  Spontaneously crystalline ground states, called quantum crystals, of a
trapped Rydberg-dressed Bose-Einstein condensate are numerically investigated.
As a result described by a mean-field order parameter, such states
simultaneously possess crystalline and superfluid properties. A hexagonal
droplet lattice is observed in a quasi-two-dimensional system when dressing
interaction is sufficiently strong. Onset of these states is characterized by a
drastic drop of the non-classical rotational inertia proposed by Leggett [Phys.
Rev. Lett. 25, 1543 (1970)]. In addition, an AB stacking bilayer lattice can
also be attained. Due to an anisotropic interaction possibly induced by an
external electric field, transition from a hexagonal to a nearly square droplet
lattice is also observed.
