Supersolid Droplet Crystal in a Dipole-Blockaded Gas

A novel supersolid phase is predicted for an ensemble of Rydberg atoms in the dipole-blockade regime, interacting via a repulsive dipolar potential softened at short distances. Using exact numerical techniques, we study the low-temperature phase diagram of this system, and observe an intriguing phase consisting of a crystal of mesoscopic superfluid droplets. At low temperature, phase coherence throughout the whole system, and the ensuing bulk superfluidity, are established through tunnelling of identical particles between neighboring droplets.

Figure 1

Snapshots of a system of bosons interacting via potential (1), at the four different temperatures 200 (a), 20 (b), 1.0 (c) and 0.1 (d), expressed in units of ${ϵ}_0$. Points shown are taken along individual particle world lines. The nominal value of $r_s$ in this case is 0.14, whereas the cutoff of the potential (1) is $R_c=0.3$.

Figure 2

Results shown are for $r_s=0.14$ and $R_c=0.3$. Temperature is in units of ${ϵ}_0$. (a) Pair correlation function $g(r)$ at a temperature $T=200$ (triangles), 20 (squares), 1.0 (diamonds) and 0.1 (circles). The simulated system comprises $N=200$ particles. (b) Superfluid density vs $T$ for systems with $N=100$ (square), and 200 (diamond) particles. (c) Frequency of occurrence of permutation cycles of length $L$ at the same four temperatures reported in panel (a). Longer permutation cycles occur at lower temperature.

Figure 3

Schematic ground state phase diagram of Eq. (2) as a function of $r_s$. The superfluid droplet crystal (SDC) is sandwiched between an insulating droplet crystal (IDC) and a superfluid (SF). For $R_c\lesssim r_s^C$, an IDC phase , a single-particle crystal (C) phase and a superfluid phase are observed. The widths of the SDC and C regions depend on the value of $R_c$.

Figure 4

Left panels: Monte Carlo snapshots of a system of $N=400$ particles, interacting via the potential (1), confined in a harmonic trap of strength $\Gamma =500{ϵ}_0$, at the two temperatures $T=100$ ${ϵ}_0$ (a) and $T=0.5$ ${ϵ}_0$ (b). Right panels: corresponding momentum distributions, all normalized to unity for comparison purposes. The value of $R_c$ in this case is 0.3. The development of secondary peaks at low temperature signals the occurrence of a supersolid phase.