  In this work, we consider the dynamics of bosons in bands with non-trivial
topological structure. In particular, we focus on the case where bosons are
prepared in a higher-energy band and allowed to evolve. The Bogoliubov theory
about the initial state can have a dynamical instability, and we show that it
is possible to achieve the interesting situation where the topological edge
modes are unstable while all bulk modes are stable. Thus, after the initial
preparation, the edge modes will become rapidly populated. We illustrate this
with the Su-Schrieffer-Heeger model which can be realized with a double-well
optical lattice and is perhaps the simplest model with topological edge states.
This work provides a direct physical consequence of topological bands whose
properties are often not of immediate relevance for bosonic systems.
