  Artificial gauge fields for neutral particles such as photons, recently
attracted a lot of attention in various fields ranging from photonic crystals
to ultracold atoms in optical lattices to optomechanical arrays. Here we point
out that, among all implementations of gauge fields, the optomechanical setting
allows for the most natural extension where the gauge field becomes dynamical.
The mechanical oscillation phases determine the effective artificial magnetic
field for the photons, and once these phases are allowed to evolve, they
respond to the flow of photons in the structure. We discuss a simple three-site
model where we identify four different regimes of the gauge-field dynamics.
Furthermore, we extend the discussion to a two-dimensional lattice. Our
proposed scheme could for instance be implemented using optomechanical
crystals.
