Title: Quench dynamics of Wannier-Stark states in an active synthetic photonic lattice

Abstract: Photonic emulators have facilitated the investigation of numerous solid-state phenomena and have contributed to the development of optical devices inspired by quantum mechanics. Although current photonic emulators are constrained to bosonic behavior with local interactions, the utilization of active synthetic lattices holds promise for surpassing these limitations. In this study, we propose employing the modulated ring fast-gain laser as a foundation for emulating quench dynamics within a synthetic lattice that conforms to equal density filling of its reciprocal space. To illustrate the effectiveness of this emulation platform, we subject a dispersed Wannier-Stark ladder to quenching and directly observe oscillations, enabled by the fast-gain, along with their coherent stabilization to a single Wannier stark state. These coherent dynamics stem directly from our lasers liquid state of light, a characteristic resulting from fast-gain and explained by the rapid decay of fluctuations occurring on the system's shortest timescale. Additionally, by adequately biasing the lattice through detuning the modulation from the cavity resonance, this process supports oscillatory dynamics within the synthetic space.