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arXiv:2605.28469

Wetting of quantum fluids: a route to free-standing shell-shaped quantum droplets

Francesco Ancilotto

Published May 27, 2026• 0 citations
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Abstract

We investigate wetting phenomena between self-bound quantum fluids in a three-component Bose mixture of $^{23}$Na, $^{39}$K, and $^{41}$K 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 a 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 new possibilities for studying capillarity, topology, and superfluidity in multicomponent quantum droplets.

DOI
10.48550/arxiv.2605.28469

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Wetting of quantum fluids: A route to free-standing shell-shaped quantum droplets

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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.

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

Francesco Ancilotto

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.

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New Journal of Physics•Sep 1, 2023•10 citations
We investigate wetting phenomena between self-bound quantum fluids in a three-component Bose mixture of 23^{23}23Na, 39^{39}39K, and 41^{41}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)(1,2)(1,2) and (2,3)(2,3)(2,3), and study the adsorption of the softer (1,2)(1,2)(1,2) liquid on a stiffer (2,3)(2,3)(2,3) substrate. By tuning the interspecies scattering length a12a_{12}a12​, we show that the surface tension of the (1,2)(1,2)(1,2) liquid can be strongly varied, driving a transition from partial wetting to complete wetting of the (2,3)(2,3)(2,3) phase. The contact angle extracted from cylindrical-cap geometries decreases continuously with increasing a12a_{12}a12​ and vanishes near a critical value a12c=−42 a0a_{12}^{c}= -42\,a_0a12c​=−42a0​. In the complete-wetting regime, a finite amount of (1,2)(1,2)(1,2) liquid wraps around a spherical (2,3)(2,3)(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.
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 study liquid quantum droplets in a mixture of two-component Bose-Einstein condensates under variable confinement introduced along one or two spatial dimensions. Although the atom-atom scattering has a three-dimensional character, discreteness of the available modes in the reduced dimension(s) strongly influences the zero-point energy, which for a weakly interacting three-dimensional system is given by the Lee-Huang-Yang term. Here, we generalize the result of Lee, Huang, and Yang and calculate the higher order corrections to the mean-field energy for a single component Bose-Einstein condensate under condition of a tight confinement in one or two spatial directions. We apply our results to the two-component mixture of bosonic species under conditions favorable for the creation of quantum liquid droplets, which constitute a perfect playground for studies of the beyond mean-field effects. Our findings allow one to analyze the properties of quantum droplets at the dimensional crossover and provide demanding conditions for accessing quasilow dimensions. They also pave a way for experimental exploration of this state of matter in reduced dimensions.
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 Na23K39K41Na^{23}K^{39}K^{41}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.
Quantum droplets are a quantum analog to classical fluid droplets in that they are self-bound and display liquid-like properties---such as incompressibility and surface tension---though their stability is the result of quantum fluctuations. One of the major systems for observing quantum droplets is two-component Bose gases. Two-component droplets are typically considered to be balanced, having a fixed ratio between the densities of the two components. This work goes beyond the fixed density ratio by investigating spherical droplets in imbalanced mixtures. With increasing imbalance, the droplet is able to lower its energy up to a limit, at which point the droplet becomes saturated with the atoms of the majority component and any further atoms added to this component cannot bind to the droplet. Analyzing the breathing mode dynamics of imbalanced droplets indicates that the droplet can emit particles, as in balanced mixtures, but the imbalance leads to an intricate superposition of multiple simultaneously decaying collective oscillations.
Abstract The static and dynamic properties of self-bound quantum droplets in a one-dimensional Bose-Bose mixture are discussed in the spirit of the Hartree–Fock-Bogoliubov theory. This latter enables us to provide beyond the Lee-Huang-Yang (LHY) quantum corrections to the equation of state at both zero and finite temperatures. In the uniform case our results for the ground-state energy and the critical temperature are confirmed through comparison with Quantum Monte-Carlo simulation and with available theoretical results. The density profiles are supported by numerical simulations of the generalized Gross-Pitaevskii equation which selfconsistently includes higher-order terms originating from the normal and anomalous fluctuations under the local density approximation. We show that the density exhibits a dip near its center in the flat-top plateau region for large interspecies interactions. We exemplify the impact of the beyond LHY corrections on the spatiotemporal evolution of the self-bound droplet in the presence of excitation induced by periodic density modulation. It is found that higher-order corrections may lead to the formation of a train of small droplets. We then extend our study for the case of inhomogeneous droplets in quasi one-dimensional Bose mixtures.