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 give rise to interesting many-body ground states different from standard FQH physics in the lowest Landau level. The nonlocal 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 <1/12, a correlated crystal of composite particles emerges already for 1/6 with a large energy gap to the simple Wigner crystal. The presence of a new length scale, the Rydberg blockade radius a₁, gives rise to a bubble crystal phase for 1/4 when the average particle distance becomes less than a₁, which describes the region of saturated, almost constant interaction potential. For larger fillings indications for strongly correlated cluster liquids are found.