  Static synthetic magnetic fields give rise to phenomena including the Lorentz
force and the quantum Hall effect even for neutral particles, and they have by
now been implemented in a variety of physical systems. Moving towards fully
dynamical synthetic gauge fields allows, in addition, for backaction of the
particles' motion onto the field. If this results in a time-dependent vector
potential, conventional electromagnetism predicts the generation of an electric
field. Here, we show how synthetic electric fields for photons arise
self-consistently due to the nonlinear dynamics in a driven system. Our
analysis is based on optomechanical arrays, where dynamical gauge fields arise
naturally from phonon-assisted photon tunneling. We study open, one-dimensional
arrays, where synthetic magnetic fields are absent. However, we show that
synthetic electric fields can be generated dynamically, which, importantly,
suppress photon transport in the array. The generation of these fields depends
on the direction of photon propagation, leading to a novel mechanism for a
photon diode, inducing nonlinear nonreciprocal transport via dynamical
synthetic gauge fields.
