We investigate the low-energy dynamics of small-amplitude surface oscillations of spherical superfluid droplets in vacuum. Starting from the effective field theory of superfluid phonons, we derive an effective action governing the surface oscillations under a fixed particle-number constraint. The normal-mode eigenfrequencies ${\omega }_{\ell }$ for each angular momentum quantum number $\ell$ are determined and shown to depend on a dimensionless parameter measuring the ratio of surface tension to bulk compressibility energy. We identify a critical value of this parameter at which the breathing mode ($\ell =0$) becomes mechanically unstable, and show that all multipole surface modes with $\ell \ge 2$ enter the low-energy regime when the surface tension is sufficiently small. Within this regime, we further quantize the surface oscillations, whose quanta correspond to ripplons, allowing the construction of general multiripplon states obeying angular momentum selection rules. We also apply our formalism to a concrete example: a weakly interacting two-component Bose mixture realizing a self-bound superfluid droplet. The resulting description is universal in the sense that it applies to surface dynamics of generic nonrelativistic superfluids with a free interface, independent of microscopic details.

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• Cold atoms & matter waves
• Superfluids
• Surfaces
• Effective field theory