Reaching the quantum Hall regime with rotating Rydberg-dressed atoms

Despite the striking progress in the field of quantum gases, one of their much anticipated applications—the simulation of quantum Hall states—remains elusive: all experimental approaches so far have failed in reaching a sufficiently small ratio between atom and vortex densities. In this paper we consider rotating Rydberg-dressed atoms in magnetic traps: these gases offer strong and tunable nonlocal repulsive interactions and very low densities; hence they provide an exceptional platform to reach the quantum Hall regime. Based on the Lindemann criterion and the analysis of the interplay of the length scales of the system, we show that there exists an optimal value of the dressing parameters that minimizes the ratio between the filling factor of the system and its critical value to enter the Hall regime, thus making it possible to reach this strongly correlated phase for more than 1000 atoms under realistic conditions.

Figure 1

Qualitative phase diagram of the Rydberg dressed gas as a function of the magnetic length $l_B$ and the interaction parameter $g^{\prime }$. For $l_B\to \infty$ (thus $B\to 0$), the system displays a superfluid (SF), supersolid (SS), or crystal (C) state. For interactions $g^{\prime }<g_o$, by decreasing $l_B$, the system presents first a crossover into the lowest Landau level triangular vortex lattice (LLL Tr. VL) (at $l_B\sim \xi /{\alpha }_{\xi }$), then a transition to the QH regime for $l_B\sim l_L/{\alpha }_L$. For $g^{\prime }>g_o$, instead, the LLL vortex lattice phase disappears and the QH regime is reached for lower values of the filling factor. The thin red lines are lines at constant filling factor.

Figure 2

Filling factor as a function of the mixing angle $\theta$ for $\delta =20\mathrm{MHz}$ and $N=15000$. The solid lines correspond to rotating gases with ${\mathrm{\Omega }}_{\mathrm{tr}}=2\pi 100\mathrm{Hz}$ and different values of $\gamma$. The green dot-dashed line is an estimate of $\nu$ for optically induced magnetic fields based on [45] obtained with counterpropagating Gaussian beams (waist $w=50\mu \mathrm{m}$, wavelength $\lambda =790\mathrm{nm}$) for ${\mathrm{\Omega }}_{\mathrm{tr}}=2\pi 20\mathrm{Hz}$. The red dashed line represents the critical filling factor assuming ${\nu }_{c,0}=8$; its cusp determines the optimal interaction point at $\theta \approx 0.05$.

Figure 3

Filling factor at the optimal interaction point [Eq. (11)] as a function of the atom number $N$ assuming ${\nu }_{c,0}=8$ [panel (a)] and ${\nu }_{c,0}=2$ [panel (b)]. The critical filling is depicted by dashed lines and the system reaches the QH regime for ${\nu }_o<{\nu }_{c,0}$. For ${\nu }_{c,0}=8$, the Rydberg-dressed gas reaches the QH regime for a large range of values of $N$ for rotation frequencies with $\gamma >0.95$. For ${\nu }_{0,c}=2$ the QH regime is reached for systems with $N\lesssim 2000$ at $\gamma =0.99$. In (b) the area on the right of the dotted black line corresponds to system with at least 200 magnetic fluxes.