Layering and superfluidity of soft-core bosons in shallow spherical traps

Abstract

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 weak trapping potential with spherical symmetry. Upon suitable tuning of the parameters, a hundred 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 non-uniform 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. All these behaviors can in principle be tested in systems of Rydberg-dressed atoms loaded into a bubble trap.

Figures (12)

• Figure 1: Structure of bosons at $R=1.15,T=0.5$, and $\lambda=0.16$. (a--c): Isodensity surfaces of the bosons at $N=200$ (a), $N=400$ (b), and $N=600$ (c). Clusters are red in the first shell and blue in the second shell; the pink cluster lies at the center of the trap. (d): Integrated radial density $n(r)$ (see text) at discrete values $r$ of the distance from the trap center. Lines are a guide for the eye: $N=200$ (grey), 300 (orange), 400 (green), 500 (blue), and 600 (red). To facilitate the comparison between different system sizes, each $n(r)$ has been divided by $N$.
• Figure 2: (a): Typical equilibrium configuration for $N=600, R=1.15,T=0.5$, and $\lambda=0.16$ ($\theta$ is the polar angle and $\phi$ is the azimuthal angle). Red (blue) symbols correspond to beads in the first (second) shell, while the beads in the central cluster have been omitted for clarity. (b): The same as (a), but for $N=480$, $R=1.05,T=0.7$, and $\lambda=0.16$. (c--d): Simplified 3D representation of the cluster structure in (a) and (b), respectively. Clusters are generated through a thresholding algorithm and their size is suggestive of the number of particles within. Lines are a guide for the eye, pointing out the formation of different polyhedral structures.
• Figure 3: System with $N=600$ bosons at $R=1.15$ and $\lambda=0.16$. (a): Distribution $P(L)$ of cycle lengths (see text) for $T=0.5$ (blue), 1.5 (grey), and 5 (red). (b): Components of the superfluid fraction $f_s$ along three mutually-orthogonal directions. (c): Integrated radial density $n(r)$ for $T=0.5$ (blue), 5 (red), 10 (green) and 20 (orange).
• Figure 4: System with $N=600$ bosons at $R=1.15$ and $T=0.5$. (a): Components of the superfluid fraction $f_s$. (b--e): Integrated superfluid radial density $n_s(r)$ (see text) vs. integrated radial density $n(r)$ at various $\lambda$.
• Figure S1: Snapshots of worldline configurations projected onto the $\phi$-$\cos \theta$ plane, at four values of $\lambda$: 0.1(a), 0.2(b), 0.35(c), 0.4(d).