Supersolid Vortex Crystals in Rydberg-Dressed Bose-Einstein Condensates

We study rotating quasi-two-dimensional Bose–Einstein condensates, in which atoms are dressed to a highly excited Rydberg state. This leads to weak effective interactions that induce a transition to a mesoscopic supersolid state. Considering slow rotation, we determine its superfluidity using quantum Monte Carlo simulations as well as mean field calculations. For rapid rotation, the latter reveal an interesting competition between the supersolid crystal structure and the rotation-induced vortex lattice that gives rise to new phases, including arrays of mesoscopic vortex crystals.

Figure 1

(a) Schematics of the considered setup in which the ground states ($|g⟩$) of condensed atoms are off-resonantly coupled to high-lying Rydberg states ($|e⟩$) with a large laser detuning $\Delta$ and a small Rabi frequency $\Omega \ll \Delta$. The resulting effective interaction, shown in (b) can lead to the formation of mesoscopic supersolids in a quasi-two-dimensional condensate, exemplarily shown in panels (c) and (d). The extended plateau of the histogram $P(k)$ of $k$-particle permutations, shown in (c) indicates a large superfluid fraction, whereas the density shown in (d) demonstrates crystallization. The results correspond to $N=3000$ rubidium atoms confined in a trap with ${\omega }_{\mathrm{tr}}/2\pi =125\mathrm{Hz}$ and dressed to $\mathrm{Rb}(50S_{1/2})$ Rydberg states with realistic laser parameters of $\Delta /2\pi =75\mathrm{MHz}$ and $\Omega /2\pi =2.2\mathrm{MHz}$. The depicted QMC results yield a large superfluid fraction $f_s=0.51(4)$ for an experimentally accessible temperature of $T=42\mathrm{nK}$.

Figure 2

(a) Temperature dependence of the superfluid fraction for different particle numbers and $\alpha N=24500$, $\gamma =0$, and $r_c=2.65$. The horizontal arrow indicates the $T=0$ MF prediction [Eq. (3)]. As shown in the inset, all data points collapse on a single curve upon scaling $T$ by $N$. The vertical arrows indicate the temperatures used in (d) and (e). (b) Comparison of the radial density $\rho$ and superfluid density ${\rho }_s$ for $N=400$. Panels (c)–(e) show the corresponding ground-state densities obtained from (a) the MF approximation Eqs. (3, 4) and (b, c) the QMC simulations.

Figure 3

“Phase diagrams” for $\gamma N={10}^4$ and (a) $r_c=1$, (b) $r_c=3$, (c) $r_c=5$. The insets display ground-state density profiles at the indicated parameters, showing only the inner trap region for better visibility, where dark shading indicates high density and vice versa. The dimension of each inset is indicated by the vertical bar corresponding to a length of $5l$. The horizontal arrows at $\Omega =0$ show the supersolid transition obtained from LDA estimates of the roton instability as described in the text.

Figure 4

Density for $\Omega =0.8$ and (a) $r_c=7$, $\alpha N/r_c^4=7.5\times {10}^4$ and (b) $r_c=9$, $\alpha N/r_c^4=9\times {10}^4$.