Intrinsic-to-extrinsic supersolid transition and fractionally modulated states in a lattice ultracold Bose gas with long-range interaction

We investigate the intrinsic-to-extrinsic supersolid (SS) transition in a lattice ultracold Bose gas with strong long-range interaction. When changing the depth of the periodic lattice potential, the transition is shown to manifest in the ground-state wave function and energy, the change of superfluid fraction ${f}_{s}$, and a roton instability. Near the transition in the extrinsic SS phase, due to the competition between the long-range interaction and the periodic potential, we show that there exist a variety of stable fractionally modulated states (FMSs) upon the change of the effective length of the long-range interaction. Consequence of the transition across different FMSs is discussed.