Macroscopic Superposition of Ultracold Atoms with Orbital Degrees of Freedom

We introduce higher dimensions into the problem of Bose-Einstein condensates in a double-well potential, taking into account orbital angular momentum. We completely characterize the eigenstates of this system, delineating new regimes via both analytical high-order perturbation theory and numerical exact diagonalization. Among these regimes are mixed Josephson- and Fock-like behavior, crossings in both excited and ground states, and shadows of macroscopic superposition states.