Controlling the spatial distribution of superfluidity in radially ordered Coulomb clusters

When a few identical charged particles are trapped in a spherical electric field at low temperature, they form concentric shells resembling atoms. The behavior of these “artificial atoms” is easily controlled by varying the field strength. In particular, it is possible to transfer the system from a liquidlike to a crystal-like state. We analyze artificial atoms consisting of Bose particles and observe superfluid behavior, which even persists in the intermediate radially ordered crystal regime. Furthermore, we demonstrate that the superfluid density can be directed in a controlled way either to the core or to the boundary of the atom.

Figure 1

(Color online) Variance of the mean relative interparticle distance fluctuations ${\sigma }_{u_r}$ vs $u_r$, Eqs. (2, 3), in the vicinity of the quantum melting transition from a mesoscopic RO solid (left of peak) to a liquid (right) for $N=19\dots 34$ particles. The red line without symbols is a parabolic fit through all data points. The peak is located at $u_r^{\text{crit}}\approx 0.25$ (vertical dotted line), except for $N=19,29$ where $u_r^{\text{crit}}\approx 0.22$. Insets show typical configurations of 29 particles at $u_r=0.16$ (left, corresponding to $\lambda =30$) and $u_r=0.4$ (right, corresponding to $\lambda =18$), as obtained in the PIMC simulations that averaged over 50,000 steps.

Figure 2

(Color online) Total superfluid fraction ${\gamma }_s$ versus coupling parameter $\lambda$ for $N=19$. RM occurs around $\lambda \approx 28$ and OM occurs around $\lambda \approx 50$. To analyze the systematic error of the computation of ${\gamma }_s$, results without particle exchange (blue dashed curve) are also shown. The straight lines are a guide to the eye.

Figure 3

(Color online) Radial distribution of the total density $\rho \left(r\right)$ (lines) and the superfluid density ${\rho }_s\left(r\right)$ (filled curves) for the magic cluster $N=19$ and the nonmagic cluster $N=21$. Both systems are in the liquid phase at $\lambda =20$ (solid black), whereas $\lambda =28$ $\left(N=19\right)$ and $\lambda =38$ $\left(N=21\right)$ correspond to solidlike configurations close to the freezing transition (dashed red). Insets sketch the ground-state shell configurations of the two clusters.

Figure 4

(Color online) Superfluid fraction ${\gamma }_{s\nu }$, Eq. (7), of shell $\nu$ vs particle number in the solid state $\lambda =28$, “Sh. 1” denotes the innermost shell. Also shown is the hexagonal symmetry parameter $P_6$ (red, uppermost curve), right axis. Numbers in parentheses indicate magic shell configurations in the cluster center (red shaded rectangles). The black shaded columns cover the region where superfluidity resides in the system core. Starting from $N=31$, a new shell is formed in the center (counted as 0-shell, ${\gamma }_{s0}$ is not shown separately).