We calculate the collective excitations of a dipolar Bose-Einstein condensate in the regime where it self-binds into droplets stabilized by quantum fluctuations. We show that the filament-shaped droplets act as a quasi-one-dimensional waveguide along which low-angular-momentum phonons propagate. The evaporation (unbinding) threshold occurring as the atom number $N$ is reduced to the critical value $N_c$ is associated with a monopolelike excitation going soft as ${\epsilon }_0\sim (N-N_c{)}^{1/4}$. Considering the system in the presence of a trapping potential, we quantify the crossover from a trap-bound condensate to a self-bound droplet.

• Received 21 March 2017

DOI:https://doi.org/10.1103/PhysRevLett.119.255302