Synchronization in rotating supersolids

Synchronization is a widespread phenomenon in natural and engineered systems, governing the emergence of collective dynamics in different domains including biology and classical and quantum physics. In quantum many-body systems, synchronization has emerged as a tool to probe out-of-equilibrium behaviour and internal correlations. Supersolids—quantum phases that combine crystalline order and superfluidity—offer a platform to explore synchronization in systems with coexisting broken symmetries. Here we investigate the dynamics of a dipolar supersolid subjected to external rotation. We show that, above a critical driving frequency, the crystal revolution undergoes a sudden synchronization with the rotating field seeded by the nucleation of quantized vortices, hallmark of superfluidity. This transition reflects the interplay between the solid-like and superfluid responses of the system. By comparing simulations of the extended Gross–Pitaevskii equation with experimental observations, we demonstrate that synchronization can serve as a dynamical indicator for vortex nucleation. This approach provides a complementary method to determine the critical rotation frequency for vortex formation in supersolids.