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We study the dynamics of bosonic atoms on a two-dimensional square lattice,where atomic interactions are long-ranged with either a box or soft-core shape.The latter can be realized through laser dressing ground-state atoms toelectronically excited Rydberg states. When the range of interactions is equalor larger than the lattice constant, the system is governed by an extendedBose-Hubbard model. We propose a quench process by varying the atomic hoppinglinearly across phase boundaries of the Mott insulator-supersolid andsupersolid-superfluid phases. Starting from a Mott insulating state, thedynamical evolution of the superfluid order parameter exhibits a universalbehaviour at the early stage, largely independent of interactions. Thedynamical evolution is significantly altered by strong, long-range interactionsat later times. Particularly, we demonstrate that density wave excitation isimportant when the quench rate is small. Moreover, we show that the quenchdynamics can be analyzed through time-of-flight images, i.e., measuring themomentum distribution and noise correlations.

Quench dynamics of Rydberg-dressed bosons on two-dimensional square lattices