Paths to Non-ergodic Quantum Dynamics: From Cavity QED to Strong Zero Modes

Recent advances in cold atoms experiments and the development of superconducting circuits have revolutionized the way we can examine, observe and implement new physical phenomena. In such systems, we can realize new classes of quantum systems which exhibit non-equilibrium quantum phenomena. These systems have attracted mcuh attention in the past two decades as they possess new physics absent in equilibrium. Beside interesting rich physics to learn more about quantum systems, understanding non-equilibrium systems are crucial in developing future technologies such as quantum computation and communication. Given that many open questions needed to be answered in the study of non-equilibrium quantum systems, in this dissertation we will present our theoretical and numerical attempts in providing answers to some of these questions. One of the key features of the non-equilibrium system is how the dynamical properties of quantum systems cane be characterized in different conditions. Here we will present our result on two different mechanism a system can avoid ergodicity. Many-body localization (MBL) is an extension of Anderson localization to interacting systems, where adding strong enough disorder (breaking translational symmetry by adding random potential such as impurity in crystals) can impede the conductivity (system becomes insulator) in the quantum system. Most of the known MBL systems are short- range interacting particles, but in this dissertation, we will discuss MBL in the presence of coupling of the matter to cavity/circuit QED mode where the combined system becomes long-range interacting. We will study the two cases of weak coupling and strong coupling regimes and will derive the effective Hamiltonian using the high-frequency expansion for each case of coupling strength. We predict that the cavity QED has new localization behaviors such as an inversion of the mobility edge where the high-energy states are localized and low-energy states are delocalized. Also in the strong coupling limit, we observed that using the idea from coherent destruction of coupling the system can show signs of localization for photon number as low as n ∼ 2. The rest of this dissertation is devoted to understanding how a clean system (no disorder) can possess symmetry-breaking edge modes indefinitely, or for a long enough but finite time. The case with infinite lifetime edge mode is called strong mode (SM) and the case with finite lifetime edge mode is known as almost strong mode (ASM). Our system of interest is a clock Z3 model which is an extension of the Ising Z2 models. In the clock model (Baxter and modified Baxter) we found that the chirality of the interaction is essential in deriving the exact edge mode in the Hermitian model but removing the hermiticity (controlled by a parameter β), the effect of chirality on the stability of the edge mode becomes less important. We attempt to use different numerical and approximation techniques such as Krylov Hamiltonian and dynamical signature to characterize the edge mode in a Z3 model.