Collective quench dynamics of active photonic lattices in synthetic dimensions.

Photonic emulators have enabled the study of many solid-state and quantum optics phenomena, such as Anderson localization, topological insulators and non-Hermitian dynamics. Current photonic emulators are generally limited to bosonic behaviour with local interactions, but the use of synthetic dimensions offers a pathway to overcome this constraint. Here we investigate the flow of liquid light in modulated fast-gain ring lasers, and we establish a platform for emulating quench dynamics within a synthetic photonic lattice with equal densities across the reciprocal space. We apply an artificial electric field to the lattice and introduce a slow timescale to the flow, given by Bloch oscillations. Despite the dispersion and dissipation in our system, which desynchronize the Wannier-Stark ladder states, we were able to directly observe coherent oscillations facilitated by the fast gain. Additionally, we quenched a steady state of a coupled system onto an uncoupled one, which revealed coherent interactions between the decaying modes. These coherent dynamics resulted from the liquid state of light, which rapidly suppressed fluctuations at the shortest timescale of the system. This platform enriches our understanding of collective dynamics in the non-perturbative regime and improves our ability to control and generate coherent, multi-frequency sources.