Hamiltonian of a Spin-1 Bose-Einstein Condensate

In this section we present the Hamiltonian description of a spinor Bose-Einstein condensate. With the motional degrees of freedom frozen out, the dynamics are within the spin. We detail the collisional interactions that lead to spin exchange among three modes. For developing intuition about the dynamics induced by spin exchange the classical phase space is discussed before the quantum mechanical treatment follows. Finally, we give an overview of the employed semi-classical simulation methods.