Reply to the Comment on "Shell-Shaped Quantum Droplet in a Three-Component Ultracold Bose Gas"

TL;DR

This paper defends the existence of a shell-shaped quantum droplet in a three-component Bose gas, showing it is an excited state that can be experimentally realized with proper protocols, and clarifies its stability and energetic properties.

Contribution

It demonstrates that the shell-shaped structure is an excited state, energetically degenerate with dimers in the thermodynamic limit, and can be experimentally produced with appropriate trap-release protocols.

Findings

Shell-shaped structure is an excited state for finite systems.

Core-shell structure becomes degenerate with dimer in thermodynamic limit.

Proper mode-matching enables experimental realization.

Abstract

In our Letter (Phys. Rev. Lett. 134, 043402 (2025)), we proposed a self-bound shell-shaped BEC in a three-component ($1,2,3$) Bose gas, where $(2,3)$ and $(1,2)$ droplets are linked as core-shell structure. A recent Comment (Ancilotto, 2505.16554) argued that a ``dimer" configuration should be instead the ground state, where $(2,3)$ and $(1,2)$ stay side-by-side. Moreover, Ancilotto also explored the state formation, finding that a naive trap-release protocol was unable to produce the core-shell structure. In this reply we show that our core-shell structure is an excited state for finite-size systems, while it becomes energetically degenerate with dimer configuration in thermodynamic limit. Furthermore, we find the core-shell structure is locally stable under external perturbations, and if one pays careful attention to mode-matching, a trap-release protocol can well produce this structure.