Fundamental theories and models of many-body physics can be probed in experiments on ultracold atoms held in place by electromagnetic fields. In particular, of considerable interest are systems under curved confinement, since they can yield exotic states of matter which would be impossible to obtain in flat space. In this study we focus on relatively small samples, where curvature effects are stronger, and analyze by Monte Carlo simulations the peculiar structure arising in an assembly of soft-core bosons subject to a trapping potential with spherical symmetry. Upon suitable tuning of the parameters, 100 particles or so group together in clusters arranged in a shell with icosahedral symmetry. As the number of particles increases, a second shell gradually develops, concentric to (and partly overlapping with) the original one, where clusters are in perfect registry with the first shell, thus forming a dodecahedral pattern. Cluster arrangements with the symmetry of other polyhedra are seen for different sets of parameters. At low temperature the superfluid density is nonuniform in the radial direction; heating the system progressively, superfluidity eventually vanishes while still clusters are present, a behavior resembling the transition from supersolid to normal solid on a plane. Two shells of clusters are also observed in systems of classical or distinguishable quantum particles, but in those cases the shells are more fragile to thermal fluctuations.
Fundamental theories and models of many-body physics can be probed in experiments on ultracold atoms held in place by electromagnetic fields. In particular, of considerable interest are systems under curved confinement, since they can yield exotic states of matter which would be impossible to obtain in flat space. In this study we focus on relatively small samples, where curvature effects are stronger, and analyze by Monte Carlo simulations the peculiar structure arising in an assembly of soft-core bosons subject to a trapping potential with spherical symmetry. Upon suitable tuning of the parameters, 100 particles or so group together in clusters arranged in a shell with icosahedral symmetry. As the number of particles increases, a second shell gradually develops, concentric to (and partly overlapping with) the original one, where clusters are in perfect registry with the first shell, thus forming a dodecahedral pattern. Cluster arrangements with the symmetry of other polyhedra are seen for different sets of parameters. At low temperature the superfluid density is nonuniform in the radial direction; heating the system progressively, superfluidity eventually vanishes while still clusters are present, a behavior resembling the transition from supersolid to normal solid on a plane. Two shells of clusters are also observed in systems of classical or distinguishable quantum particles, but in those cases the shells are more fragile to thermal fluctuations.
Confinement can have a considerable effect on the behavior of particle systems and is therefore an effective way to discover new phenomena. A notable example is a system of identical bosons at low temperature under an external field mimicking an isotropic bubble trap, which constrains the particles to a portion of space close to a spherical surface. Using path integral Monte Carlo simulations, we examine the spatial structure and superfluid fraction in two emblematic cases. First, we look at soft-core bosons, finding the existence of supersolid cluster arrangements with polyhedral symmetry; we show how different numbers of clusters are stabilized depending on the trap radius and the particle mass, and we characterize the temperature behavior of the cluster phases. A detailed comparison with the behavior of classical soft-core particles is provided too. Then, we examine the case, of more immediate experimental interest, of a dipolar condensate on the sphere, demonstrating how a quasi-one-dimensional supersolid of clusters is formed on a great circle for realistic values of density and interaction parameters. Crucially, this supersolid phase is only slightly disturbed by gravity. We argue that the predicted phases can be revealed in magnetic traps with spherical-shell geometry, possibly even in a lab on Earth. Our results pave the way for future simulation studies of correlated quantum systems in curved geometries.
We study the low-temperature states of a system of spinless bosons trapped in a broad spherical shell. In our virtual (path-integral Monte Carlo) experiments, we specifically examine how the equilibrium structure and overall superfluidity of the system are affected by a change of the interparticle-potential core from hard to increasingly soft. In this manner we bridge the gap between the behaviors of two species of bosons: Helium-like atoms, which self-assemble into ordinary crystalline solids, and Rydberg-dressed atoms, which in simulation form cluster (super)solids. We also vary the particle mass, i.e., the quantumness of the system, so as to modify the relative stability of ``solid'' and fluid states. We thus find a whole spectrum of (finite-size) phases with a curved structure, including multilayer and cluster phases, as well as superfluids and single layer supersolids. In particular, we confirm that supersolids only occur in the presence of clusters. By considering three system sizes (from 60 to 180 particles), but rescaling the trap radius so that the density stays fixed, we verify that supersolid states only exist in the same range of particle masses. Our model serves as a platform to test how emergent properties are modified, in spherical geometry, in the crossover from atoms to dressed atoms.
