Non-equilibrium dynamics in multi-mode and multi-cavity photon resonators

Abstract

This thesis explores the non-equilibrium dynamics of photons in optical micro-resonators, focusing on how coherence and collective behavior emerge in driven and dissipative systems. Starting from a microscopic description, we derive a Lindblad master equation under the assumptions of Markovian dynamics and fast molecular relaxation. By employing a cumulant expansion technique, we obtain a closed set of coupled dynamical equations for relevant observables, providing a method to analyze the system dynamics. <br/>

A central aspect of this work is the explicit incorporation of <em>U</em>(1) symmetry-breaking fields to describe photon coherence. This formulation allows us to establish a distinction between coherent (condensed) and incoherent (thermal) photon populations, even at the level of a single-mode resonator. Within this framework, we study the temporal stability of the condensate and show that its persistence is governed by a key mechanism, the presence of a so-called <em>ghost attractor</em>. Although this fixed point lies outside the physical parameter space, its basin of attraction strongly influences the system dynamics, which results in stabilizing the condensate over an extended period of time before it eventually decays to zero. <br/>

Additionally, we investigate the stability of the system by analyzing fluctuations around its fixed points. This analysis reveals the presence of exceptional points in the parameter space, signaling non-Hermitian phase transitions. These exceptional points separate the dynamics into two qualitatively different dynamical regimes, namely, a weakly-damped oscillatory regime, and a purely dissipative regime with bi-exponential decay. <br/>

Finally, we investigate the possibility of generating quantum correlations and entanglement in a system of two coupled micro-resonators. Despite the presence of coherent dynamics and inter-cavity coupling, our results show that the photon states remain separable throughout the time evolution. This conclusion is supported by the evaluation of continuous-variable entanglement criteria for Gaussian states, which naturally arise within the cumulant expansion framework.