹⁹, which might also be expected for supersolids²⁰, 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 supersolid⁷ 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.