Chiral supersolid and dissipative time crystal in Rydberg-dressed Bose–Einstein condensates with Raman-induced spin–orbit coupling

Spin–orbit coupling (SOC) is one of the crucial factors that affect the chiral symmetry of matter by causing the spatial symmetry breaking of the system. We find that Raman-induced SOC can induce a chiral supersolid phase with a helical antiskyrmion lattice in balanced Rydberg-dressed two-component Bose–Einstein condensates (BECs) in a harmonic trap by modulating the Raman coupling strength. This is in stark contrast to the mirror symmetric supersolid phase containing skyrmion–antiskyrmion lattice pair for the case of Rashba SOC. Two ground-state phase diagrams are presented as a function of the Rydberg interaction and the Raman-induced SOC. It is shown that the interplay among Raman-induced SOC, Rydberg interactions, and nonlinear contact interactions favors rich ground-state structures, including half-quantum vortex phase, stripe supersolid phase, toroidal stripe phase with a central Anderson–Toulouse coreless vortex, checkerboard supersolid phase, mirror symmetric supersolid phase, chiral supersolid phase and standing-wave supersolid phase. In addition, the effects of rotation and in-plane quadrupole magnetic field on the ground state of the system are analyzed. In these two cases, the chiral supersolid phase is broken and the ground state tends to form a miscible phase. Furthermore, we demonstrate that when the initial state is a chiral supersolid phase the rotating harmonic trapped system sustains dissipative continuous time crystal by studying the rotational dynamic behaviors of the system.