Ground-state patterns in a Rydberg-dressed Bose-Einstein condensate with spin-orbit coupling and Lee-Huang-Yang correction

Spontaneous symmetry breaking and self-organized pattern formation in nonlinear systems are fundamental phenomena with broad implications. Studying these effects in cold atomic gases, particularly through the optical control of laser-dressed Rydberg atoms, bridges atomic physics and modern optics. Here, we investigate the ground-state matter-wave pattern formation in cold Rydberg-dressed Bose-Einstein condensates (BECs) with considerations of the Lee-Huang-Yang (LHY) correction and Raman-induced spin-orbit coupling (SOC). A surprising discovery is that the combination of these effects can induce spontaneous symmetry breaking in a plane-wave state of matter waves, giving rise to a variety of exotic self-organized structures, including stripes, positive and negative hexagons, squares, black-eye patterns, and quasi-lattices, among others. Furthermore, we uncover intriguing structural behaviors by considering inter- and intra-specific nonlocal interactions and the hard-core (contact, short-range) and soft-core (long-range) interactions. Our findings advance optical control of quantum matter, with potential applications in atomic-based information processing.