  We study macroscopic superpositions in the orbital rather than the spatial
degrees of freedom, in a three-dimensional double-well system. We show that the
ensuing dynamics of $N$ interacting excited ultracold bosons, which in general
requires at least eight single-particle modes and ${N+7 \choose N}$ Fock
vectors, is described by a surprisingly small set of many-body states. An
initial state with half the atoms in each well, and purposely excited in one of
them, gives rise to the tunneling of axisymmetric and transverse vortex
structures. We show that transverse vortices tunnel orders of magnitude faster
than axisymmetric ones and are therefore more experimentally accessible. The
tunneling process generates macroscopic superpositions only distinguishable by
their orbital properties and within experimentally realistic times.

Quantum Gases;Quantum Physics