Excitation spectrum of a double supersolid in a trapped dipolar Bose mixture

Dipolar Bose-Einstein condensates are excellent platforms for studying supersolidity, characterized by coexisting density modulation and superfluidity. The realization of dipolar mixtures opens intriguing new scenarios, most remarkably the possibility of realizing a double supersolid, composed of two interacting superfluids. We analyze the complex excitation spectrum of a miscible trapped dipolar Bose mixture, showing that it provides key insights about the double-supersolid regime. We show that this regime may be readily probed experimentally by monitoring the appearance of a doublet of superfluid compressional modes, linked to the different superfluid character of each component. Additionally, the dipolar supersolid mixture exhibits a nontrivial spin nature of the dipolar rotons, the Higgs excitation, and the low-lying Goldstone modes. Interestingly, the analysis of the lowest-lying modes allows for monitoring the transition of just one of the components into the incoherent-droplet regime, whereas the other remains coherent, highlighting their disparate superfluid properties.