  We study experimentally the stability of excited, interacting states of
bosons in a double-well optical lattice in regimes where the nonlinear
interactions are expected to induce "swallowtail" looped band structure. By
carefully preparing different initial coherent states and observing their
subsequent decay, we observe distinct decay rates that provide direct evidence
for multivalued, looped band structure. The double well lattice both stabilizes
the looped band structure and allows for dynamic preparation of different
initial states, including states within the loop structure. We confirm our
state preparation procedure with dynamic Gross-Pitaevskii calculations. The
excited loop states are found to be more stable than dynamically unstable
ground states, but decay faster than expected based on a mean-field stability
calculation, indicating the importance of correlations beyond a mean field
description.
