Quantum crystallography of Rydberg-dressed Bose gases on a square lattice

We numerically investigate the quantum crystallographic phases of a Rydberg-dressed Bose gas loaded on a square lattice by using the mean-field Gross--Pitaevskii model. For a relatively weak lattice confinement, the phases of ground state undergo amorphism, polycrystal, and polymorphism following the increase of the blockade radius, and if the confinement is stronger, a single crystal with a specific filling factor will be formed. In order to distinctively characterize these phases, the structure function is also studied. In such an anisotropic system, we report that the first diagonal element of the superfluid-fraction tensor should be a measurable quantity, and an anisotropy parameter can be defined. In addition, for such crystallographic phases, the interaction potential can manifest where the grain boundaries appear.