We investigate the structural properties and superfluid behavior of soft-core bosons confined in a spherical bubble trap at large particle numbers (N≤1800). Using Path Integral Monte Carlo simulations with worm algorithm sampling in continuous space, we show that increasing N drives a sequence of layering transitions: beyond the established bilayer supersolid, a third concentric layer of clusters emerges at N≈1800. By analyzing the distribution of permutation cycles distribution, we demonstrate that a finite superfluid fraction (fs≈10%) persists even in this multi-layer regime. These findings clarify the role of particle number in driving layer formation on curved manifolds, offering a concrete guide for future experiments with bubble-trapped bosons.
We study a system of penetrable bosons embedded in a spherical surface. Under the assumption of weak interaction between the particles, the ground state of the system is, to a good approximation, a pure condensate. We employ thermodynamic arguments to investigate, within a variational ansatz for the single-particle state, the crossover between distinct finite-size ``phases'' in the parameter space spanned by the sphere radius and the chemical potential. In particular, for radii up to a few interaction ranges we examine the stability of the fluid phase with respect to a number of crystal-like arrangements having the symmetry of a regular or semiregular polyhedron. We find that, while quantum fluctuations keep the system fluid at low density, upon compression it eventually becomes inhomogeneous, i.e., particles gather together in clusters. As the radius increases, the nature of the high-density aggregate varies and we observe a sequence of transitions between different cluster phases (``solids''), whose underlying rationale is to maximize the coordination number of clusters, while ensuring at the same time the proper distance between each neighboring pair. We argue that, at least within our mean-field description, every cluster phase is supersolid.
Unveiling the principles behind self-organization in quantum systems is of paramount importance, both intrinsically and practically, in view of foreseeable technological applications. Recently, increasing attention has been paid to atomic systems in curved geometries, which are a promising platform for the discovery of new emergent phenomena. A notable example is that of a gas of ultracold atoms loaded into a thin spherical shell, according to a protocol introduced by Zobay and Garraway more than 20 years ago. However, gravity prevents a dilute assembly of atoms from uniformly spreading throughout the shell, which explains why experiments on the condensation and superfluidity of bubble-trapped gases are usually conducted in space under microgravity conditions. In this paper, we focus instead on strongly interacting quantum particles in a bubble trap, choosing the cluster supersolid of soft-core bosons as a testbed. To study the impact of gravity on supersolid order, we consider a gedanken experiment in which the strength of gravity relative to the core repulsion is gradually enhanced. Using path integral Monte Carlo simulations, we trace the parallel evolution of system structure and superfluidity at low temperature, finding that the latter is sizable only when gravity is a small perturbation or, at the other extreme, so strong that particles are all gathered in one cluster at the bottom of the trap. Finally, we assess the relevance of gravity for the equilibrium behavior of ultracold Rydberg-dressed atoms in a bubble trap, concluding that in some cases clues of the supersolid phase in the absence of gravity could be found even in a laboratory on Earth.
We study the interplay between the anisotropy of the dipole-dipole interaction and confinement in a curved geometry by means of the extended Gross-Pitaevskii equation, which allows us to characterize the ground state of a dipolar Bose gas under the confinement of a bubble trapping potential. We do so in terms of the scattering length a and the number of particles. We observe the emergence of a wide variety of dipolar solids, consisting on arrangements of different number of droplets along a ring over the equator of the spherical shell confinement. We also show that the transition between the different phases of the system can be engineered by varying a , the number of particles or the radius of the trap, parameters, which can be experimentally tuned. Finally, we show the importance of working in microgravity conditions as gravity unstabilizes the observed dipolar solids. Published by the American Physical Society 2024