Stabilizing correlated pair tunneling of spin-orbit-coupled bosons in a non-Hermitian driven double well

We present an analytical framework for stabilizing second-order correlated tunneling of two spin-orbit-coupled bosons in a periodically driven non-Hermitian double-well potential. By combining Floquet theory with multiple-scale asymptotic analysis, we derive effective second-order dynamics and exact quasienergy spectra in the strongly interacting regime. Our analysis reveals distinct stability mechanisms for three fundamental tunneling channels: interwell spin-conserving, interwell spin-flipping, and intrawell spin-flipping. For balanced gain and loss, we identify discrete, well-defined parameter regions where stable pair tunneling emerges, with the spin-flipping channel exhibiting a characteristic symmetry absent in its spin-conserving counterpart. Under unbalanced gain-loss conditions, stability is achieved only when the gain and loss coefficients satisfy specific parametric relations, enabling dissipation-controlled tunneling. Most notably, stable intrawell spin-flipping, while inherently unstable for an initial Fock state, becomes accessible when the system is prepared in a coherent superposition state, thereby revealing that initial-state coherence can serve as a control parameter for dynamical stability in non-Hermitian systems. These results expand the possibilities for controlling correlated tunneling in many-body systems with engineered dissipation.