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

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.

Figures (2)

• Figure 1: Density profile along the line passing through the center of the droplets. Panel a): shell-structure with liquid (1,2) enveloping the (2,3) core; lower panel: ground-state for the same system ("dimer" structure). Solid line: species 1;dotted line: species 2; dash-dot line: species 3.
• Figure 2: Total density maps corresponding to the two structures in Fig.1. Left: shell-shaped structure; Right: ground-state "dimer" solution.