Phase transitions in rotating binary Bose-Einstein condensates with Spin-orbit and Rabi couplings

We present the phase transition analysis of binary Bose-Einstein condensates (BECs) with spin-orbit (SO) and Rabi couplings in quasi-two-dimensional system under rotation. In particular, we investigate the superfluid properties induced by rotation and SO coupling within hydrodynamic theory which can explain the emergence of the domain wall. By calculating the evolution of angular momentum with respect to rotation frequency, we discover first-order phase transitions where the domain wall changes into the wall-vortex complex. On the other hand, the angular momentum changes continuously with SO coupling strength accompanying by the elongation of the domain wall along x-direction. When the Rabi coupling strength exceeds a critical value, we observe a transition from the domain wall to vortex lattice resulting from a significant change of angular momentum. A phase diagram demonstrating the boundary regime in the plane of SO and Rabi coupling strengths is obtained. Our result is not only motivated by the search for novel states of matter inaccessible to existing experiments, but also by the need to identify situations where the phase transitions can be benchmarked systematically.