Non-Equilibrium Probing of Topological Supersolids in Spin-Orbit-Coupled Dipolar Condensates

A chiral supersolid is a quantum phase that simultaneously exhibits crystalline order, superfluidity, and topological spin texture, with spontaneously broken translational, U(1) gauge, and chiral symmetries. Here, we demonstrate a chiral supersolid with tunable non-equilibrium dynamics in a spin-orbit coupled dipolar Bose-Einstein condensate. By adjusting dipolar interaction and spin-orbit coupling, we uncover two distinct quantum phase transitions: (i) a first-order transition from a single skyrmion superfluid to a triangular meron supersolid, and (ii) a second-order transition from this superfluid to a square skyrmion supersolid. These phases are characterized by their lattice symmetries, nonclassical rotational inertia, and spin textures. Under parity-time symmetric dissipation, we predict phase-dependent damping of the current oscillations, directly linked to the superfluid fraction. The predicted chiral supersolid phase can be experimentally observed in ultracold magnetic atoms with spin-orbit coupling. Our results establish dipolar quantum gases as a platform for designing topological matter with spintronic functionality.