Simulating electrical fields in the orbital angular momentum space of light.

We study a system of coupled degenerate cavities with a switchable beam rotator embedded in the optical path of the main cavity. By exploiting the phase shift of the beam rotator dependent on the orbital angular momentum of the optical modes, and modulating the phase imbalance in the auxiliary cavity, it is shown that the system dynamics is equivalent to that of a charged particle in a 1D lattice subject to both static and time-dependent electrical fields. We investigate interesting physics and phenomena such as Bloch oscillations that arise due to the simulated electrical fields, and discuss how they can be used for practical purposes such as storing optical signals in a quantum memory. We also present a powerful measurement scheme to detect the system dynamics that is non-intrusive and technically easy to perform.