Mesoscopic dipolar quantum crystals

The ground state of a two-dimensional, harmonically confined mesoscopic assembly of up to 30 polar molecules is studied by computer simulations. As the strength of the confining trap is increased, clusters evolve from superfluid, to supersolid, to insulating crystals. For strong confinement, the crystalline structure can be predicted based on classical energetics. However, clusters of specific numbers of particles (i.e., $N=12$ and $N=19$) display a nonclassical crystalline structure, stabilized by quantum effects, in an intermediate range of confinement strength. In these cases, coexistence of quantum and classical crystalline configurations is observed at finite temperature.

Figure 1

Radial density profiles $\rho \left(r\right)$ for a two-dimensional system of $N=12$ dipolar bosons confined in a planar harmonic trap of different characteristic length $\xi$.

Figure 2

Ground-state density maps for a two-dimensional mesoscopic system of $N=12$ dipolar bosons confined in a harmonic trap of varying characteristic length $\xi$. All lengths are in units of $a$ (see text). (a) shows a superfluid, (b) a supersolid, (c) a nonclassical crystal, and (d) a classical crystal.

Figure 3

Ground-state density maps for a two-dimensional mesoscopic system of $N=19$ dipolar bosons confined in a harmonic trap of two different characteristic lengths $\xi$. All lengths are in units of $a$ (see text). The left part shows the nonclassical crystal, while the right one shows the classical one.

Figure 4

Configurational snapshots for a two-dimensional mesoscopic system of $N=12$ dipolar bosons confined in a harmonic trap of length $\xi =0.01$. All lengths are in units of $a$ (see text). The temperature of the simulation is $T=2.4\times {10}^3{\epsilon }_0$, about 30 times higher than that which yields ground-state physics. The system is found with roughly the same frequency in both crystalline configurations shown here, namely, ${\mathcal{C}}_3$ (left) and ${\mathcal{C}}_4$ (right). In the low-temperature limit, ${\mathcal{C}}_4$ prevails, for this value of $\xi$.