Coherent spin mixing via spin-orbit coupling in Bose gases

We study beyond-mean-field properties of interacting spin-1 Bose gases with synthetic Rashba-Dressel-haus spin-orbit coupling at low energies. We derive a many-body Hamiltonian following a tight-binding approximation in quasimomentum space, where the effective spin dependence of the collisions that emerge from spin-orbit coupling leads to dominant correlated tunneling processes that couple the different bound states. We discuss the properties of the spectrum of the derived Hamiltonian and its experimental signatures. In a certain region of the parameter space, the system becomes integrable, and its dynamics becomes analogous to that of a spin-1 condensate with spin-dependent collisions. Remarkably, we find that such dynamics can be observed in existing experimental setups through quench experiments that are robust against magnetic fluctuations.