Spin-orbit-coupling-assisted roton softening and superstripes in a Rydberg-dressed Bose-Einstein condensate

Rotons can exist in ultracold atomic gases either with long-range interactions or with spin-orbit-coupled dispersions. We find that two different kinds of rotons coexist in a joint system combining long-range interactions and spin-orbit coupling. One roton originates from spin-orbit coupling and two others come from long-range interactions. Their softening can be controlled separately. The interesting phenomenon which we find is that spin-orbit-coupled roton can push down the energy of one long-range-interaction roton. The spin-orbit coupling accelerates the softening of this roton. The post phase of spin-orbit-coupling-assisted roton softening and instability is identified as a superstripe.