Collective Behaviors of Quantum Emitters Coupled to a Structured Photonic Environment

Abstract

The study of a quantum system coupled to an environment plays an indispensable role in expanding our understanding of quantum mechanics. It has a broad impact, encompassing fundamental inquiries in quantum physics as well as applications in quantum technologies. The primary focus of our work is on a ''big'' quantum system that consists of two distinct subsystems, one characterized by spin degrees of freedom and the other by bosonic degrees of freedom. Our research falls in the realm of quantum optics, where the bosonic degrees of freedom which constitute the ''environment'' are realized by photons in cavities. The spin degrees of freedom are realized by two-level quantum emitters that represent the ''system'' under study. The collective radiative behaviors of the emitters coupled to a single mode cavity are described frequently by the Dicke model, which treats a subset of the full Hilbert space. Motivated by recent experimental developments in quantum optics and circuit quantum electrodynamics (QED) platforms, we replaced the single-mode cavity by a one-dimensional array of coupled cavities with Kerr-like non-linearity. The presence of the Kerr-like non-linearity gives rise to a nontrivial mode structure of the bath that supports two-photon bound states. Working in the weak emitter-photon coupling regime, we investigated collective behaviors exhibited by a group of quantum emitters in the two-excitation manifold. We developed a theoretical atom-optical framework that treats the emitter-photon coupled system fully quantum mechanically. We covered a wide range of theoretical approaches in our study, starting from the Schroedinger equation and extending to the Markov approximation, which is critical also for quantum master equation treatment. By using the theoretical atom-optical framework, we sought to identify the radiative pathways and effective interactions of the emitters coupled to the structured photonic environment. For two excited emitters with transition energy in resonance with the two-photon bound state band, the radiative properties were studied. It was found that when the emitters are in resonance with the band edge and are well-separated, undamped Rabi oscillations occur; Rabi oscillations do not exist without the Kerr-like nonlinearity. A photonic polaron-like state that forms as a result of all-to-all interaction in the center-of-mass momentum space of the two-photon bound states was identified. For an emitter array with a large number of emitters, operating within the band gap regime, an effective spin Hamiltonian was derived. Interestingly, a reversal in the hierarchy of interaction energy scales was observed. This led to the discovery of a series of novel correlated bound states that exhibit droplet-like characteristics. The findings of our atom-optical theory provide a guide for future experimental and theoretical studies of spin-boson coupled systems. The parameter regimes considered in this thesis can be applied to several circuit QED experimental platforms and the predictions can be tested with state-of-the-art technology.