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

TL;DR

This paper critiques a recent proposal of shell-shaped quantum droplets in a three-component Bose gas, arguing they are not true ground states and likely unfeasible experimentally.

Contribution

It clarifies that the proposed shell structures are local minima, not ground states, challenging their stability and experimental realization claims.

Findings

Structures are local energy minima, not ground states.

Likely impossible to realize in practice.

Questions the stability of the proposed shells.

Abstract

In a recent paper (Y. Ma and X. Cui, Phys. Rev. Lett. 134, 043402 (2025)), a new type of shell-shaped Bose-Einstein condensate with a self-bound character has been proposed, made of three-component $Na^{23}K^{39}K^{41}$ Bose mixture (species (1,2,3) in the following), where the mixtures (1, 2) and (2, 3) both form quantum droplets. The proposed structures are made of an outer shell of liquid (1,2) enveloping a spherical core of (2,3) liquid, which is claimed to be stable without the need of any trapping potential. I comment in the following that these structures are not actually the ground-states solutions to the system but rather local energy minima, and most likely impossible to realize in practice.