Exact solutions for a spin-orbit coupled bosonic double-well system

Exact solutions for spin-orbit (SO) coupled cold atomic systems are very important and rare in physics. In this paper, we propose a simple method of combined modulations to generate the analytic exact solutions for an SO-coupled boson held in a driven double well. For the cases of synchronous combined modulations and the spin-conserving tunneling, we obtain the general analytical accurate solutions of the system respectively. For the case of spin-flipping tunneling under asynchronous combined modulations, we get the special exact solutions in simple form when the driving parameters satisfy certain conditions. Based on these obtained exact solutions, we reveal some intriguing quantum spin dynamical phenomena, for instance, the arbitrary population transfer (APT) with and/or without spin-flipping, the controlled coherent population conservation (CCPC), and the controlled coherent population inversion (CCPI). The results may have potential applications in the preparation of accurate quantum entangled states and quantum information processing.