Sound Propagation in Superfluids with Two Broken Continuous Symmetries

At ultralow temperatures, matter exhibits striking quantum phenomena, among which superfluidity plays a central role in this thesis. Initially observed in liquid helium, it features frictionless flow and persistent currents. It is closely related to Bose–Einstein condensation (BEC), where bosons coherently occupy a single quantum state. The advent of atomic BECs enabled highly tunable quantum systems, in which interatomic interactions can be controlled via Feshbach resonances. Systems with dipolar interactions have expanded the landscape of ultracold quantum gases. Their long-range, anisotropic character gives rise to distinctive features such as rotonization and the formation of droplets stabilized by beyond-mean-field effects. Incorporating these corrections into theory yields the extended Gross–Pitaevskii equation (eGPE), which successfully captures the emergence of droplet arrays exhibiting density modulation and global phase coherence — the hallmarks of a supersolid phase. This thesis investigates sound propagation in systems with two broken continuous symmetries, leading to two pairs of longitudinal modes in accordance with the Goldstone theorem. Using Gross–Pitaevskii theory and the linear response approach, we develop a protocol to excite and measure sound modes in dipolar BECs and binary Bose mixtures, confirming the existence of two sound branches consistent with hydrodynamic predictions. Measuring these velocities in dipolar condensates provides a novel method to evaluate the superfluid fraction across the superfluid–supersolid phase transition. Furthermore, due to the hybridization of sound modes, both systems exhibit an anomalous Doppler effect arising from the relative motion of their constituent fluids. Our numerical and analytical results predict regimes of negative Doppler shift in dipolar supersolids — an effect first proposed in liquid helium but never observed experimentally. These findings offer new insights into the Doppler physics of two-fluid systems and propose experimentally accessible schemes for its observation.