Characterization of Polariton Dynamics in a Multimode Cavity: Noise-enhanced Ballistic Expansion

Advances in optical measurements enable precise tracking of cavity polariton dynamics with exceptional spatiotemporal resolution. Building on these developments, we present a comprehensive theoretical analysis of wave packet dynamics in a noisy emitter lattice embedded in a multi-mode microcavity. We uncover a series of dynamic phenomena in both the noise-free and noisy cases: (i) In the noise-free case, the emitters' probability density splits into two Gaussians whose group velocities are defined by the lower and upper polariton branches. (ii) Noise induces dephasing and leads to multiple dynamical stages with different time scales spanning several orders of magnitude. These stages include, in order of increasing duration: underdamped Rabi oscillations; damping of the center of mass velocity of the emitters' probability density; population thermalization; and the transition from the ballistic to the diffusive regimes of the probability density spreading. (iii) Most strikingly, dephasing enhances the ballistic spreading, which persists for several orders of magnitude longer than it does without a cavity. Some of our predictions align with recent experimental observations, while others can be tested in existing platforms. Understanding wave packet dynamics across multiple time scales in the presence of noise is crucial for optimizing polaritonic devices. This study paves the way for future experiments focused on light-matter interactions in complex systems.