Phonon Stability and Sound Velocity of Quantum Droplets in a Boson Mixture

TL;DR

This paper investigates the stability of phonon modes in quantum droplets formed in binary boson mixtures, revealing that spin-phonon interactions stabilize phonons and providing testable predictions for sound velocity.

Contribution

It extends Bogoliubov theory by including higher-order self-energy corrections, highlighting the role of spin-phonon interactions in phonon stabilization.

Findings

Phonon modes are stabilized by spin-phonon interactions.

Derived the sound velocity for quantum droplets.

Discussed Beliaev damping effects.

Abstract

Quantum droplets have been realized in experiments on binary boson mixtures and dipolar Bose gases. In these systems, the mean-field energy of the Bose-Einstein condensation is attractive, and the repulsive Lee-Huang-Yang energy is crucial for stability. The Bogoliubov theory incorrectly predicts that the phonon mode is dynamically unstable in the long-wavelength limit. In this work, we go beyond the Bogoliubov theory to study how the phonon mode is stabilized in the quantum droplet of a binary boson mixture. Similar to Beliaev's approach to a single-component Bose gas, we compute higher-order contributions to the self-energy of the boson propagator. We find that the interaction between spin and phonon excitations is the key for the phonon stability. We obtain the sound velocity which can be tested by measuring the superfluid critical velocity of the droplet in experiments. Beliaev damping of this quantum droplet is also discussed.