Ground-state properties of dipolar Bose–Einstein condensates with spin–orbit coupling and quantum fluctuations

We study the ground-state properties of dipolar spin-1/2 Bose–Einstein condensates with quantum fluctuations and Rashba spin–orbit coupling (SOC). The combined effects of dipole–dipole interaction (DDI), SOC, and Lee-Huang-Yang (LHY) correction induced by quantum fluctuations on the ground-state structures and spin textures of the system are analyzed and discussed. For the nonrotating case and fixed nonlinear interspecies contact interaction strengths, our results show that structural phase transitions can be achieved by adjusting the strengths of the DDI and LHY correction. In the absence of SOC, a ground-state phase diagram is given with respect to the DDI strength and the LHY correction strength. We find that the system exhibits rich quantum phases including square droplet lattice phase, annular phase, loop-island structure, stripe-droplet coexistence phase, toroidal stripe phase, and Thomas–Fermi (TF) phase. For the rotating case, the increase of DDI strength can lead to a quantum phase transition from superfluid phase to supersolid phase. In the presence of SOC, the quantum droplets display obvious stretching and hidden vortex-antivortex clusters are formed in each component. In particular, weak or moderate SOC favors the formation of droplets while for strong SOC the ground state of the system develops into a stripe phase with hidden vortex-antivortex clusters. Furthermore, the system sustains exotic spin textures and topological excitations, such as composite skyrmion–antiskyrmion–meron–antimeron cluster, meron–antimeron string cluster, antimeron–meron–antimeron chain cluster, and peculiar skyrmion–antiskyrmion–meron–antimeron necklace with a meron–antimeron necklace embedded inside and a central spin Neel domain wall.