External Josephson effect in Bose-Einstein condensates with a spin degree of freedom

We consider the Josephson effect between two spatially separated Bose-Einstein condensates of atoms each of which can be in two hyperfine states. We derive simple equations of motion for this system closely analogous to the Bloch equations. We also map the dynamics of the system onto those of a classical particle in a well. We find density and spin modes of oscillation and stable equilibrium points of the motion that are unstable in the spinless case. Finally we analyze the oscillation modes in the spin-1 (F=1) case.