Nonlinear ultrastrong coupling effects in mesoscopic cQED

In the regime of ultrastrong light-matter interactions, the coupling strength is comparable to the transition frequencies in the system. Interesting phenomena have been predicted and observed, raising the interest in this regime where higher -order processes and non-perturbative effects become relevant. This precisely makes its theoretical description more involved and, for instance, no direct comparison between a microscopic theory and experiments exists. The lack of a proper theoretical description undermines the possibility to really understand the observed phenomenology, as well as to predict original results. Such an improved understanding will be essential to go beyond linear collective effects and to model the precise nature of vacuum shifts, optical nonlinearities, and other ultrastrong coupling processes at the quantum level. The general goal of mesoQED is to gain a deeper understanding of the physics of mesoscopic quantum systems interacting with a structured electromagnetic environment in the ultrastrong coupling regime. With the objective to provide fully microscopic predictions for linear and nonlinear ultrastrong coupling effects, we will explore new physical settings where these phenomena can be accessed with elementary dipoles. Firstly, we will determine the minimal effective model describing this experimental setup, with the aim to answer some fundamental questions concerning the relevance of vacuum contributions from higher electromagnetic modes and the modification of intermolecular forces. Then, we will explore the dynamics of these mesoscopic cavity QED systems under ultrastrong coupling condit ions and beyond the weak-excitation limit. Finally, we will identify the potentially accessible nonlinear effects and study their exploitation in practical applications. The results of this action are expected to propel the understanding of ultrastrong c oupling physics beyond the current state- of-the-art, addressing for the first time a comprehensive study of nonlinear effects in a mesoscopic cavity QED system .