# Collective excitations of self-bound droplets of a dipolar quantum fluid

## TL;DR

This paper investigates the collective excitations of self-bound dipolar quantum droplets, revealing phonon propagation along filament-shaped droplets and characterizing the unbinding threshold through a soft monopole-like mode.

## Contribution

It provides a detailed analysis of collective modes in self-bound dipolar droplets, including the phonon dynamics and unbinding transition, extending understanding of quantum fluctuation-stabilized systems.

## Key findings

- Filament-shaped droplets act as quasi-1D waveguides for phonons.
- Unbinding threshold associated with a soft monopole-like excitation.
- Crossover from trap-bound to self-bound droplets quantified.

## Abstract

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 monopole-like 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.