Probing superfluidity with quantum vortex necklaces and Leggett's bounds

We theoretically investigate a binary Bose-Einstein condensate in which the majority component hosts a vortex necklace, whose vortex cores act as moving effective potential wells for the minority component. This configuration represents a tunable periodic landscape whose strength is controlled by the intercomponent interaction. As the coupling increases, the minority component undergoes a crossover from a delocalized, nearly perfect superfluid to an array of localized density peaks confined within the vortex cores. Using Gross-Pitaevskii simulations, we compute the moment of inertia of the minority component and show that its superfluid fraction is tightly bracketed by Leggett's bounds constructed from its density profile. Because these bounds depend solely on the spatial density distribution, they may be extracted directly from experimentally accessible measurements. Our results identify vortex necklaces as a controllable tool for tuning and probing superfluidity in two-component condensates and provide a natural framework for exploring superfluid behavior in dynamically evolving and disordered potentials.