Merging dipolar supersolids in a double-well potential

We theoretically investigate the merging behavior of two identical supersolids through dipolar Bose-Einstein condensates confined within a double-well potential. By adiabatically tuning the barrier height and the spacing between the two wells for specific trap aspect ratios, the two supersolids move toward each other and lead to the emergence of a variety of ground-state phases, including a supersolid state, a macrodroplet state, a ring state, and a labyrinth state. We construct a phase diagram that characterizes various states seen during the merging transition.