Stability of spin dynamics for a spin-orbit coupled boson in a driven non-Hermitian double well

We study the stability of spin dynamics for a spin-orbit (SO) coupled boson held in a driven non-Hermitian double-well potential. Under high-frequency approximation, we analytically derive the Floquet states and complex Floquet quasienergies of the system and reveal a striking parity-dependent stability criterion: when the ratio of the Zeeman field strength to the driving frequency $\Omega/\omega$ is even, stable spin dynamics can be achieved for \emph{arbitrary} SO coupling strength. However, when $\Omega/\omega$ is odd, stability requires the SO coupling strength to be integer or half-integer values. Particularly, we find four types of stability boundary lines for non-zero bias field strength, in sharp contrast to the commonly observed stability regions. These results establish a tunable parity-governed mechanism for stabilizing spin dynamics in non-Hermitian cold atomic systems.