Bose-Einstein condensate shells, while occurring in ultracold systems of coexisting phases and potentially within neutron stars, have yet to be realized in isolation on Earth due to the experimental challenge of overcoming gravitational sag. Motivated by the expected realization of hollow condensates by the space-based Cold Atomic Laboratory in microgravity conditions, we study a spherical condensate undergoing a topological change from a filled sphere to a hollow shell. We argue that the collective modes of the system show marked and robust signatures of this hollowing transition accompanied by the appearance of a new boundary. In particular, we demonstrate that the frequency spectrum of the breathing modes shows a pronounced depression as it evolves from the filled sphere limit to the hollowing transition. Furthermore, when the center of the system becomes hollow surface modes show a global restructuring of their spectrum due to the availability of a new, inner, surface for supporting density distortions. We pinpoint universal features of this topological transition as well as analyse the spectral evolution of collective modes in the experimentally relevant case of a bubble-trap.
Bose-Einstein condensate shells, while occurring in ultracold systems of coexisting phases and potentially within neutron stars, have yet to be realized in isolation on Earth due to the experimental challenge of overcoming gravitational sag. Motivated by the expected realization of hollow condensates by the space-based Cold Atomic Laboratory in microgravity conditions, we study a spherical condensate undergoing a topological change from a filled sphere to a hollow shell. We argue that the collective modes of the system show marked and robust signatures of this hollowing transition accompanied by the appearance of a new boundary. In particular, we demonstrate that the frequency spectrum of the breathing modes shows a pronounced depression as it evolves from the filled sphere limit to the hollowing transition. Furthermore, when the center of the system becomes hollow surface modes show a global restructuring of their spectrum due to the availability of a new, inner, surface for supporting density distortions. We pinpoint universal features of this topological transition as well as analyse the spectral evolution of collective modes in the experimentally relevant case of a bubble-trap.
Bose-Einstein condensate shells, while occurring in ultracold systems of coexisting phases and potentially within neutron stars, have yet to be realized in isolation on Earth due to the experimental challenge of overcoming gravitational sag. Motivated by the expected realization of hollow condensates by the space-based Cold Atomic Laboratory in microgravity conditions, we study a spherical condensate undergoing a topological change from a filled sphere to a hollow shell. We argue that the collective modes of the system show marked and robust signatures of this hollowing transition accompanied by the appearance of a new boundary. In particular, we demonstrate that the frequency spectrum of the breathing modes shows a pronounced depression as it evolves from the filled-sphere limit to the hollowing transition. Furthermore, when the center of the system becomes hollow surface modes show a global restructuring of their spectrum due to the availability of a new, inner, surface for supporting density distortions. We pinpoint universal features of this topological transition as well as analyse the spectral evolution of collective modes in the experimentally relevant case of a bubble-trap.
Static, dynamic, and topological properties of hollow systems differ from those that are fully filled as a result of the presence of a boundary associated with an inner surface. Hollow Bose-Einstein condensates (BECs) naturally occur in various ultracold atomic systems and possibly within neutron stars but have hitherto not been experimentally realized in isolation on Earth because of gravitational sag. Motivated by the expected first realization of fully closed BEC shells in the microgravity conditions of the Cold Atomic Laboratory aboard the International Space Station, we present a comprehensive study of spherically symmetric hollow BECs as well as the hollowing transition from a filled sphere BEC into a thin shell through central density depletion. We employ complementary analytic and numerical techniques in order to study equilibrium density profiles and the collective mode structures of condensate shells hosted by a range of trapping potentials. We identify concrete and robust signatures of the evolution from filled to hollow structures and the effects of the emergence of an inner boundary, inclusive of a dip in breathing-mode-type collective mode frequencies and a restructuring of surface mode structure across the transition. By extending our analysis to a two-dimensional transition of a disk to a ring, we show that the collective mode signatures are an essential feature of hollowing, independent of the specific geometry. Finally, we relate our work to past and ongoing experimental efforts and consider the influence of gravity on thin condensate shells. We identify the conditions under which gravitational sag is highly destructive and study the mode-mixing effects of microgravity on the collective modes of these shells.
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.
Inspired by investigations of Bose-Einstein condensates (BECs) produced in the Cold Atom Laboratory (CAL) aboard the International Space Station, we present a study of thermodynamic properties of shell-shaped BECs. Within the context of a spherically symmetric ``bubble trap'' potential, we study the evolution of the system from small filled spheres to hollow, large, thin shells via the tuning of trap parameters. We analyze the bubble trap spectrum and states and track the distinct changes in spectra between radial and angular modes across the evolution. This separation of the excitation spectrum provides a basis for quantifying dimensional crossover to quasi-2D physics at a given temperature. Using the spectral data, for a range of trap parameters, we compute the critical temperature for a fixed number of particles to form a BEC. For a set of initial temperatures, we also evaluate the change in temperature that would occur in adiabatic expansion from small filled sphere to large thin shell were the trap to be dynamically tuned. We show that the system cools during this expansion but that the decrease in critical temperature occurs more rapidly, thus resulting in depletion of any initial condensate. We contrast our spectral methods with standard semiclassical treatments, which we find must be used with caution in the thin-shell limit. With regard to interactions, using energetic considerations and corroborated through Bogoliubov treatments, we demonstrate that they would be less important for thin shells due to reduced density but vortex physics would become more predominant. Finally, we apply our treatments to traps that realistically model CAL experiments and borrow from the thermodynamic insights found in the idealized bubble case during adiabatic expansion.
We investigate the hollowing transition of a shell-shaped Bose-Einstein condensate using collective excitations. The shell is created using an immiscible dual-species Bose-Einstein condensate mixture, with its hollowness controlled by tuning the repulsive interspecies interaction via a Feshbach resonance. Our results reveal two distinct monopole modes in which the two condensates oscillate either in phase or out of phase. The spectrum of the out-of-phase mode exhibits a nonmonotonic dependence on the interspecies interaction, providing a clear signature of the topology change from a filled to a hollow condensate. Furthermore, we find that the critical point of the hollowing transition depends strongly on the number ratio of the two species. Our findings provide a detailed understanding of the topology change in shell-shaped quantum gases and pave the way for future study of quantum many-body phenomena in curved spaces.
The recent developments of microgravity experiments with ultracold atoms have produced a relevant boost in the study of shell-shaped ellipsoidal Bose-Einstein condensates. For realistic bubble-trap parameters, here we calculate the critical temperature of Bose-Einstein condensation, which, if compared to the one of the bare harmonic trap with the same frequencies, shows a strong reduction. We simulate the zero-temperature density distribution with the Gross-Pitaevskii equation, and we study the free expansion of the hollow condensate. While part of the atoms expands in the outward direction, the condensate self-interferes inside the bubble trap, filling the hole in experimentally observable times. For a mesoscopic number of particles in a strongly interacting regime, for which more refined approaches are needed, we employ quantum Monte Carlo simulations, proving that the nontrivial topology of a thin shell allows superfluidity. Our work constitutes a reliable benchmark for the forthcoming scientific investigations with bubble traps.