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.
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.
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.
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.
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.
Shell-shaped Bose–Einstein condensates (BECs) represent a paradigmatic instance of quantum fluids in hollow geometries exhibiting phenomena that bridge from ultracold atomic to astrophysical realms. In this work, we present a comprehensive survey of the dynamics, thermodynamics, and collective excitations of shell-shaped BECs, synthesizing two decades of our group's theoretical work in light of recent experimental breakthroughs. We begin by analyzing the evolution of a BEC from filled-sphere to hollow-shell geometries, illustrating the necessity of microgravity conditions to avoid gravitational sag. We then analyze the collective mode structure across this evolution and pinpoint a universal dip in the frequency spectra as well as mode reconfiguration due to inner-surface excitations as robust signatures of the hollowing-out transition. Turning to vortex physics, we show that the closed-surface topology enforces vortex–antivortex configurations in shell-shaped BECs and that the natural annihilation of these pairs can be stabilized by rotation, with the critical rotation rate depending on shell thickness. In the thermodynamic domain, we investigate the interplay between shell inflation and the BEC phase transition, where adiabatic expansions lead to condensate depletion. This behavior motivates a study of the nonequilibrium dynamics of shell-shaped BECs; we perform such a study by constructing a time-dependent dynamic technique that can capture the evolution in both adiabatic and non-adiabatic regimes. Finally, we review recent experimental realizations of shell-shaped BECs, including the landmark creation of ultracold shells aboard the International Space Station, and outline prospects for exploring quantum fluids in curved geometries.
Ultracold quantum gases confined in three-dimensional bubble traps are promising tools for exploring many-body effects on curved manifolds. As an alternative to the conventional technique of radio-frequency dressing, we propose to create such shell-shaped Bose-Einstein condensates in microgravity based on dual-species atomic mixtures, and we analyze their properties as well as the feasibility of realizing symmetrically filled shells. Beyond similarities with the radio-frequency dressing method, as in the collective excitation spectrum, our approach has several natural advantages like the robustness of the created quantum bubbles and the possibility of magnifying shell effects through an interaction-driven expansion.