Characterizing superfluid fraction and topological property of supersolids via nonequilibrium dynamics

Supersolids—exotic quantum states that combine superfluid flow with crystalline order—have recently been realized in quantum degenerate gases, yet a direct quantitative measurement of their superfluid fraction and understanding of their topological properties have remained elusive. In this work we show that the nonequilibrium dynamics of a spin-orbit coupled dipolar Bose-Einstein condensate under PT -symmetric driving and dissipation generates an oscillating current whose frequency exhibits a strong dependence on the superfluid fraction of the underlying supersolid. This dynamical response further reveals topological phase transitions between distinct supersolid phases characterized by their spin textures. Our findings establish a platform for exploring supersolids with topological properties and provide deep insight into their nonequilibrium behavior beyond conventional closed-system scenarios.