  Synthetic dimensions provide a promising platform for photonic quantum
simulations. Manipulating the flow of photons in these dimensions requires an
electric field. However, photons do not have charge and do not directly
interact with electric fields. Therefore, alternative approaches are needed to
realize electric fields in photonics. One approach is to use engineered gauge
fields that can mimic the effect of electric fields and produce the same
dynamical behavior. Here, we demonstrate such an electric field for photons
propagating in a two-dimensional synthetic space. We achieve this using a
linearly time-varying gauge field generated by direction-dependent phase
modulations. We show that the generated electric field leads to Bloch
oscillations and the revival of the state after a certain number of steps
dependent on the field strength. We measure the probability of the revival and
demonstrate good agreement between the observed values and the theoretically
predicted results. Furthermore, by applying a nonuniform electric field, we
show the possibility of waveguiding photons. Ultimately, our results open up
new opportunities for manipulating the propagation of photons with potential
applications in photonic quantum simulations.
