Dipolar Bose-Einstein condensates provide a powerful platform for exploring supersolidity, a phase where density modulation coexists with superfluidity. The advent of dipolar mixtures introduces new and fascinating scenarios, most notably the prospect of a double supersolid formed by two interacting quantum fluids. In this work, we investigate the excitation spectrum of a miscible trapped dipolar Bose mixture and show that it reveals essential features of the double-supersolid regime. We demonstrate that this regime can be accessed experimentally by detecting the emergence of a pair of superfluid compressional modes, which reflect the distinct superfluid character of each component. Moreover, the dipolar supersolid mixture exhibits a rich spin structure involving dipolar rotons, the Higgs excitation, and low-energy Goldstone modes. Remarkably, the study of the lowest-lying modes enables one to track the transition of a single component into the incoherent-droplet regime while the other remains coherent, underscoring their contrasting superfluid behavior. Finally, we present preliminary experimental evidence for the nucleation of double supersolidity.
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