Quantum-classical correspondence of non-Hermitian spin-orbit coupled bosonic junction

We investigate the classical-quantum correspondence of non-Hermitian Spin-orbit (SO)-coupled bosonic junctions, where an effective decay term is introduced in one of the two wells. Starting from the normalized two-point functions, we analytically demonstrate that the mean-field system has a classical Hamiltonian structure, and we successfully derive a non-Hermitian discrete nonlinear Schrödinger (Gross–Pitaevskii) equation. We discover that near the symmetry-breaking phase transition point, the correspondence between classical (mean-field) and quantum dynamics is more likely to break down. Our numerical simulations of the full quantum model, limited to a finite number of particles due to computational constraints, reveal that when the effective spin–orbit coupling (SOC) strength takes half-integer values, atomic self-trapping in a non-lossy well consistently occurs regardless of the system parameters, and the corresponding quantum dynamics exhibit remarkable insensitivity to the number of particles in this scenario. Additionally, we reveal that in both the mean-field and many-particle models, the SOC effects can greatly promote the synchronous periodic oscillations between the spin-up and spin-down components, and this synchronous dynamic is closely related to symmetry.