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.