Phase transition of quantum light-matter systems

Abstract

Strong correlation e ects emerge from light-matter interactions in coupled resonator arrays, such as the Mott-Insulator to super uid phase transition of atom-photon excitations are among the most interesting phenomena in the eld of quantum optics and quantum simulations. This Thesis focuses on the study of the transition from Mott-Insulator to Super uid phase of weakly coupled resonator arrays each one doped with a two-level system. We discover that quenched dynamics of a nite-sized complex array of coupled resonators induces a rst-order like phase transition. We demonstrate that the latter is accompanied by nucleation of super uid-light domains that can be used to manipulate the photonic transport properties of the simulated super uid phase; this in turn leads to an empirical scaling law. On the other hand, adiabatic dynamics resembles a second order phase transition inducing a continous change of the state of the system. First, we study the formation of dressed quantum polariton states and the e ective photon-photon interaction between them. This system is described by the Jaynes-Cummings-Hubbard model. If the frequency of the resonator mode and the two-level system are close to resonance the e ective photonic repulsion prevents the presence of more than one polaritonic excitations in the resonator, due to the photon-blockade e ect. Detuning the atomic and photonic frequencies reduces this e ect and leads the system to a photonic super uid phase. We nd that a nucleated super uid photon state emerges in a localized way, which depends on the topology of the array. This avalanche-like behavior leads to a universal scaling law between the critical parameters of the super uid state and the average connectivity. The second problem refers to the e ect of the anisotropic distribution of lightmatter coupling across di erent sites of the array and the two level system frequency anistropy on the dynamics of the phase transition. We obtain the modulation and resonance of super uid states. This highlights the topological properties of the array, and how they can be used to manipulate the photonic transport. The validity of our results encompasses a wide range of complex architectures that might lead to a promising device for use in scaled quantum simulations.