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We propose a dynamical protocol to probe the rigidity and phase coherence of dipolar supersolids by merging initially separated fragments in quasi-one-dimensional (1D) double-well potentials. Simulations based on the extended Gross-Pitaevskii equation reveal distinct dynamical signatures across phases. Supersolids exhibit damped crystal oscillations following barrier removal, with the damping rate reflecting superfluid connectivity. A phase-imprinted jump additionally triggers metastable dark solitons, which excites second sound, as revealed by an out-of-phase drift between the droplet lattice and the superfluid background. Our results show a realizable path to dynamically detect the second sound and rigidity of supersolids, as well as to realize and probe soliton formation.
Bougas et al. (Tue,) studied this question.