Fractional quantum Hall physics with ultracold Rydberg gases in artificial gauge fields

We study ultracold Rydberg-dressed Bose gases subject to artificial gauge fields in the fractional quantum Hall (FQH) regime. The characteristics of the Rydberg interaction gives rise to interesting many-body ground states different from standard FQH physics in the lowest Landau level (LLL). The non-local but rapidly decreasing interaction potential favors crystalline ground states for very dilute systems. While a simple Wigner crystal becomes energetically favorable compared to the Laughlin liquid for filling fractions $\nu<1/12$, a correlated crystal of composite particles emerges already for $\nu \leq 1/6$ with a large energy gap to the simple Wigner crystal. The presence of a new length scale, the Rydberg blockade radius $a_B$, gives rise to a bubble crystal phase for $\nu\lesssim 1/4$ when the average particle distance becomes less than $a_B$, which describes the region of saturated, almost constant interaction potential. For larger fillings indications for strongly correlated cluster liquids are found.