Spin-Mixing Dynamics in Helicoidal Spin-Orbit-Coupled Bose–Einstein Condensates

We consider Bose–Einstein condensates with helicoidal spin-orbit coupling and study spin-mixing properties of a pseudo-spin 1/2 system through fixed point analysis. At the equilibrium condition, strength of the helicoidal gauge potential plays a significant role to create initial spin imbalance in the two-level system. The spin flipping between the two states occurs with time in the non-equilibrium condition. We see that the changes of spin imbalance with time between the two states execute periodic or quasi-periodic patterns. Amplitude and frequency of the oscillation dynamics depend sensitively on the helicoidal spin-orbit coupling and atomic interaction. We show that spin-mixing dynamics lead to various types of phase-space trajectories with the change of initial spin imbalance and helicoidal gauge potential.