Théorique, numérique
The experimental control of the coherent interaction between light and matter is one of the corner stones of the recent developments in the field of quantum technologies. In this context, cavity quantum electrodynamics has reached an important milestone in the last decade with the achievement of the ultrastrong coupling (USC) regime, where the coupling strength becomes comparable or even larger than the cavity frequency. Furthermore, recently developed quantum simulation techniques made it possible to observe the physics of the ultrastrong-coupling regime even in systems that do not naturally achieve the required interaction strength. These effective implementations of USC can reach extreme regimes of parameters, where phase transitions emerge, even in systems with a finite number of components. These finite-component phase transitions are easier to control than their many-body counterparts and offer an interesting framework for the study of critical phenomena, with possible applications to quantum metrology. The goal of the project is to explore the rich phenomenology of finite-component phase-transitions using state-of-the-art numerical methods designed to simulate open quantum systems, complemented by analytical calculations. In particular, implementation of field-theoretical tools recently developed for open quantum systems will be considered.