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.
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.
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 Na23K39K41 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.
Shell-shaped Bose-Einstein condensate is a typical quantum system in curved geometry. Here, we propose a new type of shell-shaped Bose-Einstein condensate with a self-bound character, thereby liberating it from stringent conditions such as microgravity or a fine-tuned trap. Specifically, we consider a three-component (1, 2, 3) ultracold Bose gas where (1, 2) and (2, 3) both form quantum droplets. The two droplets are mutually immiscible due to strong 1-3 repulsion, while still linked by component-2 to form a globally self-bound object. The outer droplet then naturally develops a shell structure without any trapping potential. It is shown that the shell structure can significantly modify the equilibrium density of the core, and lead to unique collective excitations highlighting the core-shell correlation. All results have been demonstrated in a realistic ^{23}Na-^{39}K-^{41}K mixture. By extending quantum droplets from flat to curved geometries, this Letter paves the way for future explorations of the interplay of quantum fluctuations and nontrivial real-space topologies in ultracold gases.
We investigate wetting phenomena between self-bound quantum fluids in a three-component Bose mixture of 23Na, 39K, and 41K atoms. Within a density-functional approach including mean-field interactions and Lee-Huang-Yang quantum-fluctuation corrections, we consider two binary quantum liquids, formed by components (1,2) and (2,3), and study the adsorption of the softer (1,2) liquid on a stiffer (2,3) substrate. By tuning the interspecies scattering length a12, we show that the surface tension of the (1,2) liquid can be strongly varied, driving a transition from partial wetting to complete wetting of the (2,3) phase. The contact angle extracted from cylindrical-cap geometries decreases continuously with increasing a12 and vanishes near a critical value a12c=−42a0. In the complete-wetting regime, a finite amount of (1,2) liquid wraps around a spherical (2,3) droplet, producing a self-bound core-shell droplet without external confinement, whose component-1 density has a shell-like, hollow projection. We further show that such shell-shaped quantum droplets can sustain quantized vortical excitations. These results identify wetting as a route to engineering free-standing shell-shaped quantum liquids and suggest new possibilities for studying capillarity, topology, and superfluidity in multicomponent quantum droplets.
We investigate wetting phenomena between self-bound quantum fluids in a three-component Bose mixture of Na 23 , K 39 , and K 41 atoms. Within a density-functional approach including mean-field interactions and Lee-Huang-Yang quantum-fluctuation corrections, we consider two binary quantum liquids formed by components (1, 2) and (2, 3) and study the adsorption of the softer (1, 2) liquid on a stiffer (2, 3) substrate. By tuning the interspecies scattering length a 12 , we show that the surface tension of the (1, 2) liquid can be strongly varied, driving a transition from partial wetting to complete wetting of the (2, 3) phase. The contact angle extracted from cylindrical-cap geometries decreases continuously with increasing a 12 and vanishes near the critical value a 12 c = − 42 a 0 . In the complete-wetting regime, a finite amount of (1, 2) liquid wraps around a spherical (2, 3) droplet, producing a self-bound core-shell droplet without external confinement, whose component-1 density has a shell-like, hollow projection. We further show that such shell-shaped quantum droplets can sustain quantized vortical excitations. These results identify wetting as a route to engineering free-standing shell-shaped quantum liquids and suggest possibilities for studying capillarity, topology, and superfluidity in multicomponent quantum droplets.
Among settings which have recently been elaborated for the creation of stable multidimensional solitons, most advanced, as concerns the theory and experiment alike, is the work with quantum droplets (QDs) in atomic BEC. Important theoretical predictions for fundamental and topologically structured soliton-like (stably self-trapped) QDs have been published in many papers, starting from the pioneering work of Petrov [Phys. Rev. Lett. 115, 155302 (2015)]. Simultaneously, the experimental advancement in the making of QDs in binary BECs, as well as in single-component BECs of atoms carrying magnetic dipole moments, have been really remarkable and unique. Successful experiments followed the first theoretical prediction of the QDs very quickly, and the progress in the experimental work was much faster than in other areas of physics where stable multidimensional solitons were predicted. The basis of these works is a correction to the MF (mean-field) BEC dynamics produced by quantum fluctuations around MF states. The correction was first predicted in 1957 by Lee, Huang, and Yang (LHY). The breakthrough proposal made by Petrov [Phys. Rev. Lett. 115, 155302 (2015)] was to use the effective higher-order (quartic) self-repulsion, produced by the LHY effect in the atomic BEC, as a mechanism arresting the collapse driven by mutual attraction of two self-repulsive components in a binary quantum bosonic gas. The balance between the inter-species attraction and LHY-induced self-repulsion gives rise to stable 3D and quasi-2D (pancake-shaped) localized bound states in the form of the quantum droplets (QDs). In single-component condensates of magnetic atoms, the attraction is provided by the long-range dipole–dipole interaction (Chomaz et al., 2016; Schmitt et al., 2016). The competition between the MF attraction and LHY repulsion maintains a superfluid state whose density (taking very low values) cannot exceed a certain maximum, thus making it effectively incompressible. This is a reason why this quantum macroscopic state of matter is identified as a superfluid. Accordingly, localized states filled by this quantum fluid are called “droplets.” In addition to the 3D QDs, droplets in the effectively 2D setting, which may exist under the action of tight confinement in one direction, imposed by an external potential, were theoretically predicted [Petrov and Astrakharchik, Phys. Rev. Lett. 117, 100401 (2016)] and experimentally created [Cabrera et al., Science 359, 301-304 (2018)] too. This chapter provides a condensed review of basic theoretical results for stable QDs in binary BECs, maintained through the stable balance between the inter-species attraction and intra-species LHY repulsion. Both fundamental modes and ones with embedded vorticity are considered. The presentation is partly based on a review article by Luo et al. [Front. Phys. 16, 32501 (2021)]. In addition to 2D and 3D self-trapped QDs in free space, the present chapter addresses 2D fundamental and vortex modes trapped in a singular attractive potential, ∼−1/r2, which are stabilized by the LHY repulsion. Two subsequent chapters present a summary of experimental findings for QDs in binary BECs and for QDs in single-component BECs of magnetic atoms.