Two-dimensional miscible-immiscible supersolid and droplet crystal state in a homonuclear dipolar bosonic mixture

The recent realization of a binary dipolar Bose-Einstein condensate [A. Trautmann et al., Phys. Rev. Lett. 121, 213601 (2018)] presents new exciting aspects for studying quantum droplets and supersolids in mixture. Motivated by this experiment, we study the ground-state phases dynamics Dy-Dy bosonic mixture exhibits qualitatively novel rich physics. Relying on three-dimensional numerical simulations extended Gross-Pitaevskii framework, unravel phase diagrams characterize their different possible phases. emergent include single-droplet (SD), multiple-droplets (MD), doubly supersolid (SS), superfluid (SF) states both miscible immiscible Intriguing mixed ground are observed an imbalanced mixture, including combination SS-SF, SS-MD, SS-SS We also explore across boundaries linear quenches interspecies intraspecies scattering lengths. During these dynamical processes, observe abrupt change which initially results some instability system forms metastable intermediate timescale. However, state produced long-time evolution is similar to our predicted state. Although demonstrate specific parameter range lengths, general valid other mixtures may become important benchmark future experimental scenarios.